Description: We consider Libor market model and calibration process. We estimate some interest rate derivatives such as Caps and Swaptions. We use Monte Carlo methods with appropriate dynamics under spot measure and forward measure. Imposing martingale discretization property, the same quantities are estimated again to see a contrast or discrepancy in light of confidence interval. Based on algorithms discussed in the paper, “Arbitrage-free discretizations of lognormal forward Libor and swap rate models” by Glasserman, P and Zhao, X 2000, the algorithms are implemented in excel VBA. Starting with current market data such as FRAs and Bond Prices, we describe steps involved to estimate the price of interest rate derivatives such as Caps and Swaptions, which would be beneficial to the practitioners in the industry.

Description: In December 2007, Goldman Sachs launched a product called QxX index swap, which is designed to allow market participants to hedge or gain exposure to longevity and mortality risks. This presentation offers a quantitative analysis of this brand new financial innovation. First of all, the presentation sets up a risk-neutral framework to price QxX index swaps. This framework, which is based on the dynamics of death rates under a two-factor stochastic mortality model in a risk-adjusted probability measure, yields prices [spreads] that are fairly close to the spreads that Goldman Sachs currently offers. The presentation then explores the uncertainty involved in this model-based pricing framework. Specifically, it studies parameter risk by using Markov Chain Monte Carlo [MCMC] and model risk by examining structural changes in mortality dynamics. The results indicate that both model risk and parameter risk are significant. Actuaries should therefore be aware of these issues when placing a value on a longevity index swap.

Description: Presented at May 1996 Spring Meeting. The investment environment has undergone significant change over the last several years through the introduction of many sophisticated investment vehicles. This session provides an update on current challenges encountered by life insurance companies in accounting for this new array of investments. Among the issues covered will be accounting for derivatives, mortgage-backed securities, and other hedging vehicles. The session also includes some of the system and projection modeling challenges encountered as a by-product of investment in these vehicles.

Description: This presentation discusses a technique to reduce the bias from using Monte Carlo simulation to value American options.

Description: Presented at June 1996 Spring Meeting. Provides overview of modern pricing of assets such as derivatives. It includes theory and practical applications, particularly how they relate to insurance companies.

Description: Presentation discussing modeling of daily and hourly rainfall, both occurrence and amount. These distributions would be needed to price derivative or insurance contracts involving rainfall amounts.