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Fuzzy Value-at-risk: Accounting for Market Liquidity

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  • Umberto Cherubini
  • Giovanni Della Lunga

Abstract

type="main" xml:lang="en"> In this paper we present a value-at-risk measure which accounts for market liquidity. We show that taking into account market liquidity implies a decoupling of valuation of long and short positions. We present a pricing model, named fuzzy measure model, that yields different values for positions of different sign and that can be usefully exploited to account for liquidity risk. This methodology is well-suited to price options when the distribution of the underlying asset is not known precisely, as in the case of implied options in corporate claims or real options. As an example, we apply our pricing technique to an option based model of value-at-risk, in line with the Merton and Perold approach, and we recover different value-at-risk figures for long and short positions. (J.E.L.: C00, D81, G12).

Suggested Citation

  • Umberto Cherubini & Giovanni Della Lunga, 2001. "Fuzzy Value-at-risk: Accounting for Market Liquidity," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 30(2), pages 293-312, July.
    • Handle: RePEc:bla:ecnote:v:30:y:2001:i:2:p:293-312
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    File URL: http://hdl.handle.net/10.1111/j.0391-5026.2001.00058.x
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    Cited by:

    1. Zmeskal, Zdenek, 2005. "Value at risk methodology of international index portfolio under soft conditions (fuzzy-stochastic approach)," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 263-275.
    2. Zmeskal, Zdenek, 2010. "Generalised soft binomial American real option pricing model (fuzzy-stochastic approach)," European Journal of Operational Research, Elsevier, vol. 207(2), pages 1096-1103, December.

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