My diploma thesis which I wrote under the supervision of Prof.
Teichmann in the summer term 2007/2008 covers the pricing of American options by simulation. This diploma thesis is based on a paper from L.C.G. Rogers (2002). In his paper he investigates a new approach using Monte Carlo techniques. He makes no attempt to determine an approximate exercise policy, but instead gives an upper bound for the true price.
The payoff of an American option depends in a highly complex path-dependent fashion on many underlyings, which means that the computing of the value and the optimal exercise is very difficult.
The overwhelming majority of traded options are of American style. In general it is not possible to find explicit formulae for American option prices, and numerical techniques or approximation schemes are required for option evaluation. For pricing European style derivatives simulation has been used extensively, but for American style claims there have been only a few attempts to use simulation techniques for pricing. The problem lies in the estimation of the exercise boundary; the Monte Carlo method entails the simulation of the evolution of the asset prices forward in time, but the determination of the optimal exercise policy requires a backward style algorithm. Monte Carlo simulation is the most popular approach in computational finance for determining the price of financial options. The accurate calculation of prices is only one objective of Monte Carlo simulation.