Communications in Mathematical Finance

The Impact of Crank-Nicolson Finite Difference Method in Valuation of Options

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• Abstract

   

  This paper presents Crank-Nicolson (CN) analysis for valuation of options. This particular method solves Black-Scholes (BS) partial differential equation (PDE) by means of numerical solutions for pricing options. The deviation values were derived from BS analytical solutions, adopting certain criteria using three standard deviations as a measure for pricing effects. Results showed when options are overpriced, underpriced as well as no-mispricing this is in line with theoretical predictions and significant improvement over previous efforts. In the same scenario, a non-parametric test discovered by Kolmogorov-Smirnov (KS) was performed; the test revealed that there exist a statistically difference between distributions of BS and CN. Also, the initial stock prices of no-mispricing were compared and it was seen that initial stock prices of 70 and 40 are the best for call and put options. The work presented here has profound implication for future studies of option prices and may one day help solve the problems of option traders.

   

  Keywords: Crank-Nicolson, Option pricing, Mispricing effects, B-S PDE and Standard Deviation.