NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH

摘要

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