Pricing The Reset Catastrophe Put Option Base On Jump-diffusion Process

The catastrophe insurance derivatives first introduced in December 1992 by the Chicago Board of Trade in order to offer insurers new ways of hedging their underwriting risks.In 1996 the first catastrophe equity put option or CatEput was issued.These derivative contracts provide underwriters and risk mangers an effect alternative to hedge and trade systematic catastrophe losses.Although catastrophe derivatives have come into the limelight in recent years,little research has been published on the pricing and hedging issues associated with these complex instruments.The main reason consists in that catastrophe option is difficult to price exactly.This paper builds up the results of Cox(2004),and focus on developing a coherent model for pricing reset catastrophe put option.For expositional simplification,we only consider one predetermined date t₁(t₁＜T) as its reset date.This thesis is divided into four chapters.Chapter 1 Document summarize.Given the background and previous results of catastrophe option.The second chapter list It(?) Integral,Brown movement,and some other basic concepts and theories of change of numeraire and change of probability measure.ChapterⅢis split into two sections.In this chapter we only give the pricing of the reset catastrophe put option when the interest rate is the function of t.ChapterⅣis split into two sections.In Section 1,we will construct the Vasicek model first,then given the Zero-coupon bond P(t,T) and its pricing process.In Section 2,we get two new measures QT and Qs,where Q_T is a risk neutral probability measure by choosing P(t,T) as a numeraire and Qs is also a risk neutral probability measure by choosing S(t) as a numeraire.At last we get the pricing formula of reset catastrophe put option by using martingale method under Vasicek model.