Master of Science
Statistics and Actuarial Sciences
Reesor, Mark R.
Wilfrid Laurier University
Since Longstaff and Schwartz  brought the amazing Regression-based Monte Carlo (LSMC) method in pricing American options, it has received heated discussion. Based on the research done by Fabozzi et al.  that applies the heteroscedasticity correction method to LSMC, we further extend the study by introducing the methods from Park  and Harvey . Our work shows that for a single stock American Call option modelled by GBM with two exercise opportunities, WLSMC or IRLSMC provides better estimates in continuation value than LSMC. However, they do not lead to better exercise decisions and hence have little to no effect on option price estimates. Our work finally indicates that in terms of real-life options pricing modelled by univariate GBM, bivariate GBM, and univariate GARCH, WLSMC or IRLSMC are not effective at producing more efficient price estimates .
Key Words: [LSMC, Regression, Heteroscedasticity Correction].
Summary for Lay Audience
As financial derivatives commonly trade in the market, options and their pricing have a long history. Back in the time when the computational power is weak, people do replicate portfolios to treat the price of an option as a combination of risk-free and risky assets. However, after the development of computational techniques and the study on continuous-time stochastic process, pricing options with certain formulas become possible.
However, there are many types of options trading in the market. The most famous two are the European option and the American option. The major difference between the two options is the European option allows option holders to exercise the option only on the maturity date while option holders can exercise the American option on any dates before maturity.
Obviously, pricing American options is tricky as the decision made by option holders to hold or exercise before maturity is unclear, and thus it has no closed-form solution. However, researchers have put a lot of effort into American options valuation techniques and come up with many fabulous ideas. The method introduced by Longstaff and Schwartz  that uses regressions (denoted as LSMC) to estimate the continuation value of American options has shown great success. As one of the most commonly used regression, ordinary least-squares requires errors to be homoscedastic. The study by Fabozzi et al.  showed heteroscedasticity exists in LSMC and suggested a method for correcting this, indicating a marginal improvement in price estimator efficiency. Here we investigate other methods to correct the heteroscedasticity in LSMC and find out to what extent the correction affects the option prices. Our work is a critical assessment of the work by Fabozzi et al. .
Zhu, Xiaotian, "An Analysis of Weighted Least Squares Monte Carlo" (2022). Electronic Thesis and Dissertation Repository. 8807.