Simplified option pricing techniques

Most of the currently known option pricing techniques utilize the underlying asset price and strike price, its volatility and time to maturity, as well as the risk free-rate. 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, the 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 least, the value of an option is an increasing function both of time and volatility.

As a matter of fact, without doubting the success and beauty of the Black-Scholes pricing formula, one should not ignore that it uses some quite strong assumptions; if lifted it is not secured that the output will still hold true. Following the above rationale we feel that by properly inserting time we can derive “nice and easy” option pricing techniques.

These observations make us believe that we could find simplified option pricing formulas depending on the underlying asset (price and strike price) and the time to maturity only. The advantage of the approach is that less simplifying assumptions are needed and much simpler methods are produced. We test our formulas against the Greek stock and derivatives market by applying the appropriate hypothesis testing.