Catastrophe equity put options with target variance

In this study, we consider a new class of catastrophe equity put options, whose payoff depends on the ratio of the realized variance of the stock over the life of the option and the target variance, which represents the insurance company's expectation of the future realized variance. This kind of options could help insurance companies raise more equity capital when a large number of catastrophic events occur during the life of the option. We employ a compound doubly stochastic Poisson process with lognormal intensity to describe accumulated catastrophe losses and assume the volatility varies stochastically. Finally, numerical results are presented to investigate the values of this class of options.