Black and Scholes (B-S) in 1973 introduced the famous B-S formula for pricing a European-style stock option. The B-S formula depends on some assumptions that are too restrictive and cannot be entirely met. This paper relaxes some of the assumptions underpinning the BS model by deriving the equity price process within the framework of a vector autoregressive (VAR) model using stock market indices. The constant risk-free interest rate is replaced by a cointegrated VAR (COVAR) model using Treasury securities. Value of a European call option via Monte Carlo simulation is provided. We used antithetic and control variates as variance reduction techniques to improve upon the accuracy of our simulation.
Mathematics Subject Classification: G12; C15; G22
Keywords: Option pricing; Vector Autoregressive; Cointegrated Vector Autoregressive; Monte Carlo; Antithetic Variates; Control Variates