Effectiveness of Tridiagonal Path Dependent Option Valuation in Weak Derivative Market Environment

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. The binary models - Black Scholes model and Longstaff methods provide an 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 equations with strong market data. As these computations are tedious, and they are rarely applied in weak and incomplete markets. In this paper, we tested the actual values of options of Tata Consultancy Services whose shares and options are actively traded on the NSE, and applied the Crank Nicolson central difference method for 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 were compared with the forecasted option values and the errors were estimated. The plots of actual option values and the forecasted values produced by the central difference method converged excellently, producing minimum sums of squared error. Even in the weak and incomplete markets, the Crank Nicolson method worked well in producing the price path of options. This algorithm will be useful for hedging decisions and also for accurate forecasting and accounting reporting.