Equivalence Of Floating And Fixed Strike Asian Options In A Semimartingale Model

This paper extends the results of the paper[11](2005). We maily study the equivalence relationship among different types of arithmetic Asian options in a semimartingale model.The paper [8] (2002) observed that a symmetry result between floating and fixed strike Asian options in the case of Black-Sholes model, then, The paper[11] extended this result by considering a general Levy process as the driving process of the underlying. This paper extends the results of [11] further. firstly, we prove a symmetry relationship between floating and fixed strike Asian options in a semimartingale ordinary exponential model, using a change of numeraire and the characteristic triplet of the dual process. then, On the basis of the relationship between stochastic and ordinary exponentials of semimartingale process, we prove a equivalence between floating and fixed strike Asian options in a semimartingale model. We also give the applications of the results on different Levy processes and obtain the equivalence results for a generalized Asian options defined in the paper[12] (2007). Lastly, by applying the same technique, we obtain the equivalence results for lookback options.