This paper considers short-dated foreign equity options (FEOs) and proposes a new model for their pricing. When time to maturity is short, the possibility of seeing jumps caused by a forthcoming big event will make the return distributions of both assets (equity and exchange rate) very fat-tailed, resulting in a much higher kurtosis compared to longer time to maturity. The impact is even stronger when the jumps from the two assets are highly and positively correlated so that their effects will add up. In the proposed BB-BAL jump-diffusion model, we use a bivariate Bernoulli (BB) distribution to model the jump indicators of the two assets. The jump sizes of two assets are assumed to follow a bivariate asymmetric Laplace (BAL) distribution which captures their tail-fatness as well as their potentially strong correlation simultaneously. We provide an analysis for the proposed model and derives the analytical results for FEO prices. Through numerical examples we show that the jump correlation may lead to very high kurtosis and have a significant impact on the short-dated FEO prices.
- Bivariate asymmetric Laplace (BAL) distribution
- Bivariate Bernoulli (BB) distribution
- Foreign equity option (FEO)
- Jump-diffusion model
- Series expansion method