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Is Jump Risk Priced? - What We Can (and Cannot) Learn From Option Hedging Errors

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  • Nicole Branger

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  • Christian Schlag

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    Abstract

    When options are traded, one can use their prices and price changes to draw inference about the set of risk factors and their risk premia. We analyze tests for the existence and the sign of the market prices of jump risk that are based on option hedging errors. We derive a closed-form solution for the option hedging error and its expectation in a stochastic jump model under continuous trading and correct model specification. Jump risk is structurally different from, e.g., stochastic volatility: there is one market price of risk for each jump size (and not just \emph{the} market price of jump risk). Thus, the expected hedging error cannot identify the exact structure of the compensation for jump risk. Furthermore, we derive closed form solutions for the expected option hedging error under discrete trading and model mis-specification. Compared to the ideal case, the sign of the expected hedging error can change, so that empirical tests based on simplifying assumptions about trading frequency and the model may lead to incorrect conclusions.

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    File URL: http://www.finance.uni-frankfurt.de/wp/686.pdf
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    Bibliographic Info

    Paper provided by Department of Finance, Goethe University Frankfurt am Main in its series Working Paper Series: Finance and Accounting with number 140.

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    Date of creation: Oct 2004
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    Handle: RePEc:fra:franaf:140

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    Keywords: Stochastic jumps; market prices of risk; discrete trading; model mis-specification; hedging error;

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