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Intrinsic Prices Of Risk

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  • Truc Le
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    Abstract

    We review the nature of some well-known phenomena such as volatility smiles, convexity adjustments and parallel derivative markets. We propose that the market is incomplete and postulate the existence of intrinsic risks in every contingent claim as a basis for understanding these phenomena. In a continuous time framework, we bring together the notion of intrinsic risk and the theory of change of measures to derive a probability measure, namely risk-subjective measure, for evaluating contingent claims. This paper is a modest attempt to prove that measure of intrinsic risk is a crucial ingredient for explaining these phenomena, and in consequence proposes a new approach to pricing and hedging financial derivatives. By adapting theoretical knowledge to practical applications, we show that our approach is consistent and robust, compared with the standard risk-neutral approach.

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    File URL: http://arxiv.org/pdf/1403.0333
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    Paper provided by arXiv.org in its series Papers with number 1403.0333.

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    Date of creation: Mar 2014
    Date of revision: Aug 2014
    Handle: RePEc:arx:papers:1403.0333

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    1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 125-144.
    2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    4. Schönbucher, Philpp J., . "A Market Model for Stochastic Implied Volatility," Discussion Paper Serie B, University of Bonn, Germany 453, University of Bonn, Germany, revised May 1999.
    5. Mark Britten-Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 55(2), pages 839-866, 04.
    6. Truc Le, 2005. "Stochastic market volatility models," Applied Financial Economics Letters, Taylor and Francis Journals, Taylor and Francis Journals, vol. 1(3), pages 177-188, May.
    7. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
    8. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    9. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    10. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 22(04), pages 419-438, December.
    11. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, Elsevier, vol. 20(3), pages 381-408, June.
    12. Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 7(2), pages 119-125.
    13. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, Elsevier, vol. 3(1-2), pages 145-166.
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