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Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy

  • João Pedro Vidal Nunes (a1)

This paper proposes an alternative characterization of the early exercise premium that is valid for any Markovian and diffusion underlying price process as well as for any parameterization of the exercise boundary. This new representation is shown to provide the best pricing alternative available in the literature for medium- and long-term American option contracts, under the constant elasticity of variance model. Moreover, the proposed pricing methodology is also extended easily to the valuation of American options on defaultable equity and possesses appropriate asymptotic properties.

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Abramowitz M., and Stegun I.. Handbook of Mathematical Functions. New York: Dover Publications (1972).
Barone-Adesi G. “The Saga of the American Put.” Journal of Banking and Finance, 29 (2005), 29092918.
Barone-Adesi G., and Whaley R.. “Efficient Analytic Approximation of American Option Values.” Journal of Finance, 42 (1987), 301320.
Bekaert G., and Wu G.. “Asymmetric Volatility and Risk in Equity Markets.” Review of Financial Studies, 13 (2000), 142.
Bensoussan A. “On the Theory of Option Pricing.” Acta Applicandae Mathematicae, 2 (1984), 139158.
Black F., and Scholes M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637654.
Boyle P., and Tian Y.. “Pricing Lookback and Barrier Options under the CEV Process.” Journal of Financial and Quantitative Analysis, 34 (1999), 241264.
Brennan M., and Schwartz E.. “The Valuation of American Put Options.” Journal of Finance, 32 (1977), 449462.
Broadie M., and Detemple J.. “American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods.” Review of Financial Studies, 9 (1996), 12111250.
Brown B.; Lovato J.; and Russell K.. “Library of Fortran Routines for Cumulative Distribution Functions, Inverses, and Other Parameters.” Working Paper, University of Texas (1997).
Bunch D., and Johnson H.. “The American Put Option and Its Critical Stock Price.” Journal of Finance, 55 (2000), 23332356.
Buonocore A.; Nobile A.; and Ricciardi L.. “A New Integral Equation for the Evaluation of First-Passage-Time Probability Densities.” Advances in Applied Probability, 19 (1987), 784800.
Campbell J., and Taksler G.. “Equity Volatility and Corporate Bond Yields.” Journal of Finance, 58 (2003), 23212349.
Carr P. “Randomization and the American Put.” Review of Financial Studies, 11 (1998), 597626.
Carr P.; Jarrow R.; and Myneni R.. “Alternative Characterizations of American Put Options.” Mathematical Finance, 2 (1992), 87106.
Carr P., and Linetsky V.. “A Jump to Default Extended CEV Model: An Application of Bessel Processes.” Finance and Stochastics, 10 (2006), 303330.
Chung S., and Shackleton M.. “Generalised Geske-Johnson Interpolation of Option Prices.” Journal of Business Finance and Accounting, 34 (2007), 9761001.
Cox J. “Notes on Option Pricing I: Constant Elasticity of Variance Diffusions.” Working Paper, Stanford University (1975). Reprinted in Journal of Portfolio Management, 23(1996), 15–17.
Cox J.; Ross S.; and Rubinstein M.. “Option Pricing: A Simplified Approach.” Journal of Financial Economics, 7 (1979), 229263.
Davydov D., and Linetsky V.. “Pricing and Hedging Path-Dependent Options under the CEV Process.” Management Science, 47 (2001), 949965.
Delbaen F., and Shirakawa H.. “A Note on Option Pricing for the Constant Elasticity of Variance Model.” Asia-Pacific Financial Markets, 9 (2002), 8599.
Dennis P., and Mayhew S.. “Risk-Neutral Skewness: Evidence from Stock Options.” Journal of Financial and Quantitative Analysis, 37 (2002), 471493.
Detemple J., and Tian W.. “The Valuation of American Options for a Class of Diffusion Processes.” Management Science, 48 (2002), 917937.
Emanuel D., and MacBeth J.. “Further Results on the Constant Elasticity of Variance Call Option Pricing Model.” Journal of Financial and Quantitative Analysis, 17 (1982), 533554.
