BFS 2002

Poster Presentation

Valuing Exotic Derivatives with Jump Diffusions: The Case of Basket Options

Dimitris Flamouris, Daniel Giamouridis

Exotic options are complicated derivatives instruments whose structure does not allow, in general for closed-form solutions, thus making their pricing and hedging a difficult task. To overcome additional complexities such products are, as a rule, priced within a Black & Scholes framework, assuming a Geometric Brownian Motion (GBM)for the dynamics of the underlying asset. This paper develops a more realistic framework for the pricing of exotic derivatives and derives closed-form analytic solutions for the pricing and hedging of Basket options. We relax the simplistic assumption of a GBM process by introducing the Bernoulli Jump Diffusion process (BJD). Assuming a different stochastic process from the GBM, rather than an alternative distribution, is preferable for exotic products because it can provide better hedging rules. Potential extension of the model with the use of Edgeworth series expansion (ESE) is also discussed. Monte Carlo simulation confirms the validity of the proposed BJD model.