Bounds and robust hedging of the American option
Neuberger, Anthony (2009) Bounds and robust hedging of the American option. Working Paper. Warwick Business School, Coventry.
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The value of an American option depends on the information that the holder will acquire over the option’s life. Much of the literature makes restrictive assumptions about information revelation – for example that the underlying price process is Markov. With a richer information structure, the American feature becomes more valuable. This paper identifies the least upper bound on the price of an American option, placing no assumptions on the information structure. It shows that the American premium in standard models is a small fraction of its upper bound, and shows what features make the American feature most valuable. The bounds can be tightened by excluding implausible processes, and these bounds are enforced by a hedging strategy that is robust to model error.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||H Social Sciences > HB Economic Theory
Q Science > QA Mathematics
|Divisions:||Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre
Faculty of Social Sciences > Warwick Business School > Finance Group
Faculty of Social Sciences > Warwick Business School
|Library of Congress Subject Headings (LCSH):||Options (Finance) -- United States, Functions of bounded variation, Markov processes, Options (Finance) -- Mathematical models|
|Publisher:||Warwick Business School|
|Place of Publication:||Coventry|
|Number of Pages:||40|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:||Andersen, L., and J. Andreasen, 2001, “Factor Dependence of Bermudan Swaptions: fact or fiction?”, Journal of Financial Economics, 62(1), 3–37. Andersen, L., and M. Broadie, 2004, “Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options”, Management Science, 50(9), 1222–1234. Avellaneda, M., A. Levy, and A. Paras, 1995, “Pricing and hedging derivative securities in markets with uncertain volatilities”, Applied Mathematical Finance, 2, 73–88. Bernardo, A.E., and O. Ledoit, 2000, “Gain, Loss, and Asset Pricing”, Journal of Political Economy, 108(1), 144–172. Britten-Jones, M., and A. Neuberger, 2000, “Option Prices, Implied Price Processes and Stochastic Volatility”, Journal of Finance, 55(2), 839-866. Broadie, M., and J. B. Detemple, 2004, “Option Pricing: Valuation Models and Applications” , Management Science, 50(9), 1145–1177. Brown, H., Hobson, D. and L.C.G. Rogers, 2001, “Robust Hedging of Barrier Options”, Mathematical Finance, 11, 285–314. Buraschi, A., and F. Corielli, 2005, “Risk management implications of timeinconsistency: Model updating and recalibration of no-arbitrage models”, Journal of Banking and Finance, 29(11), 2883-2907. Cochrane, J. H., and J. Saá-Requejo, 2000, “Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets”, Journal of Political Economy, 108(1), 79-119. Davis, M. H. A., and D. G. Hobson, 2007, “The Range of Traded Option Prices”, Mathematical Finance, 17(1), 1-14. Derman, E., and I. Kani, 1994, “Riding on a Smile”, Risk, 7, 32-39. Derman, E., D. Ergener, and I. Kani, 1995, “Static Options Replication,” Journal of Derivatives, 2, 78-95. Dupire, B., 1994, “Pricing with a smile”, Risk, 7, 18-20. Green T, C., and S. Figlewski, 1999, “Market Risk and Model Risk for a Financial Institution Writing Options”, Journal of Finance, 54, 1465-1499. Haugh, M., and L. Kogan, 2004, “Pricing American Options: A Duality Approach”, Operations Research, 52(2), 258-270. Heston, S., 1993, “A closed-form solutions for options with stochastic volatility”, Review of Financial Studies, 6, 327–343. . Longstaff, F., P. Santa-Clara and E. Schwartz, 2001, “Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaption market”, Journal of Financial Economics, 62(1), 39-66. Merton, R. C., 1973, “The Theory of Rational Option Pricing”, Bell Journal of Economics, 4, 141-183. Rogers, L. C. G., 2002, “Monte Carlo Valuation of American options”, Mathematical Finance, 12 (3), 271-286. Rumsfeld, D., 2002, Defense Secretary Rumsfeld Press Conference at NATO Headquarters, Brussels, Belgium, 6 June 2002, http://www.defenselink.mil/transcripts/ transcript.aspx?transcriptid=3490 Svenstrup, M., 2005, “On the suboptimality of single-factor exercise strategies for Bermudan swaptions”, Journal of Financial Economics, 78(3), 651-684.|
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