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C. Raja Rajeshwari

USING options as an occasional investor or a hedger or as a speculator, you could understand the changes in option premium better if you know the Greeks. Greeks help in explaining why the option premium changes the way they do.

Recap: The Greeks introduced in this column so far are delta and gamma. Delta tells you how much the option premium increases/decreases with increase/decrease in the underlying stock price.

# Calls have positive delta. Every increase in stock premium will lead to increase in the option price.

# Puts have negative delta. Every increase in stock price leads to decrease in the option premium.

Gamma, tells you the pace at which the option premium increase or decreases - effectively the rate at which delta would change.

# Unlike the delta, gamma is dependant on the position and not on the option type whether it is a call or put.

# If you have bought an option (long position) then the gamma is positive. Your long position in calls will increase at an increasing pace, if stock price increases.

# If you have sold or written an option, then the gamma is negative. Your short position in calls would decrease at an increasing rate, if stock price moves up.

# Delta and gamma would largely explain the changes in option premium with respect to the underlying option price.

# However, the option price is affected by time to expiry, volatility and interest rates too.

Effect of time to expiry: Options traded on the NSE have a trading life of three months. New options are introduced on the last Thursday of the month. These trade for three months and expire on the last Thursday of the third month. September contracts were introduced on June 26, 2003 and would expire on September 25, 2003.

If all things remain equal, then over passage of time, the option premium declines.

Why is this so?

This is because the option price is made up of two components - intrinsic value and the time value.

Intrinsic value: Options give you the right to either buy or sell an underlying stock. Therefore, as on date, the option premium would trade at a price, which or less the difference between the spot price and the strike price, if the option were exercised immediately.

For example, when Satyam Computers was at Rs 176, the July 160 call was quoting at Rs 20. Suppose you exercise this option immediately, you would get Rs 16. This is the intrinsic value of the option.

# The intrinsic value denotes the moneyness of the option, whether the option is in the money, out of the money, or at the money.

# If the difference between the spot and strike is positive, which means on immediate exercise you would receive money, then the call is in-the-money.

# If the difference between the spot and strike is negative, which means on exercise you would not receive any money, then the call is out-of-the-money.

# If the difference between the spot and strike is zero, then the call is said to be at the money.

In the above example, the July 160 call is in the money. A Satyam 175 call would be just at the money and a July 190 call is out of the money.

# For puts, it is the opposite. Only if the strike is greater than the spot then the inflow would be positive and this makes the put in the money.

Time value: This is the excess that is paid for the option over and above the intrinsic value. The excess of Rs 4 (premium-intrinsic value) for the Satyam July 160 call is the time value.

# The time value component is affected by the time to expiry. The longer the period to expiry, the higher is the time value component.

# Time value of an option decreases as the time to expiry decreases.

# The intrinsic value has a bearing on the time value too.

The farther the option is out of the money the lesser the time value component. The deep the option is in the money, the higher will the time value component be.

# Volatility of the underlying stock affects the time value.

The more volatile the stock is, the more likely is price changes, making the option in the money or out of the money. Hence, time value is higher for options on volatile stocks.

# On the time of expiry the option premium would just consist of intrinsic value.

Theta: This Greek tells you the rate at which the time value component in the option premium will decrease. This price decrease accelerates as the expiration date approaches.

American or European: American options can be exercised anytime before expiry. Hence there cannot be negative time premium. Therefore, in their case, theta can never be negative. There will only be positive theta. The options on individual stocks in the NSE are American in nature and hence carry only positive theta.

# European options, which can be exercised only on expiry, have negative or positive theta deepening on the moneyness of the option.

Long or Short: For an option buyer (long position), theta tells the daily cost of holding the option.

A theta of 0.2 means that very day the buyer is losing 0.2 in the option premium.

# For an option writer (short position), theta is the daily profit that accrues from selling the option contract.

A theta of 0.2, means that the writer of the call is accumulating 0.2 every day in the option premium.

Moneyness: Theta is small and approaches zero for out-of-the-money options.

Because deeper the option is out-of-the- money lesser would be the time value component and the chances the underlying stock price moving wildly to make it in the money is minimal.

# Theta is large for at-the-money options because for a deep in the money option, intrinsic value is high and time value is small and hence time-decay would be small.

# The same is the case with deep out-of-the-money options. The premium would be the time value component, which would be very low in value and time decay would be minimal.

# If volatility of the stock falls, then time value component reduces and theta follow suit.

How to calculate: To know the theta of an option, a Black-Scholes spreadsheet/calculator that is available in many financial web sites is needed. Such a calculator is available in www.bseindia.com too.

On input of strike price, spot price, premium/volatility, time period, dividend yield, risk free rate into the calculator it gives the values of the Greeks.

Trading with Theta: Decrease in time value of component is good for option writers (selling an option).

# Sell an option with a huge time value component and large theta and pocket the premium.

# Just before the date of expiry, the short (sell) position is squared off by buying the same option at the same strike.

# Because it is very near to time of expiry, the option premium will consist more or less only of the option's intrinsic value.

# This loss in the time value component between the time you sold the call and the time you bought the call is the profit you make.

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