The Option Greeks - A Five Factors Complete Guide
Five Factors - Delta, Gamma, Theta, Rho & Vega
What is Option Greeks ?
The Greeks are symbols assigned to the various risk characteristics that an options position entails.
The most common Greeks used include the delta, gamma, theta, rho and Vega, which are the first partial derivatives of the options pricing model.
Greeks are used by options traders and portfolio managers to understand how their options investments will behave as prices move, and to hedge their positions accordingly.
Lets understand Option Greeks ?
1. Delta:
Beginning options traders sometimes assume that when a stock moves Rs.1, the cost of all options based on it will also move Rs.1. That’s pretty silly when you think about it. The option usually costs much less than the stock. Why should you reap the same benefits as if you owned the stock? Besides, not all options are created equal. How much the option price changes compared to a move in the stock price depends on the option’s strike price relative to the actual price of the stock? So the question is, how much will the price of an option move if the stock moves Rs.1? “Delta” provides the answer: it’s the amount an option will move based on a rupee change in the underlying stock. If the delta for an option is 0.50, in theory, if the stock moves Rs.1 the option should move approximately Rs. 50 paisa. If delta is 0.25, the option should move Rs. 25 paisa for every rupee the stock moves. And if the delta is 0.75, how much should the option price change if the stock price changes Rs.1? That’s right. 75 rupee. Typically, the delta for an at-the-money option will be about 0.50, reflecting a roughly 50 percent chance the option will finish in-the-money. In-the-money options have a delta higher than 0.50. The further in-the-money an option is, the higher the delta will be. Out-of-the-money options have a delta below 0.50. The further out-of-the-money an option is, the lower its delta will be. Since call options represent the ability to buy the stock, the delta of calls will be a positive number (.50). Put options, on the other hand, have deltas with negative numbers (-.50). This is because they reflect the right to sell stock.
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2. Gamma:
It measures how fast the delta changes for small changes in the underlying stock price. i.e. delta of the delta. The option's gamma is a measure of the rate of change of its delta. The gamma of an option is expressed as a percentage and reflects the change in the delta in response to a one point movement of the underlying stock price. Like the delta, the gamma is constantly changing, even with tiny movements of the underlying stock price. It generally is at its peak value when the stock price is near the strike price of the option and decreases as the option goes deeper into or out of the money. Options that are very deeply into or out of the money have gamma values close to 0. Example Suppose for a stock XYZ, currently trading at Rs. 47, there is a FEB 50 call option selling for Rs.2 and let's assume it has a delta of 0.4 and a gamma of 0.1 or 10 percent. If the stock price moves up by Rs.1 to Rs.48, then the delta will be adjusted upwards by 10 percent from 0.4 to 0.5. However, if the stock trades downwards by Rs.1 to Rs.46, then the delta will decrease by 10 percent to 0.3.
3. Theta:
The change in option price given a one day decrease in time to expiration. Basically it is a measure of time decay. The theta value indicates how much value a stock option's price will diminish per day with all other factors being constant. If a stock option has a theta value of -0.012, it means that it will lose 1.2 cents a day. Such a stock option contract will lose 2.4 cents over a weekend. (Yes, the effect of theta value and time decay is active even when markets are closed!) The nearer the expiration date, the higher the theta and the farther away the expiration date, the lower the theta. Example A call option with a current price of Rs.2 and a theta of -0.05 will experience a drop in price of Rs.0.05 per day. So in two days' time, the price of the option should fall to Rs.1.90.
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4. Rho:
The change in option price given a 1% change in the risk free interest rate. It is sensitivity of option value to change in interest rate. Example If an option or options portfolio has a rho of 0.017, then for every percentage-point increase in interest rates, the value of the option increases `0.017. However, it is not normally needed for calculation for most option trading strategies.
5. Vega:
The option's Vega is a measure of the impact of changes in the underlying volatility on the option price. Specifically, the Vega of an option expresses the change in the price of the option for every 1% change in underlying volatility. Options tend to be more expensive when volatility is higher. Thus, whenever volatility goes up, the price of the option goes up and when volatility drops, the price of the option will also fall. Therefore, when calculating the new option price due to volatility changes, we add the Vega when volatility goes up but subtract it when the volatility falls. Example A stock XYZ is trading at Rs.46 in May and a JUN 50 call is selling for Rs.2. Let's assume that the Vega of the option is 0.15 and that the underlying volatility is 25%.
If the underlying volatility increased by 1% to 26%, then the price of the option should rise to Rs.2 + 0.15 = Rs.2.15. However, if the volatility had gone down by 2% to 23% instead, then the option price should drop to Rs.2 - (2 x 0.15) = Rs.1.70 Keep in mind: Vega doesn’t have any effect on the intrinsic value of options; it only affects the “time value” of the option’s price. Here’s an odd fact for you: Vega is not actually a Greek letter. But since it starts with a ‘V’ and measures changes in volatility, this made-up name stuck.
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Bottomline
Greeks are used by options traders and portfolio managers to understand how their options investments will behave as prices move, and to hedge their positions accordingly. The most common Greeks used include the delta, gamma, theta, rho and Vega, which are the first partial derivatives of the options pricing model.