The effect of jumps and discrete sampling on volatility and variance swaps. (English) Zbl 1180.91283
This paper studies the pricing of variance and volatility swaps in four financial models. More specifically, the authors derive analytical formulas for fair discrete variance strikes in the Black-Scholes, Heston stochastic volatility, Merton jump-diffusion and Bates and Scott stochastic volatility with jumps models.
The authors study the effect of discrete sampling and jumps on variance strikes with the latter depending on direction and magnitude of jumps. Furthermore, the paper demonstrates that the convexity correction formula to approximate fair volatility strikes does not provide suitable estimates in jump-diffusion models. Such volatility strikes are computed by numerical means.
Finally, the authors demonstrate that all the aforementioned models, fair discrete variance and volatility strikes converge in a linear manner to fair continuous variance and volatility strikes, respectively.
Reviewer’s remark: The paper is well-written and of interest to experts in both discrete sampling as well as volatility and variance swaps.
The authors study the effect of discrete sampling and jumps on variance strikes with the latter depending on direction and magnitude of jumps. Furthermore, the paper demonstrates that the convexity correction formula to approximate fair volatility strikes does not provide suitable estimates in jump-diffusion models. Such volatility strikes are computed by numerical means.
Finally, the authors demonstrate that all the aforementioned models, fair discrete variance and volatility strikes converge in a linear manner to fair continuous variance and volatility strikes, respectively.
Reviewer’s remark: The paper is well-written and of interest to experts in both discrete sampling as well as volatility and variance swaps.
Reviewer: Mark A. Petersen (Potchefstroom)
MSC:
91G20 | Derivative securities (option pricing, hedging, etc.) |
91G80 | Financial applications of other theories |
91G60 | Numerical methods (including Monte Carlo methods) |
References:
[1] | DOI: 10.1093/rfs/9.1.69 · doi:10.1093/rfs/9.1.69 |
[2] | DOI: 10.3905/jod.2008.702503 · doi:10.3905/jod.2008.702503 |
[3] | Brockhaus O., Risk 19 pp 92– |
[4] | DOI: 10.1007/s00780-006-0008-2 · Zbl 1101.91031 · doi:10.1007/s00780-006-0008-2 |
[5] | Cairns A., Interest Rate Models: An Introduction (2000) · Zbl 1140.91039 |
[6] | DOI: 10.1007/s00780-005-0155-x · Zbl 1096.91022 · doi:10.1007/s00780-005-0155-x |
[7] | DOI: 10.3905/jod.2006.616865 · doi:10.3905/jod.2006.616865 |
[8] | Demeterfi K., Journal of Derivatives 4 pp 9– |
[9] | Derman E., RISK Magazine 7 pp 32– |
[10] | DOI: 10.2469/faj.v52.n4.2008 · doi:10.2469/faj.v52.n4.2008 |
[11] | DOI: 10.1023/A:1009814324980 · Zbl 0978.91031 · doi:10.1023/A:1009814324980 |
[12] | DOI: 10.1111/1468-0262.00164 · Zbl 1055.91524 · doi:10.1111/1468-0262.00164 |
[13] | Gatheral J., The Volatility Surface: A Practitioner’s Guide (2006) |
[14] | DOI: 10.1093/rfs/6.2.327 · Zbl 1384.35131 · doi:10.1093/rfs/6.2.327 |
[15] | DOI: 10.1111/j.1540-6261.1987.tb02568.x · doi:10.1111/j.1540-6261.1987.tb02568.x |
[16] | Jacod J., The Annals of Probability 26 pp 267– |
[17] | Lipton A., Mathematical Methods for Foreign Exchange: A Financial Engineer’s Approach (2000) · Zbl 0989.91002 |
[18] | Little T., Journal of Computational Finance 5 pp 81– · doi:10.21314/JCF.2001.057 |
[19] | DOI: 10.1002/jae.689 · doi:10.1002/jae.689 |
[20] | DOI: 10.2307/3003143 · doi:10.2307/3003143 |
[21] | DOI: 10.1023/A:1009803506170 · Zbl 1028.91026 · doi:10.1023/A:1009803506170 |
[22] | K. Schürger, Advances in Finance and Stochastics, eds. K. Sandmann and P. J. Schönbucher (Springer, Berlin, 2002) pp. 287–293. |
[23] | DOI: 10.1111/1467-9965.00039 · Zbl 1020.91030 · doi:10.1111/1467-9965.00039 |
[24] | Sepp A., Journal of Computational Finance 11 pp 37– |
[25] | DOI: 10.1093/rfs/4.4.727 · Zbl 1458.62253 · doi:10.1093/rfs/4.4.727 |
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