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Long-memory volatility in derivative hedging

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  • Tan, Abby

Abstract

The aim of this work is to take into account the effects of long memory in volatility on derivative hedging. This idea is an extension of the work by Fedotov and Tan [Stochastic long memory process in option pricing, Int. J. Theor. Appl. Finance 8 (2005) 381–392] where they incorporate long-memory stochastic volatility in option pricing and derive pricing bands for option values. The starting point is the stochastic Black–Scholes hedging strategy which involves volatility with a long-range dependence. The stochastic hedging strategy is the sum of its deterministic term that is classical Black–Scholes hedging strategy with a constant volatility and a random deviation term which describes the risk arising from the random volatility. Using the fact that stock price and volatility fluctuate on different time scales, we derive an asymptotic equation for this deviation in terms of the Green's function and the fractional Brownian motion. The solution to this equation allows us to find hedging confidence intervals.

Suggested Citation

  • Tan, Abby, 2006. "Long-memory volatility in derivative hedging," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 689-696.
    • Handle: RePEc:eee:phsmap:v:370:y:2006:i:2:p:689-696
    DOI: 10.1016/j.physa.2006.02.041
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    2. Mitra, Sovan, 2013. "Operational risk of option hedging," Economic Modelling, Elsevier, vol. 33(C), pages 194-203.
    3. Viviana Fernandez & Brian M. Lucey, 2006. "Portfolio management implications of volatility shifts: Evidence from simulated data," The Institute for International Integration Studies Discussion Paper Series iiisdp131, IIIS.

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