An Actuarial Approach to Option Pricing
|School||Huazhong University of Science and Technology|
|Keywords||Option Pricing Fractional Brownian motion Insurance Actuarial Equivalent martingale FX Options Asian options|
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 .