Valuation of European options with Monte-Carlo simulation

Abstract

Stochastic volatility models are becoming more important over time in option pricing applications in the financial market since they well explain the implied volatility smiles and skews that are typically observed in the option market. The obstacle with the stochastic models, however, compared to Black Scholes model, is that they do not have the implicit solution for the prices of derivatives. For that matter, this paper evaluates option prices by running Monte Carlo simulation for models: Geometric Brownian Motion model, Heston model are compared with the Black Scholes model prices. The parameters in the Heston model are estimated from maximum likelihood estimation from historical data of SPX index, the European call option price is evaluated to be compared with the market prices of SPX options. It is observed that the calculated call option price using the Heston model gives superior results over Geometric Brownian Motion model, by comparing them with the option market price. Finally, it shows that the Heston model is the superior description of the asset price dynamics especially in the market crash period.