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Annual Review of Financial Economics

Volume 6, 2014

Optimal Exercise for Derivative Securities

Abstract

This article reviews the literature on American-style derivatives. The presentation stresses some of the major developments in the field. The focus is on the determination of optimal exercise policies and the structure of derivatives’ prices. Illustrative examples highlight the complexity of the optimal exercise decision.

Keyword(s): American-style, derivatives, exercise boundaries, exercise region, options, valuation
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2014-12-01
2024-04-26
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Literature Cited

  1. Amin K. 1993. Jump diffusion option valuation in discrete time. J. Finance 48:1833–63 [Google Scholar]
  2. Amin KI, Bodurtha JN. 1995. Discrete-time valuation of American options with stochastic interest rates. Rev. Financ. Stud. 8:193–233 [Google Scholar]
  3. Andersen A, Andreasen J. 2000. Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing. Rev. Deriv. Res. 4:231–62 [Google Scholar]
  4. Andersen L, Broadie M. 2004. A primal-dual simulation algorithm for pricing multi-dimensional American options. Manag. Sci. 50:1222–34 [Google Scholar]
  5. Andricopoulos AD, Widdicks M, Newton DP, Duck PW. 2007. Extending quadrature methods to value multi-asset and complex path dependent options. J. Financ. Econ. 83:471–99 [Google Scholar]
  6. Barone-Adesi G, Whaley RE. 1987. Efficient analytic approximation of American option values. J. Finance 42:301–20 [Google Scholar]
  7. Barraquand J, Martineau D. 1995. Numerical valuation of high dimensional multivariate American securities. J. Financ. Quant. Anal. 30:383–405 [Google Scholar]
  8. Battauz A, De Donno M, Sbuelz A. 2014. Real options and American derivatives: the double continuation region. Manag. Sci. Forthcoming. http://pubsonline.informs.org/doi/abs/10.1287/mnsc.2013.1891 [Google Scholar]
  9. Belomestny D, Bender C, Schoenmakers J. 2009. True upper bounds for Bermudan products via non-nested Monte Carlo. Math. Finance 19:53–71 [Google Scholar]
  10. Bensoussan A. 1984. On the theory of option pricing. Acta Appl. Math. 2:139–58 [Google Scholar]
  11. Bensoussan A, Lions JL. 1978. Applications des Inequations Variationelles en Contrôle Stochastique Paris: Dunod
  12. Bismut JM, Skalli B. 1977. Temps d’arrêt, théorie générale de processus et processus de Markov. Z. Wahrscheinlichkeit 39:301–13 [Google Scholar]
  13. Bjerksund P, Stensland G. 1993a. American exchange options and a put-call transformation: a note. J. Bus. Finance Account. 20:761–64 [Google Scholar]
  14. Bjerksund P, Stensland G. 1993b. Closed-form approximation of American options. Scand. J. Manag. 9:88–99 [Google Scholar]
  15. Black F, Scholes M. 1973. The pricing of options and corporate liabilities. J. Polit. Econ. 81:637–54 [Google Scholar]
  16. Bossaerts P. 1989. Simulation estimators of optimal early exercise. Work. Pap., Carnegie Mellon Univ
  17. Boyle PP. 1988. A lattice framework for option pricing with two state variables. J. Financ. Quant. Anal. 23:1–12 [Google Scholar]
  18. Boyle PP, Evnine J, Gibbs S. 1989. Valuation of options on several underlying assets. Rev. Financ. Stud. 2:241–50 [Google Scholar]
  19. Boyle PP, Lau SH. 1994. Bumping up against the barrier with the binomial method. J. Deriv. 1:6–14 [Google Scholar]
  20. Boyle PP, Tian Y. 1998. An explicit finite difference approach to the pricing of barrier options. Appl. Math. Finance 5:17–43 [Google Scholar]
  21. Breen R. 1991. The accelerated binomial option pricing model. J. Financ. Quant. Anal. 26:153–64 [Google Scholar]
  22. Brennan M, Schwartz E. 1977. The valuation of American put options. J. Finance 32:449–62 [Google Scholar]
  23. Brenner M, Courtadon G, Subrahmanyam M. 1985. Option on the spot and options on futures. J. Finance 40:1303–17 [Google Scholar]
  24. Broadie M, Detemple J. 1995. American capped call options on dividend-paying assets. Rev. Financ. Stud. 8:161–91 [Google Scholar]
