Factors affecting Option Premium

While Option premiums are largely a function of the strike price, spot price and the time to expiry, there are other major factors that affect the pricing of an Option. These are volatility (ups and downs in the price of the underlying stock), interest rate and dividends, if any, between the current date and the expiry date.

There are advanced models like the Black and Scholes’ model, which try to determine the price of an Option on the basis of a number of variables. These models also enable a trader to track the changes in pricing of Options as the parameters and variables used in the model change.

There are many factors which affect option premium. These factors affect the premium of the option with varying intensity. Some of these factors are listed here:

  • Price of the underlying: Any fluctuation in the price of the underlying (stock/index/commodity) obviously has the largest effect on premium of an option contract. An increase in the underlying price increases the premium of call option and decreases the premium of put option. Reverse is true when underlying price decreases.
  • Strike price: How far is the strike price from spot also affects option premium. Say, if NIFTY goes from 5000 to 5100 the premium of 5000 strike and of 5100 strike will change a lot compared to a contract with strike of 5500 or 4700.
  • Volatility of underlying: Underlying security is a constantly changing entity. The degree by which its price fluctuates can be termed as volatility. So a share which fluctuates 5% on either side on daily basis is said to have more volatility than e.g. stable blue chip shares whose fluctuation is more benign at 2–3%. Volatility affects calls and puts alike. Higher volatility increases the option premium because of greater risk it brings to the seller.
  • Payment of Dividend: Payment of Dividend does not have direct impact on value of derivatives but it does have indirect impact through stock price. We know that if dividend is paid, stock goes ex-dividend therefore price of stock will go down which will result into increase in Put premium and decrease in Call premium.

Apart from above, other factors like bond yield (or interest rate) also affect the premium. This is because the money invested by the seller can earn this risk-free income in any case and hence while selling option; he has to earn more than this because of higher risk he is taking.

The final three are numerical methods, usually requiring sophisticated derivatives-software, or a numeric package such as MATLAB. For these, the result is calculated as follows, even if the numerics differ:

  • A risk-neutral distribution is built for the underlying price over time (for non-European options, at least at each exercise date) via the selected model
  • The option’s payoff-value is determined at each of these prices
  • The payoffs are discounted at the risk-free rate, and then averaged. For the analytic methods, these same are subsumed into a single probabilistic result; see Black–Scholes model § Interpretation.

Options Contract Specifications, Terminologies

Options are financial instruments that are derivatives based on the value of underlying securities such as stocks. An options contract offers the buyer the opportunity to buy or sell depending on the type of contract they hold the underlying asset. Unlike futures, the holder is not required to buy or sell the asset if they choose not to.

  • Call options allow the holder to buy the asset at a stated price within a specific timeframe.
  • Put options allow the holder to sell the asset at a stated price within a specific timeframe.

Any formal agreement between two parties, option contracts clearly delineate all of the parameters of the contract between buyer and seller.

  1. Underlying stock

Option contracts are an agreement to either buy or sell 100 shares of stock. We need to specify which stock we are trading through the option contract. In our example, “XYZ” is the stock symbol that we are trading. “XYZ” could be any stock that has option contracts – Apple, Facebook, Boeing – just to name a few. The underlying stock price is one of the key inputs into the option pricing model, so this is a key piece of information when trading options.

  1. Date of expiration

Option contracts have a finite life. The expiration date tells us when the option contract will expire. In our example, “February” represents the time of expiration. Monthly options expire on the third Friday of the month: a “February” expiration option like this one will expire on the third Friday in February.

It is important to note that there are also weekly expiration dates. Weekly expiration options expire on Friday of that week. At Option Posts, however, we prefer to stick with monthly expiration contracts because weekly contracts tend to be less liquid, which is an important factor that we consider.

  1. Strike price

The third option contract specification is the strike price. Option contracts are an agreement to either buy or sell stock at a certain price in the future. This is a different number from the current stock price. The strike price specifies the price at which the stock transaction will take place, even if the stock price is currently trading at a different price. In our example, the strike price is 50. This means that the option buyer and the option seller agree to transact stock at a price of $50 per share should the option buyer choose to “exercise,” or use, the contract, even if the stock is trading at a different value, say $48, at the time the contract is made.

  1. Call vs put

Next, we must specify whether it is a call contract or a put contract. This indicates whether the option buyer wants to buy stock with a call contract, or sell stock with a put contract. In our example, it is a “call” contract, meaning the option buyer has the right but not the obligation to buy 100 shares of stock at the strike price at any point in the future up until the expiration date.

  1. Credit or debit price

Lastly, we have to indicate the price or premium paid for the option contract. This is the price that the option buyer and option seller agree upon to initiate the option contract.

Explanation about Options

Options are a versatile financial product. These contracts involve a buyer and a seller, where the buyer pays an options premium for the rights granted by the contract. Each call option has a bullish buyer and a bearish seller, while put options have a bearish buyer and a bullish seller.

