Simple processes and the pricing and hedging of cliquets. (English) Zbl 1282.91340
Summary: For data on market prices for 246 cliquets we consider pricing these exotic options using a relatively simple path space. The path space is subsequently stressed to market implied stress levels as well as stress levels predicted from contract characteristics. An additive process transitioning from a Sato process to a Levy process is formulated and estimated on vanilla options. Ask prices constructed from predicted stress levels are observed to have an in sample correlation of 92% with market prices. Interestingly, it is observed that capped cash flows have negative stress levels while uncapped products have positive stress levels. We illustrate the effect of hedging cliquet liabilities using call options as hedging assets permitting a 10% reduction in ask prices.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
References:
| [1] | Artzner, P., F.Delbaen, J.Eber, and D.Heath (1998): Definition of Coherent Measures of Risk, Math. Finance 9, 203-228. · Zbl 0980.91042 |
| [2] | Carr, P., H.Geman, and D. B.Madan (2001): Pricing and Hedging in Incomplete Markets, J. Finan. Econ. 62, 131-167. |
| [3] | Carr, P., and D. B.Madan (1999): Option Pricing Using the Fast Fourier Transform, J. Computat. Finance 2, 61-73. |
| [4] | Carr, P., H.Geman, D.Madan, and M.Yor (2002): The Structure of Asset Returns: An Empirical Investigation, J. Business 75, 305-332. |
| [5] | Carr, P., H.Geman, D.Madan, and M.Yor (2005): Pricing Options on Realized Variance, Finance Stoch. 9, 453-475. · Zbl 1096.91022 |
| [6] | Carr, P., H.Geman, D.Madan, and M.Yor (2007): Self Decomposability and Option Pricing, Math. Finance 17, 31-57. · Zbl 1278.91157 |
| [7] | Cherny, A., and D. B.Madan (2009): New Measures for Performance Evaluation, Rev. Finan. Stud. 22, 2571-2606. |
| [8] | Eberlein, E., and D. B.Madan (2010): Short Sale Restrictions, Rally Fears and Option Pricing, Appl. Math. Finance 17, 83-98. · Zbl 1229.91303 |
| [9] | Föllmer, H., and A.Schied (2004): Stochastic Finance: An Introduction in Discrete Time. Berlin : Walter de Gruyter. · Zbl 1126.91028 |
| [10] | Galloway, M. L., and C. A.Nolder (2008): Subordination, Self‐similarity, and Option Pricing, J. Appl. Math. Decision Sci. , Article Number 397028, 1-30. · Zbl 1156.91454 |
| [11] | Jaschke, S., and U.Küchler (2001): Coherent Risk Measures and Good Deal Bounds, Finance Stoch. 5, 181-200. · Zbl 0993.91023 |
| [12] | Madan, D. B. (2010): Pricing and Hedging Basket Options to a Prespecified Level of Acceptability, Quant. Finance 10, 607-615. · Zbl 1192.91183 |
| [13] | Madan, D. B., P.Carr, and E.Chang (1998): The Variance Gamma Process and Option Pricing, Eur. Finance Rev. 2, 79-105. · Zbl 0937.91052 |
| [14] | Madan, D. B., and E.Seneta (1990): The V.G. Model for Share Market Returns, J. Business 63(4), 511-52. |
| [15] | Nolder, C. A. (2003): Self‐similar Additive Processes and Financial Modelling, Proceedings of the Financial Engineering and Applications Conference, IASTED, Banff, Alberta. |
| [16] | Sato, K. (1980): Class L of Multivariate Distributions and Its Subclasses, J. Multivar. Anal. 10, 207-232. · Zbl 0425.60013 |
| [17] | Sato, K. (1991): Self Similar Processes with Independent Increments, Probab. Theory Related Fields 89, 285-300. · Zbl 0725.60034 |
| [18] | Sato, K. (1999): Lévy Processes and Infinitely Divisible Distributions. Cambridge , UK : Cambridge University Press. · Zbl 0973.60001 |
| [19] | Urbanik, K. (1972): Slowly Varying Sequences of Random Variables, Bull. Polon. Sci. Sér. Sci. Astron. Phys. 20, 679-682. · Zbl 0251.60012 |
| [20] | Urbanik, K. (1973): Limit Laws for Sequences of Normed Sums Satisfying Some Stability Conditions, in Multivariate Analysis III, P. R.Krishnaiah (ed.), ed. New York : Academic Press, 225-237. · Zbl 0303.60043 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
