Abstract

Accurate option price path is needed for risk management and for financial reporting as the accounting standards insist on mark to market value for derivative products. Binary model Black scholes model and Longstaff methods provide insight on option pricing but they are seldom validated with real data. Most of the research studies demonstrate the validity through algebra or by solving partial differential equation with strong market data. As these computations are tedious they are rarely applied in weak and incomplete markets.

In this article we test actual values of options of Tata Consultancy Services whose shares and options are actively traded in the national stock exchange of India and applied the Crank Nicholson central difference method in estimating the path of the option pricing with five exercise prices, two out of money, at the money and two in the money contracts of call and put options at three volatilities. The actual option values are compared with the forecasted option values and estimated the errors.

The plots of actual option values and the forecasted values produced by central difference method converge excellently well producing minimum sums of squared error. Even in the weak and incomplete markets the Crank Nicholson method works well in producing price path of options. This algorithm will be useful for hedging decisions and also for accurate forecasting and accounting reporting.

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