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Local Vega Index and Variance Reduction Methods

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  • Hans‐Peter Bermin
  • Arturo Kohatsu‐Higa
  • Miquel Montero

Abstract

In this article we discuss a generalization of the Greek called vega which is used to study the stability of option prices and hedging portfolios with respect to the volatility in various models. We call this generalization the local vega index. We compute through Monte Carlo simulations this index in the cases of Asian options under the classical Black‐Scholes setup. Simulation methods using Malliavin calculus and kernel density estimation are compared. Variance reduction methods are discussed.

Suggested Citation

  • Hans‐Peter Bermin & Arturo Kohatsu‐Higa & Miquel Montero, 2003. "Local Vega Index and Variance Reduction Methods," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 85-97, January.
    • Handle: RePEc:bla:mathfi:v:13:y:2003:i:1:p:85-97
    DOI: 10.1111/1467-9965.00007
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    References listed on IDEAS

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    1. Arturo Kohatsu & Roger Pettersson, 2002. "Variance reduction methods for simulation of densities on Wiener space," Economics Working Papers 597, Department of Economics and Business, Universitat Pompeu Fabra.
    2. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    3. Hans Peter Bermin & Arturo Kohatsu, 1999. "Local volatility changes in the black-scholes model," Economics Working Papers 416, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Naoto Kunitomo & Akihiko Takahashi, 2001. "The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 117-151, January.
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    Cited by:

    1. Tomonori Nakatsu, 2017. "An Integration by Parts Type Formula for Stopping Times and its Application," Methodology and Computing in Applied Probability, Springer, vol. 19(3), pages 751-773, September.
    2. Chen, Nan & Glasserman, Paul, 2007. "Malliavin Greeks without Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1689-1723, November.
    3. Arturo Kohatsu & Montero Miquel, 2003. "Malliavin calculus in finance," Economics Working Papers 672, Department of Economics and Business, Universitat Pompeu Fabra.

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