Fortet R. “Les Fonctions Aléatoires du Type de Markov Associées à Certaines Équations Linéaires aux Dérivées Partielles du Type Parabolique.” Journal des Mathématiques Pures et Appliquées, 22 (1943), 177243.
Geske R., and Johnson H.. “The American Put Option Valued Analytically.” Journal of Finance, 39 (1984), 15111524.
Huang J.; Subrahmanyam M.; and Yu G. G.. “Pricing and Hedging American Options: A Recursive Integration Method.” Review of Financial Studies, 9 (1996), 277300.
Ingersoll J. “Approximating American Options and Other Financial Contracts Using Barrier Derivatives.” Journal of Computational Finance, 2 (1998), 85112.
Jacka S. “Optimal Stopping and the American Put.” Mathematical Finance, 1 (1991), 114.
Jamshidian F. “An Analysis of American Options.” Review of Futures Markets, 11 (1992), 7280.
Johnson H. “An Analytical Approximation for the American Put Price.” Journal of Financial and Quantitative Analysis, 18 (1983), 141148.
Ju N. “Pricing an American Option by Approximating Its Early Exercise Boundary as a Multipiece Exponential Function.” Review of Financial Studies, 11 (1998), 627646.
Ju N., and Zhong R.. “An Approximate Formula for Pricing American Options.” Journal of Derivatives, 7 (1999), 3140.
Karatzas I. “On the Pricing of American Options.” Applied Mathematics and Optimization, 17 (1988), 3760.
Kim J. “The Analytic Valuation of American Options.” Review of Financial Studies, 3 (1990), 547572.
Kim J., and Yu G. G.. “An Alternative Approach to the Valuation of American Options and Applications.” Review of Derivatives Research, 1 (1996), 6185.
Kuan G., and Webber N.. “Pricing Barrier Options with One-Factor Interest Rate Models.” Journal of Derivatives, 10 (2003), 3350.
Linetsky V. “Pricing Equity Derivatives Subject to Bankruptcy.” Mathematical Finance, 16 (2006), 255282.
Longstaff F., and Schwartz E.. “A Simple Approach to Valuing Risky Fixed and Floating Rate Debt.” Journal of Finance, 50 (1995), 789819.
MacMillan L. “An Analytical Approximation for the American Put Price.” Advances in Futures and Options Research, 1 (1986), 119139.
Madan D., and Unal H.. “Pricing the Risks of Default.” Review of Derivatives Research, 2 (1998), 121160.
McKean H. “Appendix: A Free Boundary Problem for the Heat Equation Arising from a Problem in Mathematical Economics.” Industrial Management Review, 6 (1965), 3239.
Merton R. “The Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141183.
Nelson D., and Ramaswamy K.. “Simple Binomial Processes as Diffusion Approximations in Financial Models.” Review of Financial Studies, 3 (1990), 393430.
Park C., and Schuurmann F.. “Evaluations of Barrier-Crossing Probabilities of Wiener Paths.” Journal of Applied Probability, 13 (1976), 267275.
Penev S., and Raykov T.. “A Wiener Germ Approximation of the Noncentral Chi Square Distribution and of Its Quantiles.” Working Paper, University of New South Wales and Melbourne University (1997).
Press W.; Flannery B.; Teukolsky S.; and Vetterling W.. Numerical Recipes in Pascal: The Art of Scientific Computing. New York, NY: Cambridge University Press (1994).
Sbuelz A. “Analytical American Option Pricing: The Flat-Barrier Lower Bound.” Economic Notes, 33 (2004), 399413.
Schroder M. “Computing the Constant Elasticity of Variance Option Pricing Formula.” Journal of Finance, 44 (1989), 211219.
Shreve S. Stochastic Calculus for Finance II: Continuous-Time Models. New York: Springer (2004).
Sullivan M. “Valuing American Put Options Using Gaussian Quadrature.” Review of Financial Studies, 13 (2000), 7594.
Temme N. “A Set of Algorithms for the Incomplete Gamma Functions.” Probability in the Engineering and Informational Sciences, 8 (1994), 291307.
Van Moerbeke P. “On Optimal Stopping and Free Boundary Problems.” Archive for Rational Mechanics and Analysis, 60 (1976), 101148.
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