Year: 2020

Call Option

Call options are financial contracts that give the option buyer the right, but not the obligation, to buy a stock, bond, commodity or other asset or instrument at a specified price within a specific time period. The stock, bond, or commodity is called the underlying asset. A call buyer profits when the underlying asset increases in price.

A call option may be contrasted with a put, which gives the holder the right to sell the underlying asset at a specified price on or before expiration.

For options on stocks, call options give the holder the right to buy 100 shares of a company at a specific price, known as the strike price, up until a specified date, known as the expiration date.

For example, a single call option contract may give a holder the right to buy 100 shares of Apple stock at $100 up until the expiry date in three months. There are many expiration dates and strike prices for traders to choose from. As the value of Apple stock goes up, the price of the option contract goes up, and vice versa. The call option buyer may hold the contract until the expiration date, at which point they can take delivery of the 100 shares of stock or sell the options contract at any point before the expiration date at the market price of the contract at that time.

The market price of the call option is called the premium. It is the price paid for the rights that the call option provides. If at expiry the underlying asset is below the strike price, the call buyer loses the premium paid. This is the maximum loss.

If the underlying’s price is above the strike price at expiry, the profit is the current stock price, minus the strike price and the premium. This is then multiplied by how many shares the option buyer controls.

• A call is an option contract giving the owner the right, but not the obligation, to buy a specified amount of an underlying security at a specified price within a specified time.
• The specified price is known as the strike price and the specified time during which a sale is made is its expiration or time to maturity.
• Call options may be purchased for speculation, or sold for income purposes. They may also be combined for use in spread or combination strategies.

Put Option

A put option is a contract giving the owner the right, but not the obligation, to sell–or sell short–a specified amount of an underlying security at a pre-determined price within a specified time frame. This pre-determined price that buyer of the put option can sell at is called the strike price.

Put options are traded on various underlying assets, including stocks, currencies, bonds, commodities, futures, and indexes. A put option can be contrasted with a call option, which gives the holder the right to buy the underlying at a specified price, either on or before the expiration date of the options contract.

A put option becomes more valuable as the price of the underlying stock decreases. Conversely, a put option loses its value as the underlying stock increases. When they are exercised, put options provide a short position in the underlying asset. Because of this, they are typically used for hedging purposes or to speculate on downside price action.

Investors often use put options in a risk-management strategy known as a protective put. This strategy is used as a form of investment insurance; this strategy is used to ensure that losses in the underlying asset do not exceed a certain amount (the strike price.)

In general, the value of a put option decreases as its time to expiration approaches because of the impact of time decay. Time decay accelerates as an option’s time to expiration draws closer since there’s less time to realize a profit from the trade. When an option loses its time value, the intrinsic value is left over. An option’s intrinsic value is equivalent to the difference between the strike price and the underlying stock price. If an option has intrinsic value, it is referred to as in the money (ITM).

Out of the money (OTM) and at the money (ATM) put options have no intrinsic value because there is no benefit in exercising the option. Investors have the option of short selling the stock at the current higher market price, rather than exercising an out of the money put option at an undesirable strike price. However, outside of a bear market, short selling is typically riskier than buying options.

Time value, or extrinsic value, is reflected in the premium of the option. If the strike price of a put option is $20, and the underlying is stock is currently trading at $19, there is $1 of intrinsic value in the option. But the put option may trade for $1.35. The extra $0.35 is time value, since the underlying stock price could change before the option expires. Different put options on the same underlying asset may be combined to form put spreads.

There are several factors to keep in mind when it comes to selling put options. It’s important to understand an option contract’s value and profitability when considering a trade, or else you risk the stock falling past the point of profitability.

• Put options give holders of the option the right, but not the obligation, to sell a specified amount of an underlying security at a specified price within a specified time frame.
• Put options are available on a wide range of assets, including stocks, indexes, commodities, and currencies.
• Put option prices are impacted by changes in the price of the underlying asset, the option strike price, time decay, interest rates, and volatility.
• Put options increase in value as the underlying asset falls in price, as volatility of the underlying asset price increases, and as interest rates decline.
• They lose value as the underlying asset increases in price, as volatility of the underlying asset price decreases, as interest rates rise, and as the time to expiration nears.

Futures and options are tools used by investors when trading in the stock market. As financial contracts between the buyer and the seller of an asset, they offer the potential to earn huge profits. However, there are some key differences between futures and options. Click here if you want to know how to buy and sell Futures Contracts.

Obligation:

A futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future at a certain price. Here, the buyer is obliged to buy the asset on the specified future date.

An options contract gives the buyer the right to buy the asset at a fixed price. However, there is no obligation on the part of the buyer to go through with the purchase. Nevertheless, should the buyer choose to buy the asset, the seller is obliged to sell it.

Risk:

The futures contract holder is bound to buy on the future date even if the security moves against them. Suppose the market value of the asset falls below the price specified in the contract. The buyer will still have to buy it at the price agreed upon earlier and incur losses.

The buyer in an options contract has an advantage here. If the asset value falls below the agreed-upon price, the buyer can opt out of buying it. This limits the loss incurred by the buyer.

In other words, a futures contract could bring unlimited profit or loss. Meanwhile, an options contract can bring unlimited profit, but it reduces the potential loss.

Advance payment:

There is no upfront cost when entering into a futures contract. But the buyer is bound to pay the agreed-upon price for the asset eventually.

The buyer in an options contract has to pay a premium. The payment of this premium grants the options buyer the privilege to not buy the asset on a future date if it becomes less attractive. Should the options contract holder choose not to buy the asset, the premium paid is the amount he stands to lose.

Contract execution:

A futures contract is executed on the date agreed upon in the contract. On this date, the buyer purchases the underlying asset.

Meanwhile, the buyer in an options contract can execute the contract anytime before the date of expiry. So, you are free to buy the asset whenever you feel the conditions are right.

1. Contract details:

At the time of drawing up a futures or options contract, four key details will be mentioned:

• The asset that is up for trade
• The quantity of the asset that is available for buying or selling
• The price at which it will be traded
• The date on which (futures contract) or by which (options contract) it must be traded

The futures contract will also mention the method of settlement.

2. Trade venue:

The trade in futures takes place on the stock exchange. The options trade takes place both on and off the exchanges.

3. Types of assets covered:

Futures and options contracts can cover stocks, bonds, commodities, and even currencies.

4. Requirements:

You would need a margin account to trade in futures and options.

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 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.

2. 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.

3. 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.

4. 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.

5. 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.

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.

2. 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.

3. 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

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.

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.

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.