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State Price Density, Esscher Transforms, and Pricing Options on Stocks, Bonds, and Foreign Exchange Rates

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  • Yong Yao

Abstract

The state price density is modeled as an exponential function of the underlying state variables, and the Esscher transform is used to specify the forward-risk-adjusted measure. With the aid of state price densities, Esscher transforms, and characteristic functions, this paper provides a consistent framework for pricing options on stocks, interest rates, and foreign exchange rates. The framework discussed is quite general and is related to many popular models.

Suggested Citation

  • Yong Yao, 2001. "State Price Density, Esscher Transforms, and Pricing Options on Stocks, Bonds, and Foreign Exchange Rates," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(3), pages 104-117.
    • Handle: RePEc:taf:uaajxx:v:5:y:2001:i:3:p:104-117
    DOI: 10.1080/10920277.2001.10596002
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    Cited by:

    1. Gourieroux, C. & Monfort, A., 2007. "Econometric specification of stochastic discount factor models," Journal of Econometrics, Elsevier, vol. 136(2), pages 509-530, February.
    2. Andrea Macrina & Priyanka A. Parbhoo, 2011. "Randomised Mixture Models for Pricing Kernels," Papers 1112.2059, arXiv.org.
    3. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2021. "Valuation of piecewise linear barrier options," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).
    4. Andrea Macrina & Priyanka Parbhoo, 2014. "Randomised Mixture Models for Pricing Kernels," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 281-315, November.
    5. Lau, John W. & Siu, Tak Kuen, 2008. "On option pricing under a completely random measure via a generalized Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 99-107, August.
    6. Gourieroux, C. & Monfort, A. & Sufana, R., 2010. "International money and stock market contingent claims," Journal of International Money and Finance, Elsevier, vol. 29(8), pages 1727-1751, December.
    7. Bo, Lijun, 2011. "Exponential change of measure applied to term structures of interest rates and exchange rates," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 216-225, September.
    8. Dijkstra, Theo K. & Yao, Yong, 2002. "Moment generating function approach to pricing interest rate and foreign exchange rate claims," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 163-178, October.
    9. Chen, Hua & Cox, Samuel H. & Wang, Shaun S., 2010. "Is the Home Equity Conversion Mortgage in the United States sustainable? Evidence from pricing mortgage insurance premiums and non-recourse provisions using the conditional Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 371-384, April.

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