随机利率和复合泊松损失情形下的灾难期权的定价（英文）

Pricing Catastrophe Options with Stochastic Interest Rates and Compound Poisson Losses

在这篇论文中,我们运用概率测度改变及其计价单位变换方法,定价灾难事件衍生品.我们假设原生资产和被贴现的零息债券的运动分别服从一个随机过程.在随机利率假设下,我们得到显式闭解公式.我们将看到有时因为模型的考虑去改变计价单位是方便的.进一步,我们显示有时连续的跳跃幅度能被有限多个跳跃幅度代替.因此,有时我们获得的闭解公式运用能不局限有限多个跳跃幅度的假设.最后,数值实验去显示金融和灾难风险怎样影响这双扳机看跌期权的价格.

In this paper, we present an approach of changing probability measures associated with numeraire changes to the pricing of catastrophe event （CAT） derivatives. We assume that the underlying asset and a discounted zero-coupon bond follow a stochastic process, respectively. We obtain explicit closed form formulae that permit the interest rate to be random. We shall see that sometimes it is convenient to change the numeraire because of modeling considerations as well. Furthermore, we show that, for compound Poisson losses, sometimes a continuum of jump sizes can be replaced by finitely many jump sizes. Therefore, sometimes we can explore further applications of the closed-form formulae beyond the case that the compound Poisson losses are finitely many jump sizes. Finally, numerical experiments demonstrate how financial risks and catastrophic risks affect the price of double trigger put option.