Option Greeks

 Option Greeks

Option premiums change with changes in the factors that determine option pricing i.e., factors such as strike price, volatility, term to maturity, etc. The sensitivities most commonly tracked in the market are known collectively as “Greeks” represented by

Delta, Gamma, Theta, Vega and Rho.

• Delta (δ or Δ)

The most important of the ‘Greeks’ is the option’s “Delta”. This measures the sensitivity of the option value to a given small change in the price of the underlying asset. It may also be seen as the speed with which an option moves with respect to price of the underlying asset. Delta = Change in option premium/ Unit change in price of the underlying asset. Delta for call option buyer is positive. This means that the value of the contract increases as the share price rises. To that extent it is rather like a long or ‘bull’ position in the underlying asset.

 Delta for call option seller will be same in magnitude but with the opposite sign (negative). Delta for put option buyer is negative. The value of the contract increases as the share price falls. This is similar to a short or ‘bear’ position in the underlying asset. Delta for put option seller will be same in magnitude but with the opposite sign (positive). Therefore, delta is the degree to which an option price will move given a change in the underlying stock or index price, all else being equal. For example, if the delta of a call option is 0.60, it means that a small change of, say 1 rupee, in the price of the underlying asset, will lead to a change of 60 paise in the price of the call option. The knowledge of delta is of vital importance for option traders because this parameter is heavily used in margining and risk management strategies. The delta is often called the hedge ratio. For example, if you have a portfolio of ‘n’ shares of a stock then ‘n’ divided by the delta gives you the number of calls you would need to be short (i.e., the number of calls you need to write) to create a hedge. In such a “delta neutral” portfolio, any gain in the value of the shares held due to a rise in the share price would be exactly offset by a loss on the value of the calls written, and vice versa.

 

• Gamma (γ)

Gamma measures change in delta with respect to change in price of the underlying asset. This is called a second derivative of the option price with regard to price of the underlying asset. It is calculated as the ratio of change in delta for a unit change in market price of the underlying asset. Gamma = Change in an option delta / Unit change in price of underlying asset Gamma works as an acceleration of the delta, i.e. it signifies the speed with which an option will go either in-the-money or out-of-the-money due to a change in price of the underlying asset. For instance, if a call option has a delta of 0.50 and a gamma of 0.08, it means that a small increase of say, 1 rupee, in the price of the stock will cause the option delta to change by 0.08. Thus, the new call delta will be 0.58.

 

• Theta (θ)

Theta is the measure of an option’s sensitivity to time decay. Theta is the change in option price given a one-day decrease in time to expiration. It is a measure of time decay. Theta is generally used to gain an idea of how time decay is affecting your option positions. Theta = Change in an option premium / Change in time to expiry For example, if a call option with 5 days to expiry has a theta of 1.2, it means that the option price will decline by Rs.1.20 for each day till the option expiry. Usually, theta is negative for a long option, whether it is a call or a put. Other things being equal, options tend to lose time value each day throughout their life.

 

• Vega (ν)

Vega is the measure of the sensitivity of an option price to changes in market volatility. It is the change of an option premium for a given change (typically 1%) in the underlying volatility. Vega = Change in an option premium / Change in volatility Thus, if a call option has a vega of 0.80, it means that the option premium will change by 0.80 per cent for every 1 per cent change in the implied volatility of the underlying asset. Vega is positive for a long call and a long put. An increase in the assumed volatility of the underlying increases the expected payout from a buy option, whether it is a call or a put.

 

• Rho (ρ)

Rho is the change in option price given a one percentage point change in the risk-free interest rate. Rho measures the change in an option’s price per unit increase in the cost of funding the underlying. Rho = Change in an option premium / Change in cost of funding the underlying

Option Pricing Fundamentals

 Prices are never fixed by stock exchanges or SEBI or anybody for that matter. In fact, price discovery is a very critical and basic component of markets. Stock exchanges only provide a platform where buyers and sellers meet, and SEBI’s role is to ensure smooth functioning of our markets. Any option’s value increases or decreases depending upon different variables. Each variable has its impact on an option. The impact can be the same or different for a call and a put option.

As explained in the earlier section, option premium is the sum of intrinsic value and time value. As long as the option has not expired, there will always be some time value. Intrinsic value may or may not be there, depending upon whether the option is ITM, ATM or OTM.

Time value of the option in turn depends upon how much time is remaining for the option to expire and how volatile is the underlying. Thus, there are five fundamental parameters on which the option price depends upon:

1) Spot price of the underlying asset

2) Strike price of the option

3) Volatility of the underlying asset’s price

4) Time to expiration

5) Interest rates

These factors affect the premium/ price of options (both American & European) in several ways.

• Spot price of the underlying asset

The option premium is affected by the price movements in the underlying instrument. If price of the underlying asset goes up, the value of the call option increases, while the value of the put option decreases. Thus, when Nifty rises from 17500 to 18000, the price of a call option with a strike price of 17500 will increase, while the price of a put option with the same strike price will fall. Similarly, if the price of the underlying asset falls, the value of the call option decreases while the value of the put option increases.

