Futures and Options – The basics.

Understanding options Gamma.

We learned about the relevance of Delta in our last post on options. We said that Delta measure of an option will keep on changing every day due to various factors. Since Delta is never constant, an option trader will have to keep a close watch on the rate of change in Delta or the volatility factor of Delta. Gamma is a measure that tracks this rate of change in delta. So if the gamma of an option is .1, it means that the delta of that option changes 10% when there is a Re 1 change in the underlying asset. So gamma is just a continuation of Delta or it can be considered as a derivative of Delta.

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Understanding Options delta

A naïve option trader may think that if the underlying price of the stock moves up Rs 1, the option value will also move up Rs 1. This is not true. The price of an option may move in varying degrees according to changes in the underlying stock. This relation between underlying asset’s price and related option contract is explained by computing the Delta of an option . For example, if a stock option has a Delta of .50 it means that, for every Rs 10 movement in the stock’s price, the option price would move Rs 5. This is a very important information for every option trader because, it helps to reasonably estimate the profit / loss if the stock price increases / decreases to a certain level.

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Option Greeks

Greeks.

In options, ‘Greeks’ means a group of Greek alphabets that are used to represent certain values related to volatility of Option premiums. There are 5 measures of volatility – Delta (Δ), Gamma (Γ), Vega (ν), Theta (θ) and Rho (ρ) which commonly used by investors. These are called option Greeks.

We already know that option contracts keep changing in values due to changes in one or more of the several variables such as – price of the stock, the risk free rate of interest, time to expiry, volatility etc . To explain the relationship between each of these variables and option premium, a Greek letter is used as a short form- for example – Delta of an option (symbol Δ) explains the rate of change in the option price with respect to the underlying share price.

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Option valuation : Method III

The Black Scholes Model

We learned from binomial model that price change in underlying stocks can be chopped to shorter periods like 6 months or even 3 months or 1 month and a chart can be drawn which would show the probable options values. Starting from the end of the tree, we worked backwards until we got the value of the option at the beginning. It may be practical to work back three or four steps using the binomial method. But, stock market is a place where the price changes keep occurring every minute, continually.  Hence, a method will have to be found out where this chopping can extended ad infinitum.

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