Dissertation Writing Help - Valuation of American Basket Options using Quasi-Monte Carlo Methods

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The valuation of American basket options is normally done by using the Monte Carlo approach. This approach can easily deal with multiple random factors which are necessary due to the high number of state variables to describe the paths of the underlying of basket options (e.g. the German Dax consists of 30 single stocks).

In low-dimensional problems the convergence of the Monte Carlo valuation can be speed up by using low-discrepancy sequences instead of pseudorandom numbers. In high-dimensional problems, which is definitely the case for American basket options, this benefit is expected to diminish. This expectation was rebutted for different financial pricing problems in recent studies. In this thesis we investigate the effect of using different quasi random sequences (Sobol, Niederreiter, Halton) for path generation and compare the results to the path generation based on pseudo-random numbers, which is used as benchmark.

American basket options incorporate two sources of high dimensionality, the underlying stocks and time to maturity. Consequently, different techniques can be used to reduce the effective dimension of the valuation problem. For the underlying stock dimension the principal component analysis (PCA) can be applied to reduce the effective dimension whereas for the time dimension the Brownian Bridge method can be used. We analyze the effect of using these techniques for effective dimension reduction on convergence behaviour.

To handle the early exercise feature of American (basket) options within the Monte Carlo framework we consider two common approaches: The Threshold approach proposed by Andersen (1999) and the Least-Squares Monte Carlo (LSM) approach suggested by Longstaff and Schwartz (2001). We investigate both pricing methods for the valuation of American (basket) options in the equity market.