Risk managing bermudan swaptions in the libor BGM model

This article presents a novel approach for calculating swap vegaper bucket in the Libor BGM model. We show that for some forms of thevolatility an approach based on re-calibration may lead to a large uncertaintyin estimated swap vega, as the instantaneous volatility structure maybe distorted by re-calibration. This does not happen in the case of constantswap rate volatility. We then derive an alternative approach, not based onre-calibration, by comparison with the swap market model. The strength ofthe method is that it accurately estimates vegas for any volatility functionand at a low number of simulation paths. The key to the method is thatthe perturbation in the Libor volatility is distributed in a clear, stable andwell understood fashion, whereas in the re-calibration method the change involatility is hidden and potentially unstable.risk management;libor BGM model;central interest rate model;bermudan swaptions;swap market model

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

A Comparison of Single Factor Markov-Functional and Multi Factor Market Models

We compare single factor Markov-functional and multi factor market models for hedging performance of Bermudan swaptions. We show that hedging performance of both models is comparable, thereby supporting the claim that Bermudan swaptions can be adequately riskmanaged with single factor models. Moreover, we show that the impact of smile can be much larger than the impact of correlation. We propose a new method for calculating risk sensitivities of callable products in market models, which is a modification of the least-squares Monte Carlo method. The hedge results show that this new method enables proper functioning of market models as risk-management tools

Level-Slope-Curvature - Fact or Artefact?

The first three factors resulting from a principal components analysis of term structure data are in the literature typically interpreted as driving the level, slope and curvature of the term structure. Using slight generalisations of theorems from total positivity, we present sufficient conditions under which level, slope and curvature are present. These conditions have the nice interpretation of restricting the level, slope and curvature of the correlation surface. It is proven that the Schoenmakers-Coffey correlation matrix also brings along such factors. Finally, we formulate and corroborate our conjecture that the order present in correlation matrices causes slope

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

Time-consistent actuarial valuations

Time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. This method is applied to an insurance risk process in the form of a diffusion process and a jump process in order to capture the heavy tailed nature of insurance liabilities. We show that in the case of the diffusion process, the one-period time-consistent Variance premium principle converges to the non-linear exponential indifference price. Furthermore, we show that the Standard-Deviation and the Cost-of-Capital principle converge to the same price limit. Adding the jump risk gives a more realistic picture of the price. Furthermore, we no longer observe that the different premium principles converge to the same limit since each principle reflects the effect of the jump differently. In the Cost-of-Capital principle, in particular the VaRVaR operator fails to capture the jump risk for small jump probabilities, and the time-consistent price depends on the distribution of the premium jump

Advies Commissie Parameters 2022

Onderzoek van de Commissie Parameters 2022 naar de parameters, UFR-methode en economische en risico-neutrale scenario’s. Deze moeten worden gehanteerd bij diverse wettelijke toepassingen in zowel het huidige pensioenstelsel als in het nieuwe pensioenstelsel en de transitie daarnaartoe zoals voorgesteld in de Wet toekomst pensioenen