Dissertation
Dissertation > Economic > Fiscal, monetary > Insurance > Insurance Theory

An Actuarial Approach to Option Pricing

Author HanLiHua
Tutor ZuoMing
School Huazhong University of Science and Technology
Course Applied Mathematics
Keywords Option Pricing Fractional Brownian motion Insurance Actuarial Equivalent martingale FX Options Asian options
CLC F840
Type Master's thesis
Year 2007
Downloads 311
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In this paper, we consider the special pricing option pricing theory - the three aspects of the application of actuarial methods : in the pricing of foreign exchange options in the OU process of the underlying asset follow geometric fractional Brownian motion under the European Exchange Option Pricing ; ; actuarial methods in the underlying assets follow geometric fractional Brownian motion , geometric average Asian option pricing . First , Mogens Bladt and Tina Haviid Rydberg market hypothesis , actual probability price process only option Actuarial pricing model based on , and the use of stochastic integral of Hu and φksendal application the wick plot defined a geometric fractional motion of underlying assets ( foreign exchange rate ) follows a geometric fractional Brownian motion European exchange option Pricing Formula , and geometric Brownian motion is a special case of this article . Comparison with the the traditional BS formula corresponding Greek letters , can be found in the H = 12 , the Greek letters Greek letters traditional Black-Scholes option formula with the fractional Brownian motion under the Black-Scholes option formula , and have the same bullish , bearish call parity relationship . Secondly, in the case of the underlying assets ( foreign exchange rates ) to follow the OU process , using the actuarial method for European foreign exchange option pricing , and given the parity between the European foreign exchange call option and European foreign exchange puts formula . Finally , consider why he did not pay out a dividend of the underlying stock , the underlying asset follows a geometric fractional Brownian motion to establish the mathematical model , derived geometric average Asian option pricing formula using actuarial methods . Then they were known bonus rates and pay in the underlying stock, known the bonus both cases of simple geometric average Asian option pricing formula promotion .

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