Pricing and hedging bond options and sinking-fund bonds under the CIR model

Manuela Larguinho; José Carlos Dias; Carlos A. Braumann; Manuela Larguinho; José Carlos Dias; Carlos A. Braumann

doi:10.3934/QFE.2022001

Quantitative Finance and Economics

2022, Volume 6, Issue 1: 1-34. doi: 10.3934/QFE.2022001

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Research article

Pricing and hedging bond options and sinking-fund bonds under the CIR model

1.
Polytechnic of Coimbra, Coimbra Business School Research Centre — ISCAC, Coimbra, Portugal
2.
Centro de Investigação em Matemática e Aplicações, Instituto de Investigação e Formação Avançada, Universidade de Évora, Évora, Portugal
3.
Iscte - Instituto Universitário de Lisboa, Lisbon, Portugal
4.
Business Research Unit (BRU-IUL), Lisbon, Portugal
5.
Departamento de Matemática, Escola de Ciências e Tecnologia, Universidade de Évora, Évora, Portugal

Received: 27 November 2021 Revised: 13 December 2021 Accepted: 04 January 2022 Published: 10 January 2022
JEL Codes: G12, G13

This article derives simple closed-form solutions for computing Greeks of zero-coupon and coupon-bearing bond options under the CIR interest rate model, which are shown to be accurate, easy to implement, and computationally highly efficient. These novel analytical solutions allow us to extend the literature in two other directions. First, the static hedging portfolio approach is used for pricing and hedging American-style plain-vanilla zero-coupon bond options under the CIR model. Second, we derive analytically the comparative static properties of sinking-fund bonds under the same interest rate modeling setup.
- CIR model,
- bond options,
- Greeks,
- American options,
- static hedging,
- sinking-fund bonds
Citation: Manuela Larguinho, José Carlos Dias, Carlos A. Braumann. Pricing and hedging bond options and sinking-fund bonds under the CIR model[J]. Quantitative Finance and Economics, 2022, 6(1): 1-34. doi: 10.3934/QFE.2022001

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Abstract

This article derives simple closed-form solutions for computing Greeks of zero-coupon and coupon-bearing bond options under the CIR interest rate model, which are shown to be accurate, easy to implement, and computationally highly efficient. These novel analytical solutions allow us to extend the literature in two other directions. First, the static hedging portfolio approach is used for pricing and hedging American-style plain-vanilla zero-coupon bond options under the CIR model. Second, we derive analytically the comparative static properties of sinking-fund bonds under the same interest rate modeling setup.

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