Description: This article explores the effectiveness of hedging delta and rho of equity options. This provides insight into the frequency and severity of losses due to not hedging volatility risk or other higher order risks. 10yr-equity put option strategies were chosen to represent the risk of hedging guaranteed benefits attached to variable annuities, while 1-yr put and call strategies were modeled to investigate the risk of hedging equity index interest credited to fixed indexed annuities. In both cases, the value of the option was compared to the value of delta/rho hedges in the tail of both actual historical and simulated scenarios for equity returns and volatilities. The historical path of interest rates and equities was generally used to highlight the hedge impact for different implied volatility assumptions in each example.

Description: What is going on with the exchange rate, anyway? In 2002, $1 U.S. bought $C 1.60, and now in May 2005 you only get $C 1.25—that’s 20 percent less! Where’s it going next? One way to answer that question is with a time series model.

Description: By necessity, attributions of financial processes require approximations. Tools used for approximations include Aumann-Shapley, time step, step-through, average step-through, partial derivative, and average partial derivative. Significantly non-linear paths can cause problems during attribution. Time (theta) and market factors must be handled concurrently. Typically contractual factors can be handled separately. Average Step-Through, Aumann-Shapley and Aumann-Shapley-3 points perform the best given the same time period. Attribution should be done with fairly small time steps as opposed to using a lot of points in the Aumann-Shapley calculation, but using Aumann-Shapley-3 points as a last step has some advantages.

Description: The article discusses that drawbacks of the HJM Heath-Jarrow-Morton class of stochastic interest models and suggests the use of the Longstaff-Schwartz string model. It describes the use and benefits of the Lonstaff-Schwartz string model.

Description: Discussion of significant anomalies in option pricing due to the independent identically distributed assumption of the Black Scholes formula.

Description: “Many commentators have suggested that firms need to do stress tests to examine their vulnerability to adverse situations that are not within the data set used to parameterize their risk models. We suggest the adop¬tion of a terminology to describe stress tests and also a meth¬odology that can be adopted by any risk model user to test and communicate a test of the stability of model results.”

Description: As stochastic modeling has evolved, it has divided down two paths—real-world and risk-neutral. This article discusses this division and shows how these paths may be re-united through the use of deflators.

Description: In 2003, the American Academy of Actuaries Life Capital Adequacy Subcommittee LCAS published a set of 10,000 stochastic scenarios that was intended to be used to support the publication, “Recommended Approach for Setting Regulatory Risk-Based Capital Requirements for Variable Products with Guarantees Excluding Index Guarantees.” The primary purpose of this article is to illustrate statistical measures that can be used to evaluate stochastic simulations.

Description: Derives appropriate hedge ratios for CPPI strategies, taking into account discrete hedge times and market dislocations (gap risk).

Description: This article discusses asset-liability management from two different paradigms, one a simulation of the firm as an external observer e.g. shareholder would view it, and the other a “still life” at a given moment from an internal viewpoint.