Pricing and Hedging Basket Options Under Shifted Asymmetric Jump-Diffusion Processes

The empirical characteristics of the underlying asset prices should be taken into account for the pricing and hedging of options. In this paper, we show how to price basket options when assets follow the “shifted asymmetric jump-diffusion” process. The methodology is based on the Hermite polynomial expansion that can match exactly the first m moments of the model implied-probability distribution. The resultant pricing and hedging formulae are in closed-form and similar to the Black and Scholes ones.