Abstract
In this chapter, we introduce four hedging strategies for path-independent contingent claims in discrete time – superhedging, local expected shortfall-hedging, local quadratic risk-minimizing and local quadratic risk-adjusted-minimizing strategies. The corresponding dynamic programming algorithms of each trading strategy are introduced for making adjustment at each rebalancing time. The hedging performances of these discrete time trading strategies are discussed in the trinomial, Black-Scholes and GARCH models. Moreover, the hedging strategies of path-dependent contingent claims are introduced in the last section, and the hedges of barrier options are illustrated as examples.
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References
Bensaid, B., Lesne, J. P., Pagès, H., & Scheinkman, J. (1992). Derivatives asset pricing with trasaction costs. Mathematical Finance, 2, 63–86.
Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 31, 307–327.
Bowie, J., & Carr, P. (1994). Static simplicity. Risk, 7, 45–49.
Carr, P., & Lee, R. (2009). Put-call symmetry: Extensions and applications. Mathematical Finance, 19, 23–560.
Cvitanić, J., & Karatzas, I. (1999). On dynamic measures of Risk. Finance and Stochastics, 3, 451–482.
Duan, J. C. (1995). The GARCH option pricing model. Mathematical Finance, 5, 13–32.
Duan, J. C., & Simonato, J. G. (1998). Empirical martingale simulation for asset prices. Management Science, 44, 1218–1233.
Elliott, R. J., & Madan, D. B. (1998). A discrete time equivalent martingale measure. Mathematical Finance, 8, 127–152.
Föllmer, H., & Leukert, P. (2000). Efficient hedging: Cost versus shortfall risk. Finance and Stochastics, 4, 117–146.
Huang, S. F., Guo, M. H. (2009a). Financial derivative valuation - a dynamic semiparametric approach. Statistica Sinica, 19, 1037–1054.
Huang, S. F., & Guo, M. H. (2009b). Valuation of multidimensional Bermudan options. In W. Härdle (Ed.), Applied quantitative finance (2nd ed.). Berlin: Springer.
Huang, S. F., & Guo, M. H. (2009c). Multi-period hedging strategy minimizing squared risk adjusted costs. Working paper.
Huang, S. F., & Guo, M. H. (2009d). Model risk of implied conditional heteroscedastic models with Gaussian innovation in option pricing and hedging. Working paper.
Huang, S. F., & Huang, J. Y. (2009). Hedging strategies against path-dependent contingent claims. Journal of Chinese Statistical Association, 47, 194–218.
Schulmerich, M., & Trautmann, S. (2003). Local expected shortfall-hedging in discrete time. European Finance Review, 7, 75–102.
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Huang, SF., Guo, M. (2012). Dynamic Programming and Hedging Strategies in Discrete Time. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_22
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DOI: https://doi.org/10.1007/978-3-642-17254-0_22
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