  25. Broadie M, Detemple J. 1996. American option valuation: new bounds, approximations, and a comparison of existing methods. Rev. Financ. Stud. 9:1211–50 [Google Scholar]
  26. Broadie M, Detemple J. 1997. The valuation of American options on multiple assets. Math. Finance 7:241–85 [Google Scholar]
  27. Broadie M, Detemple J. 1999. American options on dividend paying assets. Fields Institute Communications, Vol. 22: Topology and Markets Chichilnisky G. 69–97 Toronto: AMS [Google Scholar]
  28. Broadie M, Glasserman P. 1997. Pricing American-style securities using simulation. J. Econ. Dyn. Control 21:1323–52 [Google Scholar]
  29. Broadie M, Glasserman P. 2004. A stochastic mesh method for pricing high-dimensional American options. J. Comput. Finance 7:35–72 [Google Scholar]
  30. Broadie M, Glasserman P, Jain G. 1997. Enhanced Monte Carlo estimates for American option prices. J. Deriv. 5:25–44 [Google Scholar]
  31. Broadie M, Yamamoto Y. 2003. Application of the fast Gauss transform to option pricing. Manag. Sci. 49:1071–88 [Google Scholar]
  32. Bunch D, Johnson H. 1992. A simple and numerically efficient valuation method for American puts using a modified Geske-Johnson approach. J. Finance 47:809–16 [Google Scholar]
  33. Carr P, Hirsa A. 2003. Why be backward? Forward equations for American options. Risk 16:103–7 [Google Scholar]
  34. Carr P, Jarrow R, Myneni R. 1992. Alternative characterizations of American put options. Math. Finance 2:87–106 [Google Scholar]
  35. Carriere JF. 1996. Valuation of the early-exercise price for options using simulations and nonparametric regression. Insur. Math. Econ. 19:19–30 [Google Scholar]
  36. Chen X, Chadam J. 2006. A mathematical analysis of the optimal exercise boundary for American put options. SIAM J. Math. Anal. 38:1613–41 [Google Scholar]
  37. Chen X, Chadam J, Jiang L, Zheng W. 2008. Convexity of the exercise boundary of the American put option on a zero dividend asset. Math. Finance 18:185–97 [Google Scholar]
  38. Chen X, Cheng H, Chadam J. 2013. Nonconvexity of the optimal exercise boundary for an American put option on a dividend-paying asset. Math. Finance 23:169–85 [Google Scholar]
  39. Chesney M, Gibson R. 1995. State space symmetry and two-factor option pricing models. Adv. Futures Options Res 8:85–112 [Google Scholar]
  40. Cheuk THF, Vorst TCF. 1996. Complex barrier options. J. Deriv. 4:8–22 [Google Scholar]
  41. Chiarella C, Kang B, Meyer GH, Ziogas A. 2009. The evaluation of American option prices under stochastic volatility and jump-diffusion dynamics using the method of lines. Int. J. Theor. Appl. Finance 12:393–425 [Google Scholar]
  42. Chiarella C, Ziogas A. 2005. Evaluation of American strangles. J. Econ. Dyn. Control 29:31–62 [Google Scholar]
  43. Chiarella C, Ziogas A. 2009. American call options under jump-diffusion processes—a Fourier transform approach. Appl. Math. Finance 16:37–79 [Google Scholar]
  44. Chiarella C, Ziveyi J. 2014. Pricing American options written on two underlying assets. Quant. Finance 14:3409–26 [Google Scholar]
  45. Chockalingam A, Muthuraman K. 2010. Pricing American options when asset prices jump. Oper. Res. Lett. 38:82–86 [Google Scholar]
  46. Chung S. 1999. American option valuation under stochastic interest rates. Rev. Deriv. Res. 3:283–307 [Google Scholar]
  47. Chung S, Hung M, Wang J. 2010. Tight bounds on American option prices. J. Bank. Finance 34:77–89 [Google Scholar]
  48. Courtadon GR. 1982. A more accurate finite difference approximation for the valuation of options. J. Financ. Quant. Anal. 17:697–703 [Google Scholar]
  49. Cox JC, Ross SA. 1976. The valuation of options for alternative stochastic processes. J. Financ. Econ. 3:145–66 [Google Scholar]
  50. Cox JC, Ross SA, Rubinstein M. 1979. Option pricing: a simplified approach. J. Financ. Econ. 7:229–63 [Google Scholar]
  51. Davis MHA, Karatzas I. 1994. A deterministic approach to optimal stopping. Probability, Statistics and Optimization: A Tribute to Peter Whittle Kelly FP. 455–66 Chichester: Wiley [Google Scholar]
  52. Dempster MAH, Hutton JP. 1997. Fast numerical valuation of American, exotic and complex options. Appl. Math. Finance 4:1–20 [Google Scholar]
