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Quadratic-Variation-Based Dynamic Strategies

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  • Avi Bick

    (Faculty of Business Administration, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6)

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    Abstract

    The paper analyzes a family of dynamic trading strategies which do not rely on any stochastic process assumptions (aside from continuity and positivity) and in particular do not require predicting future volatilities. Derivative payoffs can still be replicated, except that this occurs at the stopping time at which the "realized cumulative squared volatility" hits a predetermined level. The application of these results to portfolio insurance is emphasized, and hedging strategies studied by Black and Jones and by Brennan and Schwartz are generalized. Classical results on European-style options arise as special cases. For example, the initial cost of replicating a call or a put under the new method is given by a generalized Black-Scholes formula, which yields the ordinary Black-Scholes formula when the volatility is derterministic.

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    File URL: http://dx.doi.org/10.1287/mnsc.41.4.722
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 41 (1995)
    Issue (Month): 4 (April)
    Pages: 722-732

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    Handle: RePEc:inm:ormnsc:v:41:y:1995:i:4:p:722-732

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    Related research

    Keywords: trading strategies; Black-Scholes formula; portfolio insurance; quadratic variation; ito's Lemma;

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    Cited by:
    1. Geman, Hélyette, 2005. "From measure changes to time changes in asset pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2701-2722, November.
    2. Li, Minqiang & Mercurio, Fabio, 2013. "Closed-Form Approximation of Timer Option Prices under General Stochastic Volatility Models," MPRA Paper 47465, University Library of Munich, Germany.
    3. Dimitris Bertsimas & Leonid Kogan & Andrew W. Lo, 1997. "Pricing and Hedging Derivative Securities in Incomplete Markets: An E-Aritrage Model," NBER Working Papers 6250, National Bureau of Economic Research, Inc.
    4. Li, Minqiang, 2014. "Analytic Approximation of Finite-Maturity Timer Option Prices," MPRA Paper 54597, University Library of Munich, Germany.
    5. Lan Zhang, 2012. "Implied and realized volatility: empirical model selection," Annals of Finance, Springer, vol. 8(2), pages 259-275, May.
    6. Li, Minqiang, 2014. "Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach," MPRA Paper 54595, University Library of Munich, Germany.
    7. Bertsimas, Dimitris. & Kogan, Leonid, 1974- & Lo, Andrew W., 1997. "Pricing and hedging derivative securities in incomplete markets : an e-arbitrage approach," Working papers WP 3973-97., Massachusetts Institute of Technology (MIT), Sloan School of Management.

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