The Pricing Of European Power Option In An Actuarial Approach

This paper mainly studies the pricing of power options, and it consists of four chap-ters. ChapterⅠlists the basic concepts firstly, such as option pricing, the pricing in anactuarial approach, and power options; it also generalizes the previous result on Europeanpower options. ChapterⅡpresents the fundamental definitions and theorems of this paper,including Brown movement, Itffo Integral, and Poisson jump-diffusion. ChapterⅢstudiesthe pricing of European power options in an actuarial approach under three conditions re-spectively, i.e. under continuous dividend, random rates of interest, and non-homogeneousPoisson jump-diffusion. ChapterⅢconsists of 3 sections. Section 1 expounds the pricingformula and put-call equal relations of power options pricing in an actuarial approach undercontinuous dividend; section 2 expounds the pricing formula and put-call equal relations ofpower options pricing in an actuarial approach under random rates of interest; and section3 expounds the pricing formula and put-call equal relations of power options pricing in anactuarial approach under non-homogeneous Poisson jump-diffusion. ChapterⅣis the em-pirical analysis part about the justification above with two sections. Section 1 presents thetest simulation of options pricing in an actuarial approach under random rates of interest;and section 2 analyzes the simulation results, and gets the final conclusion, i.e. the actuarialapproach is superior to Equivalent Martingale approach remarkably.