Numerical Techniques for Determining Unknown Parameters in Option Pricing

Abstract

The Black-Scholes model assume that volatility and interest rates are constant. However, in reality, volatility cannot be stable nor can interest rates be constant. This thesis developed a model to recover unknown non-constant volatilities from one option contract period using simulated data, by taking the derivative with respect to volatility in the theoretical model to obtain non-constant volatilities. Non-constant volatility recovered from the market using this model matched with non-constant market volatility from simulated data.