Options contracts usually represent 100 shares of the underlying security, and the buyer will pay a premium fee for each contract. For example, if an option has a premium of 35 cents per contract, buying one option would cost $35 ($0.35 x 100 = $35). The premium is partially based on the strike price the price for buying or selling the security until the expiration date. Another factor in the premium price is the expiration date. Just like with that carton of milk in the refrigerator, the expiration date indicates the day the option contract must be used. The underlying asset will determine the use-by date. For stocks, it is usually the third Friday of the contract’s month.

Traders and investors will buy and sell options for several reasons. Options speculation allows a trader to hold a leveraged position in an asset at a lower cost than buying shares of the asset. Investors will use options to hedge or reduce the risk exposure of their portfolio. In some cases, the option holder can generate income when they buy call options or become an options writer. Options are also one of the most direct ways to invest in oil. For options traders, an option’s daily trading volume and open interest are the two key numbers to watch in order to make the most well-informed investment decisions.

American options can be exercised any time before the expiration date of the option, while European options can only be exercised on the expiration date or the exercise date. Exercising means utilizing the right to buy or sell the underlying security.

Options Trading Terminology

Call Option

A call option gives the buyer the right to buy 100 shares at a fixed price (strike price) before a specified date (expiration date). Likewise, the seller (writer) of a call option is obligated to sell the stock at the strike price if the option is exercised.

Put Option

A put option gives the buyer the right to sell 100 shares at a fixed price (strike price) before a specified date (expiration date). Likewise, the seller (writer) of a put option is obligated to purchase the stock at the strike price if exercised.

Strike (or Exercise) Price

The strike price is the price per share at which the holder can purchase (for call options) or sell (for put options) the underlying stock.

Exercise

Exercise is the process by which an option buyer (holder) invokes the terms of the option contract. If exercising, calls will buy the underlying stock, while put owners will sell the underlying stock under the terms set by the option contract. All option contracts that are in-the-money (i.e. have at least one cent of intrinsic value) at expiration will be automatically exercised.

Expiration Date

The expiration date is the last day on which the option may be exercised. Monthly listed stock options cease trading on the third Friday of each month and expire the next day. Weekly options cease trading on Friday of that week.

Hedging

Hedging is a conservative strategy used to reduce investment risk by implementing a transaction that offsets an existing position.

Covered Call

A covered call is a call option that is written (sold) against an existing stock position. The call is said to be “covered” by the underlying stock, which could be delivered if the call option is exercised.

Intrinsic Value

The intrinsic value of an option is the amount of profit that can be theoretically obtained if the option is exercised at that moment and the stock either purchased (for calls) or sold (for puts) at the current market price. If an option has positive intrinsic value, it is said to be “in-the-money” (ITM) and if it has negative intrinsic value it is said to be “out-of-the-money” (OTM). For instance an XYZ January 25 Call would have $1.50 of intrinsic value if the stock were trading at $26.50, regardless of its market price at the time.

Time Value

Time value is the amount by which an option’s market price exceeds its intrinsic value. In the case above with the XYZ January 25 Call priced at $3.00 while XYZ stock is trading at $26.50, the intrinsic value is $1.50 and the remaining $1.50 is time value. If an option is out-of-the-money (i.e. has no intrinsic value) then the entire market price is considered time value.

Premium

The price of an option is called its premium. Prices are quoted per share, but premium is usually the entire dollar value of the contract (price per share X 100 shares = total premium).

Time Decay

Because options have an expiration date, all options are wasting assets whose time value erodes to zero by expiration. This erosion is known as time decay. Time value varies with the square root of time, so that as an option approaches its expiration date, the rate of time decay increases.

Long

To be “long” an option simply means to have purchased it in an opening transaction and thus to own or hold it.

Short

To be short an option means to have sold the option in an opening transaction. (A short position is carried as a negative on a statement and must be purchased later to close out.)

LEAPS (Long-term Equity AnticiPation Securities)

These are long-term options with expiration dates as far out as three years, usually expiring in January.

Trading of Options

An option is a contract that is written by a seller that conveys to the buyer the right but not an obligation to buy (for a call option) or to sell (for a put option) a particular asset, at a specific price (strike price/exercise price) in future.

In return for granting the option, the seller collects a payment (known as a premium) from the buyer.

Participants in Options

  1. Buyer of an Option: The one who by paying the premium, buys the right to exercise his option on the seller/writer.
  2. Writer/seller of an Option: The one who receives the premium of the option and thus is obliged to sell/buy the asset if the buyer of the option exercises it.
  3. Call Option: An option that provides the holder the right but not the obligation to buy an asset at a set price before a certain date.
  4. Put Option: An option that offers the holder, the right but not the obligation, to sell an asset at a set price before a certain date.

Types in Options Trading

  1. Premium: The price that the option buyer pays to the option seller is referred to as the option premium.
  2. Expiry date: The date specified in an option contract is known as the expiry date or the exercise date.
  3. Strike price: The price at which the contract is entered is the strike price or the exercise price.
  4. American option: The option that can be exercised at any date until the expiry date.
  5. European option: The option that can be exercised only on the expiry date.

