The Pricing Of Fixed-strike Arithmetic Asian Powered Options And Power Asian Options

In the process of sustained development of financial market,derivatives market has also emerged a large number of new varieties derived from standard options besides standard options such as European options and American options,which we call exotic options or new options.Asian options,power options and powered options are several of them.These exotic options are widely used in investment and risk management by banks,companies and institutional investors.This paper leads to the definitions of Asian powered options and power Asian options from the concepts of Asian option,power options and powered options,derives the pricing formulas of fixed-strike arithmetic average Asian powered options and power Asian options via the first-order and quadratic Taylor's approximations and the risk-neutral valuation method,and obtains their approximate pricing formulas.Option pricing is a hot issue that people pay attention to,especially for the more complex Asian powered options and power Asian options,its pricing research is of great important significance.In this paper,we derives the approximate pricing formulas of arithmetic average Asian powered options and power Asian options with fixed strike prices.The full text is divided into six chapters.The first chapter is introduction.It mainly introduces the definition and classification of options,the emergence and development of option pricing theory,and summarizes several commonly used options pricing methods.The second chapter is the preliminary knowledge.It mainly introduces the basic principles and ideas of option pricing,then deduces the Black-Scholes formula of European options by risk-neutral pricing method.Finally,it gives some special functions and important lemmas.The third chapter is a brief introduction of Asian options.It mainly introduces the basic forms and pricing models of Asian options,and gives pricing formulas under geometric and arithmetic averages.The fourth chapter is a brief introduction of power options and powered options.It mainly introduces the basic forms and pricing models of power options and powered options,and gives their pricing formulas.The fifth chapter is the pricing of arithmetic average Asian powered options and power Asian options with fixed strike price.It mainly introduces the basic forms of the two new options,deduces their approximate analytical pricing formulas by Taylor approximation method,and gives specific numerical examples.The sixth chapter is a summary and outlook.It mainly summarizes the conclusions and of this paper and prospects the future development trend of this research field.