New method to option pricing for the general black-scholes model—An actuarial approach

Abstract

Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black-Scholes model is generalized to the case where the risk-less asset (bond or bank account) earns a time-dependent interest rate and risk asset (stock) has time-dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put-call parity of European option are obtained. The general approach of option pricing is given for the general Black-Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put-call parity of European option on a stock whose price process is driven by general Ornstein-Uhlenback (O-U) process are given by actuarial approach.