Profitability Scenario in Options

  1. In-the-Money Option

In-the-money (ITM) option is the one that leads to positive cash flow to the holder if it was exercised immediately.

For example, in a call option on the index, if the current index value is higher than the strike price (spot price > strike price), the option is said to be in-the-money.

  1. At-the-Money Option

At-the-money (ATM) option is an option that leads to zero cash flow ( a situation of no profit/no loss) if it were exercised immediately.

For example, in the previous case, if the current index value is equal to strike price (spot price = strike price), the option is ATM.

  1. Out-of-the-Money Option

Out-of-the-money (OTM) option is an option that would lead to negative cash flow if it were exercised immediately.

For example, in the previous case, if the index value is lower than the strike price (spot price < strike price), the option is said to be OTM.

Strategies in Option Trading

  • Long call options trading strategy
  • Short call options trading strategy
  • Long put options trading strategy
  • Short put options trading strategy
  • Long straddle options trading strategy
  • Short straddle options trading strategy

Valuation of Options Contract

In finance, a price (premium) is paid or received for purchasing or selling options.

The value of an option can be estimated using a variety of quantitative techniques based on the concept of risk neutral pricing and using stochastic calculus. In general, standard option valuation models depend on the following factors:

  • The current market price of the underlying security
  • The strike price of the option, particularly in relation to the current market price of the underlying asset (in the money vs. out of the money)
  • The cost of holding a position in the underlying security, including interest and dividends
  • The time to expiration together with any restrictions on when exercise may occur, and
  • An estimate of the future volatility of the underlying security’s price over the life of the option.

Binomial Option Pricing Model

The simplest method to price the options is to use a binomial option pricing model. This model uses the assumption of perfectly efficient markets. Under this assumption, the model can price the option at each point of a specified time frame.

Under the binomial model, we consider that the price of the underlying asset will either go up or down in the period. Given the possible prices of the underlying asset and the strike price of an option, we can calculate the payoff of the option under these scenarios, then discount these payoffs and find the value of that option as of today.

Figure 1. Two-period binomial tree

Black-Scholes Model

The Black-Scholes model is another commonly used option pricing model. This model was discovered in 1973 by the economists Fischer Black and Myron Scholes. Both Black and Scholes received the Nobel Memorial Prize in economics for their discovery.

The Black-Scholes model was developed mainly for pricing European options on stocks. The model operates under certain assumptions regarding the distribution of the stock price and the economic environment. The assumptions about the stock price distribution include:

  • Continuously compounded returns on the stock are normally distributed and independent over time.
  • The volatility of continuously compounded returns is known and constant.
  • Future dividends are known (as a dollar amount or as a fixed dividend yield).

The assumptions about the economic environment are:

  • The risk-free rate is known and constant.
  • There are no transaction costs or taxes.
  • It is possible to short-sell with no cost and to borrow at the risk-free rate.

Nevertheless, these assumptions can be relaxed and adjusted for special circumstances if necessary. In addition, we could easily use this model to price options on assets other than stocks (currencies, futures).

 The main variables used in the Black-Scholes model include:

  • Price of underlying asset (S) is a current market price of the asset
  • Strike price (K) is a price at which an option can be exercised
  • Volatility (σ) is a measure of how much the security prices will move in the subsequent periods. Volatility is the trickiest input in the option pricing model as the historical volatility is not the most reliable input for this model
  • Time until expiration (T) is the time between calculation and an option’s exercise date
  • Interest rate (r) is a risk-free interest rate
  • Dividend yield (δ) was not originally the main input into the model. The original Black-Scholes model was developed for pricing options on non-paying dividends stocks.

From the Black-Scholes model, we can derive the following mathematical formulas to calculate the fair value of the European calls and puts:

The formulas above use the risk-adjusted probabilities. N(d1) is the risk-adjusted probability of receiving the stock at the expiration of the option contingent upon the option finishing in the money. N(d2) is the risk-adjusted probability that the option will be exercised. These probabilities are calculated using the normal cumulative distribution of factors d1 and d2.

The Black-Scholes model is mainly used to calculate the theoretical value of European-style options and it cannot be applied to the American-style options due to their feature to be exercised before the maturity date.

Monte-Carlo Simulation

Monte-Carlo simulation is another option pricing model we will consider. The Monte-Carlo simulation is a more sophisticated method to value options. In this method, we simulate the possible future stock prices and then use them to find the discounted expected option payoffs.

In this article, we will discuss two scenarios: simulation in the binomial model with many periods and simulation in continuous time.

Scenario 1

Under the binomial model, we consider the variants when the asset (stock) price either goes up or down. In the simulation, our first step is determining the growth shocks of the stock price. This can be done through the following formulas:

h in these formulas is the length of a period and h = T/N and N is a number of periods.

After finding future asset prices for all required periods, we will find the payoff of the option and discount this payoff to the present value. We need to repeat the previous steps several times to get more precise results and then average all present values found to find the fair value of the option.

Scenario 2

In the continuous time, there is an infinite number of time points between two points in time. Therefore, each variable carries a particular value at each point in time.

