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Pricing and Hedging Derivative Securities with Unknown Local Volatilities

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  • Kerry W. Fendick

Abstract

A common assumption in financial engineering is that the market price for any derivative coincides with an objectively defined risk-neutral price - a plausible assumption only if traders collectively possess objective knowledge about the price dynamics of the underlying security over short time scales. Here we assume that traders have an objective knowledge about the underlying security's price trajectories only for large time scales. We show that avoidance of arbitrage that is still feasible uniquely determines the prices of options with large expiration times, and we derive limit theorems useful for estimation of model parameters and present-value analysis of derivative portfolios.

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  • Kerry W. Fendick, 2013. "Pricing and Hedging Derivative Securities with Unknown Local Volatilities," Papers 1309.6164, arXiv.org, revised Oct 2013.
    • Handle: RePEc:arx:papers:1309.6164
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    1. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. "General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Ward Whitt, 1992. "Asymptotic Formulas for Markov Processes with Applications to Simulation," Operations Research, INFORMS, vol. 40(2), pages 279-291, April.
    4. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    5. Conrad, Jennifer & Kaul, Gautam, 1988. "Time-Variation in Expected Returns," The Journal of Business, University of Chicago Press, vol. 61(4), pages 409-425, October.
    6. Emanuel Derman & Nassim Nicholas Taleb, 2005. "The illusions of dynamic replication," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 323-326.
    7. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    8. Bassler, Kevin E. & McCauley, Joseph L. & Gunaratne, Gemunu H., 2006. "Nonstationary increments, scaling distributions, and variable diffusion processes in financial markets," MPRA Paper 2126, University Library of Munich, Germany.
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2002. "Estimating quadratic variation using realized variance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 457-477.
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