Risk Managing Bermudan Swaptions in the Libor BGM Model

This article presents a novel approach for calculating swap vega per bucket in the Libor BGM model. We show that for some forms of the volatility an approach based on re-calibration may lead to a large uncertainty in estimated swap vega, as the instantaneous volatility structure may be distorted by re-calibration. This does not happen in the case of constant swap rate volatility. We then derive an alternative approach, not based on re-calibration, by comparison with the swap market model. The strength of the method is that it accurately estimates vegas for any volatility function and at a low number of simulation paths. The key to the method is that the perturbation in the Libor volatility is distributed in a clear, stable and well understood fashion, whereas in the re-calibration method the change in volatility is hidden and potentially unstable.central interest rate model, Libor BGM model, swaption vega, risk management, swap market model, Bermudan swaption

Approximation solutions for indifference pricing under general utility functions

With the aid of Taylor-based approximations, this paper presents results for pricing insurance contracts by using indifference pricing under general utility functions. We discuss the connection between the resulting "theoretical" indifference prices and the pricing rule-of-thumb that practitioners use: Best Estimate plus a "Market Value Margin". Furthermore, we compare our approximations to known analytical results for exponential and power utility

Risico en Rendement in Balans voor Verzekeraars

Antoon Pelsser (1968) is Head of the Asset-Liability Matching department of ING-Insurance. The ALM department advises the board on the optimal asset allocation to cover the insurance liabilities. The department is also responsible for the calculation of market values and risk measures of insurance contracts. He also holds a part-time position as Professor of Mathematical Finance at the Econometric Institute at the Erasmus University in Rotterdam. His research interests focus on pricing models for interest rate derivatives, the pricing of insurance contracts and Asset-Liability Management of insurance contracts. He has published in several academic journals including Finance and Stochastics, Journal of Derivatives, European Journal of Operational Research and European Finance Review. He is also author of the book Efficient Methods for Valuing Interest Rate Derivatives, published by Springer Verlag.In this inaugural address Professor Pelsser investigates how one can strike a balance between investmens with a high expected return and high risk (e.g. stocks) versus low-risk investments with a low return (e.g.bonds). Using an example of a life-insurance company he shows in this address how one can employ optimisation-techniques to make a trade-off between the desire to find an investment return as high as possible under the constraint that the insurance company should be able to meet its obligations to the policyholders under all economic circumstances

Pricing and Hedging Guaranteed Annuity Options via Static Option Replication

In this paper we derive a market value for Guaranteed Annuity Option using martingale modeling techniques. Furthermore, we show how to construct a static replicating portfolio of vanilla interest rate swaptions that replicates the Guaranteed Annuity Option. Finally, we illustrate with historical UK interest rate data from the period 1980 until 2000 that the static replicating portfolio is extremely effective as a hedge against the interest rate risk involved in the GAO, that the static replicating portfolio is considerably cheaper than up-front reserving and also that the replicating portfolio provides a much better level of protection than an up-front reserve

Fast drift approximated pricing in the BGM model

This paper shows that the forward rates process discretized by a single time step together with a separability assumption on the volatility function allows for representation by a low-dimensional Markov process. This in turn leads to e±cient pricing by for example finite differences. We then develop a discretization based on the Brownian bridge especially designed to have high accuracy for single time stepping. The scheme is proven to converge weakly with order 1. We compare the single time step method for pricing on a grid with multi step Monte Carlo simulation for a Bermudan swaption, reporting a computational speed increase of a factor 10, yet pricing sufficiently accurate.BGM model, predictor-corrector, Brownian bridge, Markov processes, separability, Feynman-Kac, Bermudan swaption