| With the improvement of people’s living standards,and the financial markets has become more and more perfect.Besides standard options,such as European and American options in the financial market,there exists many kinds of new derivatives.Asian powered option,one of the new derivative derived from standard options,has both the advantages of standard options and the distinctive characters,and plays an important role in the financial market.Therefore,Asian powered option pricing research is of great significance.In this paper,we mainly derive the pricing formulas for European-style geometric Asian call powered options with fixed strike and floating strike in the Black-Scholes(B-S)framework respectively.Firstly,for European-style geometric Asian call powered option with fixed strike,we first suppose the exponent a is a positive integer,then we use the binomial expansion technique to derive the closed pricing formula of the price at time t under the risk-neutral measure.Then we let the exponent a be an ordinary positive number,which can be divided into integral part and fractional part.The integral part is easy to be implemented.For the fractional part,we derive the closed pricing formula by using Taylor series expansion.We mainly divide this paper into six parts.The background,significance,formation and development of option pricing,are introduced in Chapter 1.Some useful symbols,definitions,lemmas,theorems with respect to option pricing are presented in Chapter2.The third chapter mainly introduces the B-S framework,and the pricing formula for Asian call options with geometric average fixed strike and European powered options in B-S framework,which provides theoretical basis for later research.In the fourth chapter and the fifth chapter,we mainly study pricing of European-style geometric Asian call powered option with fixed strike and European-style geometric Asian call powered option with floating strike,and we derive the closed pricing formula.The sixth chapter is about the summary and prospect.This chapter mainly summarizes the conclusions of this paper and analyzes the advantages and disadvantages about this paper and then point out the next research direction. |
