Option pricing with bivariate risk-neutral density via copula and heteroscedastic model: A Bayesian approach

Abstract

Multivariate options are adequate tools for multi-asset risk management. The pricing models derived from the pioneer Black and Scholes method under the multivariate case consider that the asset-object prices follow a Brownian geometric motion. However, the construction of such methods imposes some unrealistic constraints on the process of fair option calculation, such as constant volatility over the maturity time and linear correlation between the assets. Therefore, this paper aims to price and analyze the fair price behavior of the call-on-max (bivariate) option considering marginal heteroscedastic models with dependence structure modeled via copulas. Concerning inference, we adopt a Bayesian perspective and computationally intensive methods based on Monte Carlo simulations via Markov Chain (MCMC). A simulation study examines the bias, and the root mean squared errors of the posterior means for the parameters. Real stocks prices of Brazilian banks illustrate the approach. For the proposed method is verified the effects of strike and dependence structure on the fair price of the option. The results show that the prices obtained by our heteroscedastic model approach and copulas differ substantially from the prices obtained by the model derived from Black and Scholes. Empirical results are presented to argue the advantages of our strategy.