SIMPLIFIED OPTION PRICING TECHNIQUES

Abstract

In this paper we provide alternative methods for pricing European and American call and put options. Our contribution lies in the simplification attempted in the models developed. Such simplification is feasible due to our observation that the value of the option can be derived as a function of the underlying stock price, strike price and time to maturity. This route is supported by the fact that both the risk-free rate and the volatility of the stock are captured by the move of the underlying stock price. Moreover, looking at the properties of the Brownian motion, widely used to map the move of the stock price, we realize that volatility is well depicted by time. Last but not the least, the value of an option is an increasing function of both time and volatility. We find simplified option pricing formulas depending on the underlying asset (price and strike price) and the time to maturity only. We test our formulas against the S&P 500 index options; the advantage of the approach is that less simplifying assumptions are needed and much simpler methods are produced. We provide alternative formulas for pricing European- and American-type options.