Under this scenario, we will use the Geometric Brownian Motion of the stock price which implies that the stock follows a random walk. Random walk means that the future stock prices cannot be predicted by the historical trends because the price changes are independent of each other.

In the Geometric Brownian Motion model, we can specify the formula for stock price change:

Where:

S – stock price

ΔS – change in stock price

µ – expected return

t – time

σ – standard deviation of stock returns

– random variable µ 

Unlike the simulation in a binomial model, in continuous time simulation, we do not need to simulate the stock price in each period, but we need to determine the stock price at the maturity, S(T), using the following formula:

We generate the random number  and solve for S(T). Afterward, the process is similar to what we did for simulation in the binomial model: find the option’s payoff at the maturity and discount it to the present value.

Futures Contract Specification, Terminologies, Participant

In finance, a futures contract (sometimes called futures) is a standardized legal agreement to buy or sell something at a predetermined price at a specified time in the future, between parties not known to each other. The asset transacted is usually a commodity or financial instrument. The predetermined price the parties agree to buy and sell the asset for is known as the forward price. The specified time in the future which is when delivery and payment occur is known as the delivery date. Because it is a function of an underlying asset, a futures contract is a derivative product.

Contracts are negotiated at futures exchanges, which act as a marketplace between buyers and sellers. The buyer of a contract is said to be the long position holder, and the selling party is said to be the short position holder. As both parties risk their counter-party walking away if the price goes against them, the contract may involve both parties lodging a margin of the value of the contract with a mutually trusted third party. For example, in gold futures trading, the margin varies between 2% and 20% depending on the volatility of the spot market.

The first futures contracts were negotiated for agricultural commodities, and later futures contracts were negotiated for natural resources such as oil. Financial futures were introduced in 1972, and in recent decades, currency futures, interest rate futures and stock market index futures have played an increasingly large role in the overall futures markets. Even organ futures have been proposed to increase the supply of transplant organs.

Expiration

Expiration (also known as maturity or expiry date) refers to the last trading day of the futures contract. After the expiry of a futures contract, final settlement and delivery is made according to the rules laid down by the exchange in the contract specifications document.

Contract Size

Contract size, or lot size, is the minimum tradable size of a contract. It is often one unit of the defined contract.

Initial Margin

Initial margin is the minimum collateral required by the exchange before a trader is allowed to take a position. Initial margins can be paid in various forms as laid down by the exchange and varies from commodity to commodity as well as from time to time. The level of initial margin is dependent on the price volatility of the contract. More volatile commodities generally have higher margin requirements.

Price Quotation

Price Quotation is the units in which the traded price of a contract is displayed. It can be different from the trading size of a contract and is often based on industry practices and conventions.

Tick Size

Tick Size is the minimum movement allowed by the exchange in Price Quotation.

Tick Value

Tick Value refers to the minimum profit or loss that can arise from holding a position of one contract. Tick value depends on the size of the contract and its tick size. While it is often explicitly mentioned in contract specifications, it can be calculated by the formula:

Tick Value = Contract Size x Tick Size

Mark to Market

Mark to market refers to the process by which the exchange calculates and values all open positions according to pre-defined rules and regulations. Mark-to-market is an essential feature of exchange-traded futures contracts whereby the exchange ensures that all profit and losses are recognized by pricing them according to accurate market conditions. It is also an important feature for the risk management of positions of participants.

Delivery Date

Delivery date or delivery period refers to the time specified by the exchange during or by which the seller has to make delivery according to contract specifications and regulations. Delivery date is often later than expiry date of a contract, especially in case of physically delivered commodities.

Daily Settlement

Daily settlement refers to the process whereby the exchange debits and credits all accounts with daily profits and losses as calculated by the mark-to-market process. Daily settlement is necessary in order to recover losses and pay profits to respective accounts.

Advantages and risks of futures contracts:

The existence and the utility of a futures market benefits a lot of market participants:

  • It allows hedgers to shift risks to speculators.
  • It gives traders an efficient idea of what the futures price of a stock or value of an index is likely to be.
  • Based on the current future price, it helps in determining the future demand and supply of the shares.
  • Since it is based on margin trading, it allows small speculators to participate and trade in the futures market by paying a small margin instead of the entire value of physical holdings.

However, you must be aware of the risks involved too. The main risk stems from the temptation to speculate excessively due to a high leverage factor, which could amplify losses in the same way as it multiplies profits. Further, as derivative products are slightly more complicated than stocks or tracking an index, lack of knowledge among market participants could lead to losses.

Stock futures:

Stock futures are derivative contracts that give you the power to buy or sell a set of stocks at a fixed price by a certain date. Once you buy the contract, you are obligated to uphold the terms of the agreement.

