Sunday, February 10, 2013

Free online Black Scholes option value and option greeks calculator

How to use the calculator
Input data for all variables available under "grey cells". Refresh the page to load default values. Below is a short description of how these variables will impact option premium value.

Price of the underlying (stock price) - The higher the stock price, the more a call is worth. (The less a put is worth.)

Strike price - The higher the strike price, the less a call (the more a put) is worth.

Time to expiration (days left) - The more time left before the option expires, the more any option is worth.

Dividend yield (%) - An option holder is not entitled to cash dividends, and dividends reduce the price of the stock (when the stock goes ex-dividend, the stock price is decreased by the amount of the dividend).   The higher the dividend, the less a call is worth, and the more a put is worth.

Risk-free rate of interest(%) - The higher the interest rate, the more the call (less the put) is worth. This is because a call buyer uses less cash to buy the call than he would use to buy stock, and the difference can be invested to earn interest.  The more interest earned, the more a call buyer is willing to pay for the option.

Annual volatility (%) - The is the only one of the factors that is not known. (Of course dividends, interest rates, stock prices and time to expiration are constantly changing, but they are known at the time the option transaction is made.) The volatility used in the model is an estimate of the potential price movement that will occur during the life of the option. The higher the volatility, the more any option is worth because a high volatility increases the probability that the option will make a large favorable move for the holder of the option. Since a change in the volatility estimate changes the value of an option by a large amount, and since this volatility a difficult factor to estimate, there is often a significant disagreement as to the fair value of an option.

Option Greeks - Along with the option premium calculation, you will be able to see the values of various option greeks. Below is a short description of popular option greeks and what their importance is with respect to option premium valuation.

Delta - Delta measures the expected change in option premium for one unit change in the underlying price. The delta for call option is always positive as the value of call option increases as the underlying goes up. The delta for put option is always negative as the value of put option decreases as the underlying goes up.

Theta - Theta measures the expected change in premium for one unit change in time to expiry of the options. Theta is always negative for both call and put, as the value of both call and put goes down as the time to expiry decreases. In other words, it gives the buyer of the option the value he would lose every day if his view is not correct.

Gamma - Gamma measures the expected change in delta of an option for one unit change in the price of underlying. This means that as the underlying price changes, delta of the option changes. Now changed delta is the expected change in value of option for unit change of the underlying price. Gamma is significantly higher when an option is near its expiry. So writers of an option must closely watch their position when the option is very near its expiry. For buyers these are golden days to maximize their returns.

Vega - Vega measures the expected change in value of option for 1 unit change in volatility of the underlying. Vega is always positive for both call and put, as the value of both calls and puts increases as the volatility increases and vice-versa

Rho - Rho measures the expected change in value of an option for 1 unit change in interest rate. Generally this is considered insignificant for option valuation because interest rate does not change in wide range in short term.


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