Pricing European Options with the Black-Scholes and Monte Carlo Methods: a Comparative Study

Abstract

Option pricing is a central concept in finance. Since F. Black and M. Scholes in troduced their formula for pricing options in 1973 it has been widely adopted, but it has also been proven to have some limitations in its inherent assumptions and thus subsequent performance. In this thesis we compare and evaluate the accu racy of the famous Black-Scholes option pricing model with a Jump-Diffusion model implemented using Monte Carlo simulations. The two models were compared for European options of different strike prices, maturities, asset volatilities, and mar ket trends. The analysis was carried out on historical market data from the OMX Stockholm 30 index where the models’ predicted option prices were compared to the options’ discounted value at expiration. The results obtained from the analysis suggest that the two models are similar in performance. However, the Monte Carlo Jump-Diffusion model has a higher pricing accuracy on stocks with low to moder ately high volatility, and the Black-Scholes model has a higher accuracy on high volatility stocks. The market trend does not seem to affect the prediction accuracy of the models, but the sparse selection of historical market periods limits the cer tainty of this result. Potential improvements include volatility estimation of shorter time periods to limit the influence of large market movements in the long term, a maximum likelihood estimation to tune the parameters of the Jump-Diffusion pro cess, as well as an expansion of the scope to include more time periods than the three chosen. Future work might include an extension into stochastic volatility.