Here are some more characteristics of futures contracts:

  • Lot/Contract size: In the derivatives market, contracts cannot be traded for a single share. Instead, every stock futures contract consists of a fixed lot of the underlying share. The size of this lot is determined by the exchange on which it is traded on. It differs from stock to stock. For instance, a Reliance Industries Ltd. (RIL) futures contract has a lot of 250 RIL shares, i.e., when you buy one futures contract of RIL, you are actually futures trading 250 shares of RIL. Similarly, the lot size for Infosys is 125 shares.*
  • Expiry: All three maturities are traded simultaneously on the exchange and expire on the last Thursday of their respective contract months. If the last Thursday of the month is a holiday, they expire on the previous business day. In this system, as near-month contracts expire, the middle-month (2 month) contracts become near-month (1 month) contracts and the far-month (3 month) contracts become middle-month contracts.
  • Duration: Contract is an agreement for a transaction in the future. How far in the future is decided by the contract duration. Futures contracts are available in durations of 1 month, 2 months and 3 months. These are called near month, middle month and far month, respectively. Once the contracts expire, another contract is introduced for each of the three durations. The month in which it expires is called the contract month. New contracts are issued on the day after expiry.
  • Example: If you want to purchase a single July futures contract of ABC Ltd., you would have to do so at the price at which the July futures contracts are currently available in the derivatives market. Let’s say that ABC Ltd July futures trading are at Rs 1,000 per share. This means, you are agreeing to buy/sell at a fixed price of Rs 1,000 per share on the last Thursday in July. However, it is not necessary that the price of the stock in the cash market on Thursday has to be Rs 1,000. It could be Rs 992 or Rs 1,005 or anything else, depending on the prevailing market conditions. This difference in prices can be taken advantage of to make profits.

Participant

Eligible contract participants like financial institutions, insurance companies, and investment management firms have sufficient regulatory status

Concept of Convergence

Convergence is the movement of the price of a futures contract toward the spot price of the underlying cash commodity as the delivery date approaches. It simply means that, on the last day that a futures contract can be delivered to fulfill the terms of the contract, the price of the futures and the price of the underlying commodity will be nearly equal. The two prices must converge. If not, an arbitrage opportunity exists and the possibility for a risk-free profit.

Convergence happens because the market will not allow the same commodity to trade at two different prices at the same place at the same time. For example, you rarely see two gasoline stations on the same block with two very different prices for gas at the pump. Car owners will simply drive to the place with the lower price.

In the world of futures and commodities trading, big differences between the futures contract (near the delivery date) and the price of the actual commodity are illogical and contrary to the idea that the market is efficient with intelligent buyers and sellers. If significant price differences did exist on the delivery date, there would be an arbitrage opportunity and the potential for profits with zero risk.

Arbitrage

The idea that the spot price of a commodity should equal the futures price on the delivery date is straightforward. Purchasing the commodity outright on Day X (paying the spot price) and purchasing a contract that requires delivery of the commodity on Day X (paying the futures price) are essentially the same thing. Buying the futures contract adds an extra step to the process: step one is to buy the futures contract, and step two is to take delivery of the commodity. Still, the futures contract should trade at or near the price of the actual commodity on the delivery date.

If these prices somehow diverged on the delivery date, there is probably an opportunity for arbitrage. That is, there is the potential to make a functionally risk-free profit by purchasing the lower-priced commodity and selling the higher-priced futures contract assuming the market is in contango. It would be the opposite if the market were in backwardation.

  • Convergence is the movement in the price of a futures contract toward the spot or cash price of the underlying commodity over time.
  • The price of the futures contract and the spot price will be roughly equal on the delivery date.
  • If there are significant differences between the price of the futures contract and the underlying commodity price on the last day of delivery, the price difference creates a risk-free arbitrage opportunity.
  • Risk-free arbitrage opportunities rarely exist because the price of the futures contract converges toward the cash price as the delivery date approaches.

Convergence trade is a trading strategy consisting of two positions: buying one asset forward i.e., for delivery in future (going long the asset) and selling a similar asset forward (going short the asset) for a higher price, in the expectation that by the time the assets must be delivered, the prices will have become closer to equal (will have converged), and thus one profits by the amount of convergence.

Convergence trades are often referred to as arbitrage, though in careful use arbitrage only refers to trading in the same or identical assets or cash flows, rather than in similar assets.

Formally, convergence trades refer to trading in similar assets in the expectation that they will converge in value. Arbitrage is a stricter notion, referring to trading in identical assets or cash flows, while relative value is a looser notion, referring to using valuation methods (value investing) to take long-short positions in similar assets without necessarily assuming convergence, and is more associated with equities. For example, in relative value investing one may believe that the stock of one mining company is undervalued relative to some valuation, while another stock is overvalued (relative to this or another valuation), and thus one will expect the undervalued stock to outperform the overvalued stock, even if these are quite different companies.

Risks

The risk of a convergence trade is that the expected convergence does not happen, or that it takes too long, possibly diverging before converging. Price divergence is particularly dangerous because convergence trades are necessarily synthetic, leveraged trades, as they involve a short position. Thus if prices diverge so that the trade temporarily loses money, and the trader is accordingly required to post margin (faces a margin call), the trader may run out of capital (if they run out of cash and cannot borrow more) and go bankrupt even though the trades may be expected to ultimately make money. In effect, convergence traders synthesize a put option on their ability to finance themselves.

