Accuracy of Premium Calculation Models for CAT Bonds - An Empirical Analysis (original) (raw)
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Analysis of Risk Premium Determinants on Cat Bonds
Procedia Economics and Finance, 2015
This paper presents an analysis of the risk premium determinants on catastrophe bonds (cat bonds). Firstly, from a theoretical point of view, the existing models used for determining the level of risk premiums will be presented through a comparative analysis. Then, through an empirical approach we'll present our results by taking into consideration cat bonds covering earthquake risk issued during 1999-2012. The first model shows the existing relationship between the expected losses of the company that requires coverage through an alternative risk transfer instrument such as cat bonds and the level of risk premium. By estimating our model in different conditions, taking as parameters the location and the frequency of the events, the fluctuations of risk premiums can be observed. In case of cat bonds covering USA earthquakes the risk premium is greater than those covering Japan earthquakes. Through the second model we aim to observe the determinants that influence risk premium. The explanatory variables taken into consideration are: the issuing amount, the probability of event occurrence, conditional expected loss, the probability of exhaustion, maturity, the rating and the trigger type of each bond. The results show that the probability of event occurrence and credit rating of the bond are significant determinants of risk premium, being considered by the investors when they decide to diversify their portfolio through financial instruments that are not affected by the volatility from financial markets. These results are mostly consistent with existing theoretical models but can also be observed certain differences which will be discussed. The moment when investors start to lose money is perceived more serious than the amount they will lose. As regards the rating, it offers information about the quality of the bond. Given the importance of this risk premium determinant we'll also present the main factors considered by the rating agencies in the moment of setting a certain rating for a cat bond.
A simple robust model for Cat bond valuation
Finance Research Letters, 2010
This note provides a simple closed form solution for valuing Cat bonds. The formula is consistent with any arbitrage-free model for the evolution of the Libor term structure of interest rates. The crucial inputs to the valuation formula are the likelihood of the catastrophe event, per unit time, and the percentage loss rate realized if an event occurs. The pricing methodology is based on the reduced form models used to price credit derivatives.
Pricing Cat Bonds: Regressions and Machine Learning -Some observations, some lessons
Pricing financial assets or liabilities is hard. A variety of mechanisms-rational analysis, auctions, surveys or just gut instinct-are used, and market participants become adept at setting those prices or they fail at their business. Academics on the other hand have the more analytic task of "explaining" the factors that determine those prices post-auction. The most common weapon for that analysis is statistical regression. Indeed, most economic empirical research involves regression. And, under the most desirable of outcomes a good "explanation" can lead to good "prediction".
Pricing Default-Risky CAT Bonds With Moral Hazard and Basis Risk
Journal of Risk & Insurance, 2002
This article develops a contingent claim model to price a default-risky, catastrophe-linked bond. This model incorporates stochastic interest rates and more generic loss processes and allows for practical considerations of moral hazard, basis risk, and default risk. The authors compute default-free and default-risky CAT bond prices by using the Monte Carlo method. The results show that both moral hazard and basis risk drive down the bond prices substantially; these effects should not be ignored in pricing the CAT bonds. The authors also show how the bond prices are related to catastrophe occurrence intensity, loss volatility, trigger level, the issuing firm's capital position, debt structure, and interest rate uncertainty.
CAT Bond Spreads via HARA Utility and Nonparametric Tests
The Journal of Fixed Income
Previous empirical studies on catastrophe (CAT) bond premiums rely mostly on actuarial models, and usually compare their accuracy in terms of in-sample fit and out-of-sample predictive power. After deriving a utility-based specification for pricing CAT bonds under Hyperbolic Absolute Risk Aversion (HARA), we propose two specification tests that use nonparametric estimation techniques to test simultaneously for all possible mis-specifications. Existing pricing models with our new one are then estimated and tested with data from the primary market for CAT bonds. Our results suggest that the utility-based model we propose not only is well-suited for explaining the risk-return relationship observed in the CAT bond market but also delivers the best performance among the tested models. We also provide new empirical evidence that the aggregate utility function of CAT investors exhibits decreasing absolute risk aversion.
A general class of distortion operators for pricing contingent claims with applications to CAT bonds
Scandinavian Actuarial Journal
The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the Wang (2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g., skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.
A Model of Implied Expected Bond Returns
We propose, analyze, and implement a model for the estimation of expected bond returns (EBR) based on a discrete time Markov process of rating transition. We use US corporate bond transaction data and a rating agency transition matrix to extract the term structure of EBR. We propose a modified breakdown of the risky bond yield to its components; show that EBR includes a certainty equivalence premium which is related to the CAPM. To facilitate the analysis we present a simplified model of EBR and analyze it. We describe some early results of the properties of this EBR model and outline our plans to explore its applicability in research and practice for bond yield related topics such as credit risk, liquidity premium, and implied recovery rates.
2015
This paper develops a simple arbitrage approach to valuing insurance-linked securities, which ac-counts for catastrophic events and interest rate randomness, notwithstanding a framework of non-traded underlyings. It shows that holders of catastrophe bonds are in a short position on one-touch binary options based upon risk-tracking indexes that obey jump-diffusion processes. Using first-passage time distribu-tions, this contribution provides a closed-form valuation expression in the context of pure crashes, while it resorts to numerical simulations in the case of mid-range catastrophes. Comparative statics results point out that the term structure of yield spreads of catastrophe bonds is hump-shaped as for corporate bonds.
QMC techniques for CAT bond pricing *
Monte Carlo Methods and Applications, 2000
Pricing of catastrophe bonds leads to integrals with discontinuous and formally infinite-dimensional integrands. We investigate the suitability of Quasi-Monte Carlo methods for the numerical evaluation of these integrals and develop several variance-reduction algorithms. Furthermore, the performance of Quasi-Monte Carlo sequences for asymptotically efficient rare event simulation is examined. Various numerical illustrations are given.
The valuation of catastrophe bonds with exposure to currency exchange risk
International Review of Financial Analysis, 2014
In this paper, we present a new model that takes an arbitrage approach to the valuation of catastrophic risk bonds (CAT bonds). The model considers the sponsor's exposure to currency exchange risk and the risk of catastrophic events. We use a jump-diffusion process for catastrophic events, a three-dimensional stochastic process for the exchange rate and domestic and foreign interest rates, and a hedging cost for the currency risk to derive a semi-closed-form formula for the CAT bond price. We also extend to three factors Joshi and Leung's (2007) Monte Carlo simulation approach to obtain numerical results showing the following: in addition to catastrophic risk, the CAT bond price is affected mainly by the volatility of the exchange rate and its correlations with domestic and foreign interest rates. The first two factors have a negative impact while the third has a positive impact.