Pricing Catastrophe Put Options Using Methods in Ruin Theory

Series: 
Mathematical Finance/Financial Engineering Seminar
Tuesday, November 3, 2009 - 15:00
1 hour (actually 50 minutes)
Location: 
Skiles 269
,  
Department of Statistics, University of Toronto
Organizer: 
The discounted penalty function proposed in the seminal paper Gerber and Shiu (1998) has been widely used to analyze the time of ruin, the surplus immediately before ruin and the deficit at ruin of insurance risk models in ruin theory. However, few of its applications can be found beyond, except that Gerber and Landry (1998) explored its use for the pricing of perpetual American put options. In this talk, I will discuss the use of the discounted penalty function and mathematical tools developed for the function for perpetual American catastrophe put options. Assuming that catastrophe losses follow a mixture of Erlang distributions, I will show that an analytical (semi-closed) expression for the price of perpetual American catastrophe put options can be obtained. I will then discuss the fitting of a mixture of Erlang distributions to catastrophe loss data using an EM algorithm.