Prices may diverge during a financial crisis, often termed a “flight to quality”; these are precisely the times when it is hardest for leveraged investors to raise capital (due to overall capital constraints), and thus they will lack capital precisely when they need it most.

Further, if other market participants are aware of the positions, they can engineer such price divergences, driving the convergence trader into bankruptcy compare short squeeze.

As with arbitrage, convergence trading has negative skew in return distributions it produces, resulting from the concave payoff characteristic of most such high-probability low-return strategies. Operators engaging in such trades will usually make consistent but relatively small profits, occasionally offset by significant losses, consuming previous profits earned over a long period of time. The low probability of encountering a loss in such strategies can lead inexperienced traders to underestimate the severity of such a loss, and assume excessive levels of leverage, potentially leading to bankruptcy.

On the run/off the run

On the run bonds (the most recently issued) generally trade at a premium over otherwise similar bonds, because they are more liquid there is a liquidity premium. Once a newer bond is issued, this liquidity premium will generally decrease or disappear.

Junk Bond/Treasury convergence

Typically junk bonds, given their speculative grade, are undervalued as people avoid them. Therefore the spread over treasuries is more than the risk of default, by buying junk bonds and selling treasuries, to hedge interest rate risk. Often profits can be achieved by buying junk bonds and selling treasuries, unless the junk bond defaults.

Reverse

A reverse version of this strategy also exists. This is when a trader believes that the futures contract is undervalued and the underlying asset overvalued. Instead of shorting the futures contract the trader would long this, and short the underlying asset.

Relationship between Futures Price & Expected Spot Price

A futures contract is nothing more than a standardized forwards contract. The price of a futures contract is determined by the spot price of the underlying asset, adjusted for time and dividend accrued till the expiry of the contract. When the futures contract is initially agreed to, the net present value must be equal for both the buyer and the seller else there would be no consensus between the two. This difference in price between the futures price and the spot price is called the “basis or spread”.

The futures pricing formula is used to determine the price of the futures contract and it is the main reason for the difference in price between the spot and the futures market. The spread between the two is the maximum at the start of the series and tends to converge as the settlement date approaches. The price of the futures contract and its underlying asset must necessarily converge on the expiry date.

The spot future parity i.e. difference between the spot and futures price arises due to variables such as interest rates, dividends, time to expiry, etc. It is a mathematical expression to equate the underlying price and its corresponding futures price.

According to the futures pricing formula:

Futures price = (Spot Price*(1+rf))- Div)

Where,

Spot Price is the price of the stock in the cash market.

rf = Risk free rate (T Bill/ Government securities)

d: Dividend paid by the company

A key point to take note of is ‘r’ is the risk free interest that we can earn for the entire year but since the future contracts expires in 1, 2 or 3 months, we require to adjust the formula proportionately.

Futures price = Spot price * [1+ rf*(x/365) – d]

x = number of days to expiry

One can take the RBI’s 91 or 182 days Treasury bill as a proxy for the short term risk free rate. The ongoing rate can be referred from RBI’s website. The prevailing rate in the market for 91 and 182 day t bill is ~6.68% and ~6.92% respectively.

Buying vs. selling futures contracts: Futures are a standardized legal agreements. The buyer has a long position, and a seller has a short position in the futures.

Clearing house: Futures are traded in an active market through an exchange, also called a clearing house. In India, the National Stock Exchange of India Limited (NSE) partakes in futures trading through futures index.

Margin requirement: Margin is the amount deposited in the clearing house by the parties. It acts as an assurance that parties will honor the contract when the time comes. Both parties need to deposit a margin at the beginning of the trade. Due to marking to market process, if the initial margin falls below the maintenance amount, the party receives a margin call.

Marking to market:  It is a process to settle future prices daily. The futures price rise or fall daily because of active trading. Clearing houses have adopted a means to pay the price difference after each trading by debiting and crediting the differential amount from the margin amount deposited by the parties.

Expected Spot Price

The market’s average opinion about what the spot price of an asset will be at a specific time in the future. This is usually based on the returns investors require on an investment in the asset underlying a futures contract. In turn, these returns depend on the systematic risk of an investment. When the return from the underlying asset is uncorrelated with the broader stock market, the futures price can be viewed as an unbiased estimate of the expected future spot price. If the return is positively correlated with the broader market, the asset underlying the futures contract has positive systematic risk, and the futures price is lower than the expected future spot price. This situation is known as normal backwardation.

However, if the return from the asset is negatively correlated with the broader market, then the asset underlying the futures contract has negative systematic risk, and the futures price is higher than the expected future spot price. This situation is known as contango.

Pricing of Futures Contract

Futures are derivative products whose value depends largely on the price of the underlying stocks or indices. However, the pricing is not that direct. There remains a difference between the prices of the underlying asset in the cash segment and in the derivatives segment. This difference can be understood through two simple pricing models for futures contracts. These will allow you to estimate how the price of a stock futures or index futures contract might behave. These are:

  • The Cost of Carry Model
  • The Expectancy Model

However, remember that these models merely give you platform on which to base your understanding of futures prices. That said, being aware of these theories gives you a feel of what you can expect from the futures price of a stock or an index.

