Domain of influence of Local Volatility Function on the Solutions of the General Black-Scholes Equation
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We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo method. Next, we define the inner and outer domains to find the effective volatility region. In the computational experiments, to investigate the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational results show that there is an effective region which dominates the option pricing
Abstract
We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo method. Next, we define the inner and outer domains to find the effective volatility region. In the computational experiments, to investigate the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational results show that there is an effective region which dominates the option pricing
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