An improved least squares Monte Carlo valuation method based on heteroscedasticity

• Published in: European journal of operational research Vol. 263; no. 2; pp. 698 - 706
• Main Authors: Fabozzi, Frank J., Paletta, Tommaso, Tunaru, Radu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-12-2017
• Subjects: American options; Finance; Heteroscedasticity; Least squares Monte Carlo pricing method; Weighted least squares; American options; Weighted least squares; Finance; Least squares Monte Carlo pricing method; Heteroscedasticity
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2017.05.048

•Least square Monte Carlo algorithm assumes homoscedastic errors.•Models in finance have heteroscedastic errors that impact estimation.•We improve American option pricing by correcting for heteroscedasticity.•We demonstrate significant pricing for single-asset and multi-asset payoffs.•The new method is superior to other competing methods when using real data.
Longstaff–Schwartz’s least squares Monte Carlo method is one of the most applied numerical methods for pricing American-style derivatives. We examine the algorithms regression step, demonstrating that the OLS regression is not the best linear unbiased estimator because of heteroscedasticity. We prove the existence of heteroscedasticity for single-asset and multi-asset payoffs numerically and theoretically, and propose weighted-least squares MC valuation method to correct for it. An extensive numerical study shows that the proposed method produces significantly smaller pricing bias than the Longstaff–Schwartz method under several well-known price dynamics. An empirical pricing exercise using market data confirms the advantages of the improved method.