An Actuarial Approach To Option Pricing

In this paper we consider three applications of a special approach for option pricing—an actuarial approach: pricing Foreign currency option on underlying assets driven by geometric fractional brownian motion or exponential Ornstein—Uhlenback process, an actuarial approach on Asian option pricing when underlying assets driven by geometric fractional brownian motion.Firstly, without any market assumptions, Mogens Bladt and Tina Haviid Rydberg use merely probability measure of price process and actuarial consideration for pricing options.While on geometric fractional brownian motion Hu andφksendal used wick product gave a definition of stochastic integrals. Based on their work, this paper obtains European Foreign currency option pricing formula when underlying assets are driven by geometric fractional Brownian motion, and point out geometric Brownian motion is a special case of our model. Besides, we compare to the Greece letters of traditional B-S formula, and we find that when H= 12 ,the Greece letters of traditional B-S formula and fractional B-S formula are the same, the call and put have the same parity relations.Secondly, in the third part, when underlying assets driven by exponential Ornstein—Uhlenback process, we used the actuarial approach to price the European Foreign currency option and gave the parity relations between the call and put.Finally, when underlying assets driven by geometric fractional brownian motion, we made a mathematical model leave out of account the underlying assets pay bonus, and then we obtained geometric average Asian option pricing formula by actuarial approach. Then, we extended geometric average Asian option pricing in the cases of underlying assets with a known bonus interest rate or known bonus.