Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-25T20:37:09.555Z Has data issue: false hasContentIssue false
  • English
  • Français

Analytical Upper Bounds for American Option Prices

Published online by Cambridge University Press:  06 April 2009

Ren-Raw Chen  and
Shih-Kuo Yeh
Ren-Raw Chen
Affiliation:
rchen@rci.rutgers.edu, Rutgers Business School, Rutgers University, 94 Rockafeller Road, Piscataway, NJ 08854
Shih-Kuo Yeh
Affiliation:
seiko@ccms.nkfu.edu.tw, Department of Financial Operations, National Kaohsiung First University of Science and Technology, 1 University Road, Kaohsiung, Taiwan 824.
Get access Rights & Permissions [Opens in a new window]

Abstract

American options require numerical methods, namely lattice models, to provide accurate price estimates. The computations can become expensive when more than one state variable is involved. Analytical upper bounds can therefore provide a useful guideline for how high American values can reach. In this paper, we derive analytical (closed-form) upper bounds for American option prices under stochastic interest rates, stochastic volatility, and jumps where American option prices are difficult to compute with accuracy. In a stochastic volatility model (Heston (1993) and Scott (1997)) that has two random factors, we demonstrate that the upper bound only takes a very small fraction of the time that the American option needs to compute.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 37 , Issue 1 , March 2002 , pp. 117 - 135
Copyright
Copyright © School of Business Administration, University of Washington 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Models.” Journal of Finance, 52, (1997), 2003–2049.CrossRefGoogle Scholar
Broadie, M., and Detemple, J.. “American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods.” Review of Financial Studies, 9 (1996), 1211–1250.CrossRefGoogle Scholar
Broadie, M., and Detemple, J.. “The Valuation of American Options on Multiple Assets.” Mathematical Finance, 7 (1997), 241–286.CrossRefGoogle Scholar
Carr, P.; Jarrow, R.; and Myneni, R.. “Alternative Characterizations of American Put Options.” Mathematical Finance, 2 (1992), 87–106.CrossRefGoogle Scholar
Chaudhury, M., and Wei, J.. “Upper Bounds for American Futures Options: A Note.” Journal of Futures Markets, 14 (1994), 111–116.CrossRefGoogle Scholar
Chen, R., and Scott, L.. “Interest Rate Options in Multi-Factor Cox-Ingersoll-Ross Models of the Term Structure.” Journal of Derivatives, 3 (1995), 53–72.CrossRefGoogle Scholar
Cox, J.; Ingersoll, J.; and Ross, S.. “The Relation between Forward Prices and Futures Prices.” Journal of Financial Economics, 9 (1981), 321–346.CrossRefGoogle Scholar
Heston, S. “A Closed Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327–343.CrossRefGoogle Scholar
Hull, J., and White, A.. “The Pricing of Options on Assets with Stochastic Volatilities.” Journal of Finance, 42 (1987), 281–300.CrossRefGoogle Scholar
Jamshidian, F. “Pricing of Contingent Claims in The One-Factor Term Structure Model.” Working Paper, Merrill Lynch Capital Markets (1987).Google Scholar
Jamshidian, F.. “An Exact Bond Option Formula.” Journal of Finance, 44 (1989), 205–210.CrossRefGoogle Scholar
Johnson, H. “An Analytic Approximation for the American Put Price.” Journal of Financial and Quantitative Analysis, 18 (1983), 141–148.CrossRefGoogle Scholar
Johnson, H. “Options on the Maximum or the Minimum of Several Assets.” Journal of Financial and Quantitative Analysis, 22 (1987), 277–284.CrossRefGoogle Scholar
Johnson, H., and Shanno, D.. “Option Pricing when the Variance Is Changing.” Journal of Financial and Quantitative Analysis, 22 (1987), 143–152.CrossRefGoogle Scholar
Levy, H. “Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach.” Journal of Finance, 40 (1985), 1197–1217.CrossRefGoogle Scholar
Lo, A. “Semi-Parametric Upper Bounds for Option Prices and Expected Payoff.” Journal of Financial Economics, 19 (1987), 373–388.CrossRefGoogle Scholar
Perrakis, S. “Option Pricing Bounds in Discrete Time: Extensions and the Pricing of the American Put.” Journal of Business, 59 (1986), 119–141.CrossRefGoogle Scholar
Perrakis, S., and Ryan, J.. “Option Pricing in Discrete Time.” Journal of Finance, 39 (1984), 519–525.CrossRefGoogle Scholar
Ritchken, P. “On Option Pricing Bounds.” Journal of Finance, 40 (1985), 1219–1233.CrossRefGoogle Scholar
Ritchken, P., and Kuo, S.. “Option Bounds with Finite Revision Opportunities.” Journal of Finance, 43 (1988), 301–308.CrossRefGoogle Scholar
Scott, L. “Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application.” Journal of Financial and Quantitative Analysis, 22 (1987), 419–438.CrossRefGoogle Scholar
Scott, L. “Pricing Stock Options in a Jump-Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods.” Mathematical Finance, 7 (1997), 413–426.CrossRefGoogle Scholar
Stulz, R. “Options on the Minimum or the Maximum of Two Risky Assets: Analysis and Applications.” Journal of Financial Economics, 10 (1982), 161–185.CrossRefGoogle Scholar
Vasicek, O. “An Equilibrium Characterization of the Term Structure.” Journal of Financial Economics, 5 (1977), 177–188.CrossRefGoogle Scholar
Wiggins, J. “Option Values under Stochastic Volatility: Theory and Empirical Estimates.” Journal of Financial Economics, 19 (1987), 351–372.CrossRefGoogle Scholar
Zhang, P. “Bounds for Option Prices and Expected Payoffs.” Review of Quantitative Finance and Accounting, 4 (1994), 179–197.CrossRefGoogle Scholar