A closed-form exact solution for pricing fixed-income variance swaps with affine-jump model |
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Affiliation: | 1. Institute of Business and Management, National Yang Ming Chiao Tung University, 118 Chung-Hsiao West Road, Section 1, Taipei, Taiwan;2. Graduate Institute of Finance, National Taiwan University of Science and Technology, 43, Keelung Rd., Section 4, Taipei, Taiwan;3. Center for General Education, Chung Yuan Christian University, 200 Chung Pei Road, Chung Li District, Taoyuan City, Taiwan;4. Science and Technology Policy Research and Information Center, National Applied Research Laboratories, 106 Heping East Road, Section 2, Taipei, Taiwan;5. Power Generation Division, Taiwan Power Company, 242, Roosevelt Road, Section 3, Taipei, Taiwan;1. Graduate Program in Economics, Federal University of Santa Catarina, 88049-970 Florianopolis S.C., Brazil;2. Department of Economics, Federal University of Santa Catarina, 88049-970 Florianopolis S.C., Brazil;3. Department of Statistics, University of Brasilia, 70910-900 Brasilia, D.F., Brazil;4. Graduate Program in Business Administration, University of Brasilia, 70910-900 Brasilia D.F., Brazil;5. Graduate Program in Economics, Federal University of Espirito Santo, 29075-910 Vitoria E.S., Brazil |
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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. |
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Keywords: | Affine model Fix-income variance swaps Closed-form solution Stochastic volatility Jumps |
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