Futures Price = Spot Price + Net cost of Carry

The Cost of Carry Model assumes that markets tend to be perfectly efficient. This means there are no differences in the cash and futures price. This, thereby, eliminates any opportunity for arbitrage, the phenomenon where traders take advantage of price differences in two or more markets.

When there is no opportunity for arbitrage, investors are indifferent to the spot and futures market prices while they trade in the underlying asset. This is because their final earnings are eventually the same. The model also assumes, for simplicity sake, that the contract is held till maturity, so that a fair price can be arrived at.

In short, the price of a futures contract (FP) will be equal to the spot price (SP) plus the net cost incurred in carrying the asset till the maturity date of the futures contract.

FP = SP + (Carry Cost – Carry Return)

Here Carry Cost refers to the cost of holding the asset till the futures contract matures. This could include storage cost, interest paid to acquire and hold the asset, financing costs etc. Carry Return refers to any income derived from the asset while holding it like dividends, bonuses etc. While calculating the futures price of an index, the Carry Return refers to the average returns given by the index during the holding period in the cash market. A net of these two is called the net cost of carry.

The bottom line of this pricing model is that keeping a position open in the cash market can have benefits or costs. The price of a futures contract basically reflects these costs or benefits to charge or reward you accordingly.

Carry cost – Carry Return = Net cost of Carry

Expectancy Model of futures pricing

The Expectancy Model of futures pricing states that the futures price of an asset is basically what the spot price of the asset is expected to be in the future. This means, if the overall market sentiment leans towards a higher price for an asset in the future, the futures price of the asset will be positive.

In the exact same way, a rise in bearish sentiments in the market would lead to a fall in the futures price of the asset.

Unlike the Cost of Carry model, this model believes that there is no relationship between the present spot price of the asset and its futures price. What matters is only what the future spot price of the asset is expected to be. This is also why many stock market participants look to the trends in futures prices to anticipate the price fluctuation in the cash segment.

Speculation & Arbitrage using Futures

When the securities are bought with the sole object of selling them in future at higher prices or these are sold now with the intention of buying at a lower price in future, are called speculation transactions. The main objective of such transactions is to take advantage of price differential at different times. The stock exchange also provides for settlement of such transactions even by receiving or paying, as the case may be, just the difference in prices.

For example, Ramu bought 200 shares of Tata Steel Ltd. at Rs. 210 per share and sold them at Rs. 235 per share. He does not take and give delivery of the shares but settles the transactions by receiving the difference in prices amounting to Rs. 5,000 minus brokerage. In another case, Manu bought 200 shares of ONGC Ltd. at Rs. 87 per share and sold them at Rs. 69 per share. He settles these transactions by simply paying the difference amounting to Rs. 3600 plus brokerage. However, now-a days stock exchanges have a system of rolling settlement. Such facility is limited only to transactions of purchase and sale made on the same day, as no carry forward is allowed.

Speculation: As a matter of basic intention

Though speculation and investment are different in some respects, in practice it is difficult to say who is a genuine investor and who is a pure speculator. Sometimes even a person who has purchased the shares as a long-term investment may suddenly decide to sell to reap the benefit if the price of the share goes up too high or do it to avoid heavy loss if the prices starts declining steeply. But he cannot be called a speculator because his basic intention has been to invest. It is only when a person’s basic intention is to take advantage of a change in prices, and not to invest, then the transaction may be termed as speculation.

Speculation = Settlement by paying difference in price without delivery of securities

In strict technical terms, however, the transaction is regarded as speculative only if it is settled by receiving or paying the difference in prices without involving the delivery of securities. It is so because, in practice, it is quite difficult to ascertain the intention. Some people regard speculation as nothing but gambling and consider it as an evil. But it is not true because while speculation is based on foresight and hard calculation, gambling is a kind of blind and reckless activity involving high degree of chance element. No only that, speculation is a legal activity duly recognised as a prerequisite for the success of stock exchange operations while gambling is regarded as an evil and a punishable activity. However, reckless speculation may take the form of gambling and should be avoided.

Arbitrageurs

Arbitrage is the simultaneous purchase and sale of equivalent assets at prices which guarantee a fixed profit at the time of the transactions, although the life of the assets and, hence, the consummation of the profit may be delayed until some future date. The key element in the definition is that the amount of profit be determined with certainty. It specifically excludes transactions which guarantee a minimum rate of return but which also offer an option for increased profits. Arbitrageurs are in business to take advantage of a discrepancy between prices in two different markets (Eg : NSE and BSE) . If, for example, they see the futures price of an asset getting out of line with the cash price, they will take offsetting positions in the two markets to lock in a profit.

This is the most important part of the arbitrage transaction. You have locked in a riskless arbitrage profit but how do you actually realize the profits that you have locked. In the cash market you can actually realize profits by selling your shares. In the arbitrage market there are actually two ways of realizing the lock-in profit on the arbitrage transaction.

