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Decisions in Economics and Finance

Erschienen in:

02.03.2020

Pricing and hedging defaultable participating contracts with regime switching and jump risk

verfasst von: Olivier Le Courtois, François Quittard-Pinon, Xiaoshan Su

Erschienen in: Decisions in Economics and Finance | Ausgabe 1/2020

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Abstract

This paper develops a transform-based approach for the pricing of participating life insurance contracts with a constant or floating guaranteed rate. Our analysis incorporates credit, market (jump), and economic (regime switching) risks, where the evolution of the reference portfolio is described by a regime switching double exponential jump-diffusion model. We provide semi-analytical formulas for the contract value by using a Laplace or Laplace–Fourier transform that involves matrix Wiener–Hopf factors. Then, the price is obtained by implementing the matrix Wiener–Hopf factorization and by performing a numerical Laplace and Fourier inversion. By comparing the results with Monte Carlo simulations, we show that our pricing method is easy to implement and accurate. We also show that the contract with a floating guaranteed rate is riskier but more profitable than the contract with a constant guaranteed rate. Two hedging strategies are introduced to hedge jump and regime switching risks in the participating contracts.

Vorheriger Artikel Trading strategy with stochastic volatility in a limit order book market

Nächster Artikel Optimal reinsurance and investment in a diffusion model

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Our Matlab computations are launched on a PC with an Intel Core i5 endowed with 2 CPUs and running at 2.9 GHz and with 8 GB of RAM. The computation time for obtaining one price with our method is only about 0.3 minute, while the simulation method takes about 30 minutes to generate one value.

The computation time for obtaining one price is again close to 0.3 min within our approach, whereas simulations with 10,000 time steps and 100,000 sample paths take about 30 min.

Note that the default probabilities that are computed here are derived in the risk-neutral world. These default probabilities can differ by an important order of magnitude from the default probabilities that are computed in the historical world and that are useful for risk management purposes. For a broader and more technical discussion of this question, please see Le Courtois and Quittard-Pinon (2006).

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Titel: Pricing and hedging defaultable participating contracts with regime switching and jump risk
verfasst von: Olivier Le Courtois
François Quittard-Pinon
Xiaoshan Su
Publikationsdatum: 02.03.2020
Verlag: Springer International Publishing
Erschienen in: Decisions in Economics and Finance / Ausgabe 1/2020
Print ISSN: 1593-8883
Elektronische ISSN: 1129-6569
DOI: https://doi.org/10.1007/s10203-020-00276-w

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