Monte-Carlo Based Pricing of American Options Using Known Characteristics of the Expected Continuation Value Function

Sammanfattning: The problem of pricing American stock options is far more complex than pricing European options due to the possibility of early execution. This feature means that the decision to either hold on to the option or exercising it early must be continually evaluated, leading to closed form solutions such as the Black-Scholes Formula to not be applicable on American options written on dividend paying assets. In 2001, F. Longstaff and E. Schwartz developed a Monte Carlo-based pricing algorithm to handle this. The algorithm simulates a large number of stock price trajectories, evaluates the value of early exercise versus the expected value of holding on to the option using polynomial regression of the continuation value function at each time step and then values the option based on the optimal exercise times. However, this method does not utilize some known characteristics of the expected continuation value function such as convexity, non-negativity, an absolute value of its derivative not greater than 1, and decreasing or increasing depending on the option type. The aim of this thesis is to utilize these characteristics in the regression of the expected continuation value. Four different stock dynamic models are used to simulate the stock price trajectories - Black-Scholes, Merton Jump Diffusion, Finite Moment Log Stable and Heston dynamics. The model parameters are fitted to the market using non-linear least squares optimization. The pricing algorithm resulted in somewhat improved results, with estimates placed within the bid-ask spreads 39.2% of the time using the constraints compared to 35.8% without. The Finite Moment Log Stable stock dynamics performed best with an overall pricing accuracy of 54.9%. Finally, put options were overall more accurately priced than calls, possibly due to constant deterministic interest rates and computational complexities.