You can realize the profit on arbitrage by unwinding your trade; that means you reverse your long position in equity and your short position in futures simultaneously

You can hold on to your cash market position in your portfolio, but you can roll over your futures position to the next contract based on the spread

Unwinding your arbitrage trade:

As we are aware, in an arbitrage trade you buy in the cash market and sell in the futures market. That means you are long in cash market and short in the futures market on the same stock and in the same quantity. What is interesting to note is that you do not have to wait till the date of expiry to unwind your position. You can even unwind your arbitrage earlier if the spread has come down substantially.

Long Hedge & Short Hedge

Hedging can be performed by using different derivatives. The first method is by using futures. Both producers and end-users can use futures to protect themselves against adverse price movements. They offset their price risk by obtaining a futures contract on a futures exchange, hereby securing themselves of a pre-determined price for their product.

An important factor in determining the eventual price, is the basis. The basis is calculated by deducting the futures price form the spot price. By successfully predicting the basis of a commodity, the eventual price of a commodity can be calculated at the moment the hedge is placed.

Long Hedge

End-users take a long position when they are hedging their price risks. By buying a futures contract, they agree to buy a commodity at some point in the future. These contracts are rarely executed, but are mostly offset before their maturity date. Offsetting a position is done by obtaining an equal opposite on the futures market on your current futures position. The profit or loss made on this transaction is then settled with the spot price, where the producer will buy his commodity.

A long hedge refers to a futures position that is entered into for the purpose of price stability on a purchase. Long hedges are often used by manufacturers and processors to remove price volatility from the purchase of required inputs. These input-dependent companies know they will require materials several times a year, so they enter futures positions to stabilize the purchase price throughout the year.

For this reason, a long hedge may also be referred to as an input hedge, a buyer’s hedge, a buy hedge, a purchaser’s hedge, or a purchasing hedge.

A long hedge represents a smart cost control strategy for a company that knows it needs to purchase a commodity in the future and wants to lock in the purchase price. The hedge itself is quite simple, with the purchaser of a commodity simply entering a long futures position. A long position means the buyer of the commodity is making a bet that the price of the commodity will rise in the future. If the good rises in price, the profit from the futures position helps to offset the greater cost of the commodity.

Futures price – Basis + broker commission = Net Purchasing price

Short Hedge

Producers of commodities take a short position when hedging their price risks. They sell their product using a futures contract, for a delivery somewhere later in the future. They hedge their price risk similar to long hedgers. They sell a futures contract, which they offset come the maturity date by buying an equal futures contract. The profit or loss made by offsetting the position is then settled with the price obtained at the spot market. This will be the actual price the producer has obtained for selling their product. Just like a long hedge, the prediction of the basis is a crucial factor for determining the price a producer will receive before hedging the commodity. This price can be calculated using the following formula

Futures price + basis – broker commission = net selling price

A short hedge is an investment strategy used to protect (hedge) against the risk of a declining asset price in the future. Companies typically use the strategy to mitigate risk on assets they produce and/or sell. A short hedge involves shorting an asset or using a derivative contract that hedges against potential losses in an owned investment by selling at a specified price.

A short hedge can be used to protect against losses and potentially earn a profit in the future. Agriculture businesses may use a short hedge, where “anticipatory hedging” is often prevalent.

Anticipatory hedging facilitates long and short contracts in the agriculture market. Entities producing a commodity can hedge by taking a short position. Firms in need of the commodity to manufacture a product will seek to take a long position.

Companies use anticipatory hedging strategies to manage their inventory prudently. Entities may also seek to add additional profit through anticipatory hedging. In a short-hedged position, the entity is seeking to sell a commodity in the future at a specified price. The firm seeking to buy the commodity takes the opposite position on the contract known as the long-hedged position. Companies use a short hedge in many commodity markets, including copper, silver, gold, oil, natural gas, corn, and wheat.

Commodity Price Hedging

Commodity producers can seek to lock in a preferred rate of sale in the future by taking a short position. In this case, a company enters into a derivative contract to sell a commodity at a specified price in the future. The company then determines the derivative contract price at which they seek to sell and the specific contract terms. The company typically monitors this position throughout the holding period for daily requirements.

A producer can use a forward hedge to lock in the current market price of the commodity that they are producing, by selling a forward or futures contract today, in order to negate price fluctuations that may occur between today and when the product is harvested or sold. At the time of sale, the hedger would close out their short position by buying back the forward or futures contract while selling their physical good.

  • A short hedge protects investors or traders against price declines.
  • It is a trading strategy that takes a short position in an asset where the investor or trader is already long.
  • Commodity producers can similarly use a short hedge to lock in a known selling price today so that future price fluctuations will not matter for their operations.

Long Hedges vs. Short Hedges

Basis risk makes it very difficult to offset all pricing risk, but a high hedge ratio on a long hedge will remove a lot of it. The opposite of a long hedge is a short hedge, which protects the seller of a commodity or asset by locking in the sale price.

Hedges, both long and short, can be thought of as a form of insurance. There is a cost to setting them up, but they can save a company a large amount in an adverse situation.

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