Pricing And Properties Of Asian Option Under Lévy Model

The main purpose of this article is to provide a analytical price formula of con-tinuous geometric average European Asian options and prove a symmetry relationshipbetween floating strike and fixed strike Asian options under Lévy model.We model the risk asset price S_t as dS_t=S_t-[μdt+σdB_t+∫_R0 K(x)(?)(dt, dx)],0≤t≤T, where (B_t, t≥0) is a standard Brown motion,μ,σ＞0 are constants, (?)(t,·)is a compensated poisson random measure with Lévy measure v(·), K(x) is a deter-mined function. In the third chapter, we prove the poisson process(N(t, A), 0≤t≤T)with intensity v(A) is also a poisson process under a change of measure as in thearticle, but the new intensity is changed; further more, we provide the price formula ofAsian options using the risk minimum principle under equivalent martingale mea-sure; in the end, we provide a analytical price formula of continuous geometric aver-age European Asian options by interlacing process. In the fourth chapter, we prove thesymmetry relationship between floating strike and fixed strike Asian options by usingproper changes of measure, the more we extend the conclusion of [1],[19].