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Approximating payoffs and pricing formulas

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Listed author(s):
  • Darolles, Serge
  • Laurent, Jean-Paul

Abstract

We use the ideas developed by Madan and Milne (1994. Mathematical Finance 3, 223-245), Lacoste (1996. Mathematical Finance 6, 197-213) to explore the optimality of polynomial approximations in pricing securities. In particular, we look at the approximations for security payoffs as well as the associated pricing formula in a L2 framework. We apply these ideas to two examples, one where the state variable follows an Ornstein-Uhlenbeck process and one based on Brownian motion with reflecting barriers, to illustrate the strengths and weaknesses of the approach.

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File URL: http://www.sciencedirect.com/science/article/pii/S0165-1889(99)00092-5
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Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 24 (2000)
Issue (Month): 11-12 (October)
Pages: 1721-1746

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Handle: RePEc:eee:dyncon:v:24:y:2000:i:11-12:p:1721-1746
Contact details of provider: Web page: http://www.elsevier.com/locate/jedc

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  1. Bansal, Ravi & Viswanathan, S, 1993. " No Arbitrage and Arbitrage Pricing: A New Approach," Journal of Finance, American Finance Association, vol. 48(4), pages 1231-1262, September.
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  3. repec:crs:wpaper:9736 is not listed on IDEAS
  4. Hansen, Lars Peter & Jagannathan, Ravi, 1997. " Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
  5. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
  6. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  7. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
  8. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245.
  9. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
  10. Chapman, David A, 1997. " Approximating the Asset Pricing Kernel," Journal of Finance, American Finance Association, vol. 52(4), pages 1383-1410, September.
  11. Bansal, Ravi & Hsieh, David A & Viswanathan, S, 1993. " A New Approach to International Arbitrage Pricing," Journal of Finance, American Finance Association, vol. 48(5), pages 1719-1747, December.
  12. Peter A. Abken & Dilip B. Madan & Buddhavarapu Sailesh Ramamurtie, 1996. "Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options," FRB Atlanta Working Paper 96-5, Federal Reserve Bank of Atlanta.
  13. Vincent Lacoste, 1996. "Wiener Chaos: A New Approach To Option Hedging," Mathematical Finance, Wiley Blackwell, vol. 6(2), pages 197-213.
  14. Amershi, Amin H, 1985. " A Complete Analysis of Full Pareto Efficiency in Financial Markets for Arbitrary Preferences," Journal of Finance, American Finance Association, vol. 40(4), pages 1235-1243, September.
  15. Florens, Jean-Pierre & Renault, Eric & Touzi, Nizar, 1998. "Testing For Embeddability By Stationary Reversible Continuous-Time Markov Processes," Econometric Theory, Cambridge University Press, vol. 14(06), pages 744-769, December.
  16. John, Kose, 1984. "Market Resolution and Valuation in Incomplete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 19(01), pages 29-44, March.
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Cited by:

  1. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2016. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility and Jumps," Swiss Finance Institute Research Paper Series 16-73, Swiss Finance Institute.
  2. Darolles, Serge & Florens, Jean-Pierre & Gourieroux, Christian, 2004. "Kernel-based nonlinear canonical analysis and time reversibility," Journal of Econometrics, Elsevier, vol. 119(2), pages 323-353, April.

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