QMC techniques for CAT bond pricing *

Albrecher, Hansjörg; Hartinger, Jürgen; Tichy, Robert F.

doi:10.1515/mcma.2004.10.3-4.197

Cited by 14 publications

(10 citation statements)

References 22 publications

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“…We model all terms in discrete time. 2 The simulation starts at time t = 0 and ends at time t = T . The time interval [0, T ] is decomposed into K periods [t k−1 , t k ] with t k = k ∆t and period length ∆t = T /K.…”

Section: Overall Model Structurementioning

confidence: 99%

“…One the other hand, numerical experiments showed that QMC methods are faster and more accurate than MC for certain financial problems even in hundreds of dimensions, like the pricing of bonds [32], options [1] and mortgage backed securities [11,37], the valuation of catastrophe bonds [2] and the computation of the value at risk of asset portfolios [36]. Similar results have been observed for the SG methods, which were applied successfully to the valuation of performancedependent options [17], the pricing of mortgage backed securities [14,15] and to likelihood estimation [23].…”

Section: Impact Of the Dimensionmentioning

confidence: 99%

“…Examples are the pricing of bonds [2,32], options [1,17] and mortgage backed securities [11,14,15,37]. To our knowledge, it is so far not known if deterministic methods can also be successfully applied to ALM simulations.…”

Section: Introductionmentioning

confidence: 99%

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Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance

Gerstner¹,

Griebel²,

Holtz³

2009

Insurance: Mathematics and Economics

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Section: Overall Model Structurementioning

confidence: 99%

Section: Impact Of the Dimensionmentioning

confidence: 99%

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Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance

Gerstner¹,

Griebel²,

Holtz³

2009

Insurance: Mathematics and Economics

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“…In turn, the approach from Burnecki et al (2003) is applied in Härdle and Lopez (2010) for the cat bonds connected with earthquakes in Mexico. In Albrecher et al (2004) the doubly stochastic compound Poisson process is used and reporting lags of the occurred claims are incorporated to the model. The model behavior is analyzed with application of QMC algorithms.…”

Section: Introductionmentioning

confidence: 99%

Valuing catastrophe bonds involving correlation and CIR interest rate model

Nowak

Romaniuk

2016

Comp. Appl. Math.

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Natural catastrophes lead to problems of insurance and reinsurance industry. Classic insurance mechanisms are often inadequate for dealing with consequences of catastrophic events. Therefore, new financial instruments, including catastrophe bonds (cat bonds), were developed. In this paper we price the catastrophe bonds with a generalized payoff structure, assuming that the bondholder's payoff depends on an underlying asset driven by a stochastic jump-diffusion process. Simultaneously, the risk-free spot interest rate has also a stochastic form and is described by the multi-factor Cox-Ingersoll-Ross model. We assume the possibility of correlation between the Brownian part of the underlying asset and the components of the interest rate model. Using stochastic methods, we prove the valuation formula, which can be applied to the cat bonds with various payoff functions. We use adaptive Monte Carlo simulations to analyze the numerical properties of the obtained pricing formula for various settings, including some similar to the practical cases.

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“…[3]), the pricing of stop-loss reinsurance contracts or the valuation of catastrophe risk bonds within a collective risk model (e.g. [1]). Due to the fact that closed-form solutions in general are unavailable for this kind of problems and naive Monte Carlo methods typically perform rather poor when u is large, there was a great amount of effort to construct suitable Monte Carlo estimators throughout the last decade.…”

Section: Introductionmentioning

confidence: 99%