Bridge Copula Model for Option Pricing

Résumé : In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset pricing model arises by employing copula methods. In particular, all discounted single-asset price processes are modeled as martingale diffusions under a risk-neutral measure. The price processes are so-called UOU diffusions and they are each generated by combining a variable (Ito) transformation with a measure change performed on an underlying Ornstein-Uhlenbeck (Gaussian) process. Consequently, we exploit the use of a normal bridge copula for coupling the single-asset dynamics while reducing the distribution of the multi-asset price process to a multivariate normal distribution. Such an approach allows us to simulate multidimensional price paths in a precise and fast manner and hence to price path-dependent financial derivatives such as Asian-style and Bermudan options using the Monte Carlo method. We also demonstrate how to successfully calibrate our multi-asset pricing model by fitting respective equity option and asset market prices to the single-asset models and their return correlations (i.e. the copula function) using the least-square and maximum-likelihood estimation methods.