Valuing catastrophe bonds involving correlation and CIR interest rate model
- Systems Research Institute Polish Academy of Sciences (Poland)
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.
- OSTI ID:
- 22769383
- Journal Information:
- Computational and Applied Mathematics, Vol. 37, Issue 1; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Article Copyright (c) 2016 The Author(s); Country of input: International Atomic Energy Agency (IAEA); ISSN 0101-8205
- Country of Publication:
- United States
- Language:
- English
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