Description: In this paper, we illustrate how to value American-style options using the Least-Squares Monte Carlo LSM approach proposed by Longstaff and Schwartz 2001 and investigate whether there exists an optimal regression complexity in the LSM framework for options pricing. In particular, we use the smoothing spline in the regression step, which allows us to control the regression complexity on a continuous scale with just one tuning parameter. Numerical results on American put options indicate that we need to use more than a linear regression, but as the regression becomes more complex, the accuracy of the LSM method quickly deteriorates. From 39th Actuarial Research Conference.

Description: This article, with some humor, describes a movement known as “econophysics” of physicists modeling economic systems, including capital markets, using techniques and concepts developed in studying the out-of-equilibrium dynamics of complex systems. A version of this article appeared in The Actuary UK in August 2004. Reprinted with permission.

Description: This article considers considers how the assumptions and statistical methods used to analyze investments are likely to change as a result of the events of Black Monday, October 19, 1987.

Description: This paper discusses the theoretic framework of modeling captial markets: index-based composition methodology and statisical procedure of model construction and extension: wavelets-based financial signal processing technique. It also discusses the implications and applications, measuring the market uncertainty and volatility highlighting the S&P 500 as an example.

Description: This article focuses on one fundamental modeling assumption — the choice of a benchmark rate or risk-free rate. The author looks at this bond market assumption as a case study of how one needs to monitor fundamental market changes for their impact on assumptions.

Description: This article introduces the reader to probabilistic methods used to model interactions in the financial market place. Three topics are specifically discussed, two concern modeling methods and the other concerns data analysis methods.