A Poisson-Gaussian model to price European options on the extremum of several risky assets within the HJM framework

This paper generalizes European call options on the extremum of several risky assets in a Poisson-Gaussian model which allows both the risky assets and stochastic interest rates moving randomly with jump risks. The stochastic interest rate is assumed to follow an extended multi-factor HJM model with jumps. The authors provide explicitly the closed-form solutions of these options through the change of numeraire technique and examine the effects of both jump risks and stochastic interest rate on the option price with numerical experiment. The model can be seen as an extension of Stulz (1982), Johnson (1987) and Lindset (2006).