A closed-form exact solution for pricing fixed-income variance swaps with affine-jump model

Shaoyu Li, Yuanyuan Zhang and Chunhui Zhu

The North American Journal of Economics and Finance, 2021, vol. 58, issue C

Abstract: Fixed-income variance swaps became popular for investors to trade and hedge the fluctuation of interest rates after the recent global financial crisis over the past few decades, however, their valuations and risk management have not been studied sufficiently. This paper presents an analytic approach for pricing some discretely sampled fixed-income variance swaps under an affine-jump model with stochastic mean, stochastic volatility, and jumps. We employ a generalized characteristic function to derive the closed-form pricing formulas of these swaps, including two kinds of zero-coupon bond variance swap, Libor variance swap, and bond yield variance swap, to be precise. We also perform some numerical studies based on these models, which suggest that the fair strike values of these variance swaps are within a reasonable range regardless of estimation risk with data dependence and near-zero short rate regime. Our numerics show that the influences of varying sampling frequency and time-to-maturity on the values of these swaps are significant, and highlight the risks of specifying short rate model. Furthermore, the sensitivity analysis on the key parameters finds that the risks of stochastic volatility and jumps play prominent roles in pricing these variance swaps under the near-zero short rate regime.

Keywords: Affine model; Fix-income variance swaps; Closed-form solution; Stochastic volatility; Jumps (search for similar items in EconPapers)
JEL-codes: C32 C63 G13 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecofin:v:58:y:2021:i:c:s1062940821001479

DOI: 10.1016/j.najef.2021.101532

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