A forward started jump-diffusion model and pricing of cliquet style exotics
- Gabriel G. Drimus
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In this paper we present an alternative model for pricing exotic options and structured products with forward-starting components. As presented in the recent study by Eberlein and Madan (Quantitative Finance 9(1):27–42, 2009), the pricing of such exotic products (which consist primarily of different variations of locally/globally, capped/floored, arithmetic/geometric etc. cliquets) depends critically on the modeling of the forward–return distributions. Therefore, in our approach, we directly take up the modeling of forward variances corresponding to the tenor structure of the product to be priced. We propose a two factor forward variance market model with jumps in returns and volatility. It allows the model user to directly control the behavior of future smiles and hence properly price forward smile risk of cliquet-style exotic products. The key idea, in order to achieve consistency between the dynamics of forward variance swaps and the underlying stock, is to adopt a forward starting model for the stock dynamics over each reset period of the tenor structure. We also present in detail the calibration steps for our proposed model.
- Backus, D., Foresi, S., & Wu, L. (2004). Accounting for Biases in Back-Scholes, available at SSRN: http://ssrn.com/abstract=585623.
- Bakshi, G., Cao, C., Chen, Z. (1997) Empirical performance of alternative option pricing models. The Journal of Finance LII 5: pp. 2003-2049 CrossRef
- Barndorff-Nielsen, O. E., Shephard, N. (2001) Non-Gaussian Ornstein–Uhlenbeck based models and some of their uses in financial econometrics. Journal of the Royal Statistical Society 63: pp. 167-241 CrossRef
- Bates, D. (1996) Jumps and stochastic volatility: The exchange rate processes implicit in Deutschemark options. Review of Financial Studies 9: pp. 69-107 CrossRef
- Bates, D. (2000) Post-’87 crash fears in S&P500 futures options. Journal of Econometrics v.95: pp. 181-238 CrossRef
- Bergomi, L. (2004). Smile dynamics 1. Risk, September. London: Incisive Media.
- Bergomi, L. (2005). Smile dynamics 2. Risk, October. London: Incisive Media.
- Black, F., Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81: pp. 637-654 CrossRef
- Carr, P., Ellis, K., Gupta, V. (1998) Static hedging of exotic options. Journal of Finance 53: pp. 1165-1190 CrossRef
- Carr, P., Geman, H., Madan, D., Yor, M. (2003) Stochastic volatility for Levy processes. Mathematical Finance 13: pp. 345-382 CrossRef
- Carr, P., Madan, D. Towards a theory of volatility trading, volatility. In: Jarrow, R. eds. (1998) Volatility: New estimation techniques for pricing derivatives. Risk Publications, London, pp. 417-427
- Cont, R., & Tankov, P. (2004). Financial modeling with jump processes. Chapman & Hall, CRC Financial Mathematics Series. ISBN 1-58488-413-4.
- Duffie, D., Pan, J., Singleton, K. (2000) Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68: pp. 1343-1376 CrossRef
- Eberlein, E., Madan, D. (2009) Sato processes and the valuation of structured products. Quantitative Finance 9: pp. 27-42 CrossRef
- Kemma, A. G. Z., Vorst, A. C. F. (1990) A pricing method for options based on average asset values. Journal of Banking and Finance 14: pp. 113-129 CrossRef
- Mehta, N. B., Molisch, A. F., Wu, J., & Zhang, J. (2006). Approximating the sum of correlated Lognormal or Lognormal-Rice random variables. IEEE International Conference on Communications (ICC) (Vol. 4, pp. 1605–1610). June, ISSN: 8164-9547.
- Merton, R. (1976) Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics 3: pp. 125-144 CrossRef
- Milevsky, M.A., Posner, S.E. (1998) Asian options, the sum of lognormals and the reciprocal gamma distribution. The Journal of Financial and Quantitative Analysis 33: pp. 409-422 CrossRef
- Overhaus, M. et al. (2007). Equity hybrid derivatives. Wiley.
- Poulsen, R. (2006) Barrier options and their static hedges: Simple derivations and extensions. Quantitative Finance 6: pp. 327-335 CrossRef
- Schoutens, W., Simons, E., & Tistaert, J. (2004). A perfect calibration! Now what? Wilmott, March. Wiley.
- A forward started jump-diffusion model and pricing of cliquet style exotics
Review of Derivatives Research
Volume 13, Issue 2 , pp 125-140
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Exotic options
- Forward volatility smiles
- Variance swaps
- Industry Sectors
- Author Affiliations
- 1. Department of Mathematical Sciences, University of Copenhagen, Universitetparken 5, 2100, Copenhagen, Denmark