Comparison of European and Asian valuation of options with underlying average and stochastic interest rate by Monte Carlo simulation

This paper proposes a methodology to obtain the price of an asian option with underlying averagethrough Monte Carlo simulation. It is assumed that the interest rate is driven by a mean reversion process of Vasicek and CIR type with parameters calibrated by maximum likelihood. The simulation includes the quadratic resampling which reduces the use of computational resources, in particular the method improves the generation of variance covariance matrix. The proposed methodology is applied in the valuation of options with underlying price AMXL. The results show that by comparing prices of european options, with both simulated and published by MexDer with their asian counterparts, asian options prices are lower in the case of call and put options in the money. For put options simulated prices were lower in all cases. It was also found that the difference increases as the time to maturity of the option increases