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State prices implicit in valuation formulae for derivative securities: a martingale approach

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  • Rady, Sven

Abstract

Derivative assets analysis usually takes a model of the underlying price process as given and attempts to value derivative securities relative to that model. This paper studies the following "inverse" problem: given a valuation formula for a derivative asset, what can be inferred about the underlying asset price process? Assuming continuous sample paths, we show that a sufficiently regular pricing formula for some derivative asset completely determines the risk-neutral law of underlying price. In particular, such a valuation formula implies a unique set of state prices for payoffs contingent on the price path of the underlying security. As an illustration of our main result, we analyse certain pricing formulae for European options on zero-coupon bonds.

Suggested Citation

  • Rady, Sven, 1994. "State prices implicit in valuation formulae for derivative securities: a martingale approach," LSE Research Online Documents on Economics 119180, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:119180
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    Cited by:

    1. 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.
    2. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    3. 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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    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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