Pricing catastrophe risk bonds: A mixed approximation method

Ma, Zonggang; Ma, Chaoqun

doi:10.1016/j.insmatheco.2012.12.007

Cited by 58 publications

(82 citation statements)

References 42 publications

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“…The CAT bond threshold level is assumed to be in line with that used by Ma and Ma (2013) (that is D, D COUPON ∈ [3740, 44880] million), and we set T ∈ (0, 2] years, ρ = 0.5 and r = 0.06 in Equations (12) The behavior of our approximation appears to vary according to the underlying severity distributional assumption. It appears that within the realm of our numerical calculations, the closer to unity the power law exponent of the severity distribution, the less well-behaved the approximation (compared to MC estimation and the FSRLP approximation) for low threshold levels and times to maturity.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…In this paper, we considered index-linked ZC and CP CAT bonds under the pricing framework of Ma and Ma (2013). As the pricing formulae obtained under this framework were not in closed-form, we invoked a weak approximation of the ALP (assumed to be a compound renewal process) to α-stable Lévy motion.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, it is of interest to obtain an approximation to the aforementioned probability. In their index-linked CAT bond pricing framework, Ma and Ma (2013) considered a mixed approximation to this probability. However, their approximation, which relies on higher-order moments and cumulants of the loss process, was not always valid since many of their fitted severity distributions did not possess finite second-order (and higher) moments and cumulants.…”

Section: Weak Approximation Of Tail Probabilities Of Compound Renewalmentioning

confidence: 99%

“…We use the preference-free index-linked CAT bond pricing framework of Ma and Ma (2013), with the assumption of a constant interest rate. Importantly, we motivate the use of their pricing framework by the fact that we extend it to circumstances where the underlying distributions are assumed to be heavy-tailed.…”

Section: Classical Catastrophe Bond Pricingmentioning

confidence: 99%

“…Ma and Ma (2013) derived Equation (10) under a risk-neutral measure using the diversification arguments of Merton (1976). However, due to their assumption that catastrophe risk variables are measure independent, Equation (10) is consequently reflected under P. It must be noted that similar arguments, based on the work of Merton (1976), were also used recently in the context of catastrophe reinsurance contracts by Chang and Chang (2017).…”

Section: General Pricing Rulementioning

confidence: 99%

See 4 more Smart Citations

Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

Burnecki

Giuricich

2017

Risks

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Abstract:We consider the subject of approximating tail probabilities in the general compound renewal process framework, where severity data are assumed to follow a heavy-tailed law (in that only the first moment is assumed to exist). By using the weak convergence of compound renewal processes to α-stable Lévy motion, we derive such weak approximations. Their applicability is then highlighted in the context of an existing, classical, index-linked catastrophe bond pricing model, and in doing so, we specialize these approximations to the case of a compound time-inhomogeneous Poisson process. We emphasize a unique feature of our approximation, in that it only demands finiteness of the first moment of the aggregate loss processes. Finally, a numerical illustration is presented. The behavior of our approximations is compared to both Monte Carlo simulations and first-order single risk loss process approximations and compares favorably.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Weak Approximation Of Tail Probabilities Of Compound Renewalmentioning

confidence: 99%

Section: Classical Catastrophe Bond Pricingmentioning

confidence: 99%

Section: General Pricing Rulementioning

confidence: 99%

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Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

Burnecki

Giuricich

2017

Risks

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Sensitivity Analysis of Catastrophe Bond Price Under the Hull–White Interest Rate Model

Malyarenko

Röman

Schyberg

2016

Springer Proceedings in Mathematics &Amp; Statistics

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A stochastic exposure model for seismic risk assessment and pricing of catastrophe bonds

Mistry

Lombardi

2023

Nat Hazards

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Risk-based catastrophe bonds require the estimation of losses from the convolution of hazard, exposure and vulnerability models. These models are affected by different uncertainties that arise from the definition of their input parameters. In this paper, we propose a stochastic approach to treat the uncertainty in the asset location and attributes of the exposure model. The proposed method uses the Monte Carlo sampling approach to generate a stochastic exposure database, where each asset location is generated randomly within the geometric bound of the administration, while the asset attributes (i.e. construction type and material, number of storey, building activity type and number of dwelling) are sampled from distributions built from census data. Finally, a sensitivity analysis is performed to investigate the influence of the spatial resolution of the exposure model on the average annual losses (AAL) and catastrophe bond prices. To this end, we implement four exposure models, with spatial resolution at the asset, municipality and province levels, on a study region comprising ten provinces in southern Italy. Compared to the proposed model, the exposure model where assets are relocated and aggregated at the geometric centroid of the municipality underestimates AAL by $$8\%$$ 8 % , while a higher difference (up to $$20\%$$ 20 % ) is observed for the exposure model where assets are relocated and aggregated at the geometric centroid of the province. We also consider an exposure model whose asset locations are extracted from publicly available building footprints. Yet, this latter model was incomplete for some provinces resulting in underestimation of AAL up to $$90\%$$ 90 % . Differences in catastrophe bond prices obtained from the four exposure models are less evident, with the exposure model built based on the building footprints showing a difference up to $$9.5\%$$ 9.5 % .

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Pricing catastrophe risk bonds: A mixed approximation method

Cited by 58 publications

References 42 publications

Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

Stable Weak Approximation at Work in Index-Linked Catastrophe Bond Pricing

Sensitivity Analysis of Catastrophe Bond Price Under the Hull–White Interest Rate Model

A stochastic exposure model for seismic risk assessment and pricing of catastrophe bonds

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