# Valuing catastrophe bonds involving correlation and CIR interest rate model

## Abstract

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.

- Authors:

- Systems Research Institute Polish Academy of Sciences (Poland)

- Publication Date:

- OSTI Identifier:
- 22769383

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal 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); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; COMPUTERIZED SIMULATION; FUNCTIONS; INTEREST RATE; MONTE CARLO METHOD; STOCHASTIC PROCESSES

### Citation Formats

```
Nowak, Piotr, and Romaniuk, Maciej.
```*Valuing catastrophe bonds involving correlation and CIR interest rate model*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0348-2.

```
Nowak, Piotr, & Romaniuk, Maciej.
```*Valuing catastrophe bonds involving correlation and CIR interest rate model*. United States. doi:10.1007/S40314-016-0348-2.

```
Nowak, Piotr, and Romaniuk, Maciej. Thu .
"Valuing catastrophe bonds involving correlation and CIR interest rate model". United States. doi:10.1007/S40314-016-0348-2.
```

```
@article{osti_22769383,
```

title = {Valuing catastrophe bonds involving correlation and CIR interest rate model},

author = {Nowak, Piotr and Romaniuk, Maciej},

abstractNote = {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.},

doi = {10.1007/S40314-016-0348-2},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 1,

volume = 37,

place = {United States},

year = {2018},

month = {3}

}