• Strike Price

If all the other factors remain constant but the strike price of option increases, intrinsic value of the call option will decrease and hence its value will also decrease. For example, when Nifty is at 17562, a call option with a strike price of 17600 will trade at a higher price than a call option with the same maturity but with a strike price of 17700. This is because the intrinsic value is progressively lower for higher strike prices of calls. On the other hand, with all the other factors remaining constant, increase in strike price of option increases the intrinsic value of the put option which in turn increases its option value. Thus, a put option with a strike price of 17700 will trade at a higher premium than a put option with the same maturity but a strike price of 17600.

• Volatility

It is the magnitude of movement in the underlying asset’s price, either up or down. It affects both call and put options in the same way. Higher the volatility of the underlying stock, higher the premium because there is a greater possibility that the option will move in-the-money during the life of the contract. Hence, when the index or stock volatility shoots up because of some unexpected event, the prices of both calls and puts on the index or stock will increase. Higher volatility = Higher premium, Lower volatility = Lower premium (for both call and put options).

• Time to expiration

The effect of time to expiration on both call and put options is similar to that of volatility on option premiums. Generally, longer the maturity of the option, greater is the uncertainty and hence the higher is the premium. Thus, an option with a strike price of 17500 and maturing in October 2021 will generally trade at a higher price than an option with the same strike price but expiring in September 2021. If all other factors affecting an option’s price remain the same, the time value portion of an option’s premium will decrease with the passage of time. This is also known as time decay. Options are known as ‘wasting assets’, due to this property where the time value gradually falls to zero.

It is also interesting to note that of the two component of option pricing (time value and intrinsic value), one component (the Time Value) is inherently biased towards reducing in value. So, if all things remain constant throughout the contract period, the option price will always fall in price by expiry. Thus, option sellers are at a fundamental advantage as compared to option buyers as there is an inherent tendency in the price to go down.

• Interest Rates

Interest rates are slightly complicated because they affect different options, differently. For example, interest rates have a greater impact on options with individual stocks an d indices compared to options on futures. To put it in a simpler way, high interest rates  will result in an increase in the value of a call option and a decrease in the value of a put option.

Moneyness of an option

 Options can be classified into three categories, viz., in-the-money, at-the-money and

out-of-the-money options.

• In-the-money (ITM) option: This option would give the option holder a positive cash flow, if it were exercised immediately. A call option is said to be ITM, when spot price is higher than strike price. A put option is said to be ITM when spot price is lower than strike price. In our examples, the call option is in-the-money.

• At-the-money (ATM) option: At-the-money option would lead to zero cash flow if it were exercised immediately. Therefore, for both call and put ATM options, strike price is equal to spot price.

• Out-of-the-money (OTM) option: Out-of-the-money option is one with strike price worse than the spot price for the holder of option. In other words, this option would give the holder a negative cash flow if it were exercised immediately. A call option is said to be OTM, when spot price is lower than strike price. A put option is said to be OTM when spot price is higher than strike price. In our examples, the put option is out-of-the-money.

Products in Derivatives Market

•  Forwards

It is a contractual agreement between two parties to buy/sell an underlying asset at a certain future date for a particular price that is pre-decided on the date of contract. Both the contracting parties are committed and are obliged to honour the transaction irrespective of price of the underlying asset at the time of delivery. Since forwards are negotiated between two parties, the terms and conditions of contracts are customized. These are Over-the-counter (OTC) contracts.

 

• Futures

A futures contract is similar to a forward, except that the deal is made through an organized and regulated exchange rather than being negotiated directly between two parties. Futures are also standardized contracts (in terms of their lot size, maturity date, etc.) so that they can be traded on the exchange. Indeed, we may say futures are exchange traded forward contracts.

 

• Options

An Option is a contract that gives the right, but not an obligation, to buy or sell the underlying on or before a stated date and at a stated price. While buyer of option pays the premium and buys the right, writer/seller of option receives the premium with obligation to sell/ buy the underlying asset, if the buyer exercises his right.

 

• Swaps

A swap is an agreement made between two parties to exchange cash flows in the future according to a prearranged formula. Swaps are, broadly speaking, series of forward contracts. Swaps help market participants manage risk associated with volatile interest rates, currency exchange rates and commodity prices.

Derivatives Market – History & Evolution

 History of Derivatives may be mapped back to several centuries. Some of the specific

milestones in evolution of Derivatives Market Worldwide are given below:

• 12th Century - In European trade fairs, sellers signed contracts promising future delivery

of the items they sold.

• 13th Century - There are many examples of contracts entered into by English Cistercian

Monasteries, who frequently sold their wool up to 20 years in advance, to foreign

merchants.

• 1634-1637 - Tulip Mania in Holland: Fortunes were lost after a speculative boom in tulip

futures burst.

• Late 17th Century - In Japan at Dojima, near Osaka, a futures market in rice was

developed to protect rice producers from bad weather or warfare.

• In 1848, The Chicago Board of Trade (CBOT) facilitated trading of forward contracts on

various commodities.

• In 1865, the CBOT went a step further and listed the first “exchange traded” derivative

contract in the US. These contracts were called “futures contracts”.

• In 1919, Chicago Butter and Egg Board, a spin-off of CBOT, was reorganised to allow

futures trading. Later its name was changed to Chicago Mercantile Exchange (CME).

• In 1972, Chicago Mercantile Exchange introduced International Monetary Market

(IMM), which allowed trading in currency futures.

• In 1973, Chicago Board Options Exchange (CBOE) became the first marketplace for

trading listed options.