  53. Dempster MAH, Hutton JP. 1999. Pricing American stock options by linear programming. Math. Finance 9:229–54 [Google Scholar]
  54. Detemple J. 2001. American options: symmetry properties. Handbooks in Mathematical Finance: Topics in Option Pricing, Interest Rates and Risk Management Cvitanic J, Jouini E, Musiela M. 67–104 Cambridge, UK: Univ. Press [Google Scholar]
  55. Detemple J, Emmerling T. 2009. American chooser options. J. Econ. Dyn. Control 33:128–53 [Google Scholar]
  56. Detemple J, Feng S, Tian W. 2003. The valuation of American call options on the minimum of two dividend-paying assets. Ann. Appl. Probab. 13:953–83 [Google Scholar]
  57. Detemple J, Tian W. 2002. The valuation of American options for a class of diffusion processes. Manag. Sci. 48:917–37 [Google Scholar]
  58. D’Halluin Y, Forsyth PA, Labahn G. 2004. A penalty method for American options with jump diffusion processes. Numer. Math. 97:321–52 [Google Scholar]
  59. D’Halluin Y, Forsyth PA, Vetzal KR. 2005. Robust numerical methods for contingent claims under jump diffusion processes. IMA J. Numer. Anal. 25:87–112 [Google Scholar]
  60. Ekstrom E. 2004. Convexity of the optimal stopping boundary for the American put option. J. Math. Anal. Appl. 299:147–56 [Google Scholar]
  61. El Karoui N. 1981. Les Aspects Probabilistes du Controle Stochastique. Lect. Notes Math. 876:73–238 [Google Scholar]
  62. Evans JD, Kuske R, Keller JB. 2002. American options on assets with dividends near expiry. Math. Finance 12:219–37 [Google Scholar]
  63. Fakeev AG. 1971. Optimal stopping of a Markov process. Theory Probab. Appl. 16:694–96 [Google Scholar]
  64. Feng L, Kovalov P, Linetsky V, Marcozzi M. 2007. Variational methods in derivatives pricing. Handbooks in Operations Research and Management Sciences, Vol. 15: Financial Engineering Birge JR, Linetsky V. 301–42 Amsterdam: Elsevier [Google Scholar]
  65. Figlewski S, Gao B. 1999. The adaptive mesh model: a new approach to efficient option pricing. J. Financ. Econ. 53:313–51 [Google Scholar]
  66. Gao B, Huang JZ, Subrahmanyam M. 2000. The valuation of American barrier options using the decomposition technique. J. Econ. Dyn. Control 24:1783–827 [Google Scholar]
  67. Garcia D. 2003. Convergence and biases of Monte Carlo estimates of American option prices using a parametric exercise rule. J. Econ. Dyn. Control 27:1855–79 [Google Scholar]
  68. Geltner D, Riddiough T, Stojanovic S. 1996. Insights on the effect of land use choice: the perpetual option on the best of two underlying assets. J. Urban Econ. 39:20–50 [Google Scholar]
  69. Geman H, El Karoui N, Rochet JC. 1995. Changes of numéraire, changes of probability measure and option pricing. J. Appl. Probab. 32:443–58 [Google Scholar]
  70. Gerber HU, Shiu ESW. 1996. Martingale approach to pricing perpetual American options on two stocks. Math. Finance 6:303–22 [Google Scholar]
  71. Geske R, Johnson H. 1984. The American put option valued analytically. J. Finance 39:1511–24 [Google Scholar]
  72. Glowinski R. 1984. Numerical Methods for Nonlinear Variational Problems Berlin: Springer
  73. Glowinski R, Lions JL, Tremolieres R. 1981. Numerical Analysis of Variational Inequalities Amsterdam: North-Holland
  74. Goodman J, Ostrov D. 2002. On the early exercise boundary of the American put option. SIAM J. Appl. Math. 62:1823–35 [Google Scholar]
  75. Grabbe OJ. 1983. The pricing of call and put options on foreign exchange. J. Int. Money Finance 2:239–53 [Google Scholar]
  76. Gukhal CR. 2001. Analytical valuation of American options on jump-diffusion processes. Math. Finance 11:97–115 [Google Scholar]
  77. Harrison M, Kreps D. 1979. Martingales and arbitrage in multiperiod security markets. J. Econ. Theory 20:381–408 [Google Scholar]
  78. Harrison M, Pliska S. 1981. Martingales and stochastic integrals in the theory of continuous trading. Stoch. Proc. Appl. 11:215–60 [Google Scholar]
  79. Haugh M, Kogan L. 2004. Approximating pricing and exercising of high-dimensional American options: a duality approach. Oper. Res. 52:258–70 [Google Scholar]
  80. Ho TS, Stapleton RC, Subrahmanyam MG. 1997. The valuation of American options with stochastic interest rates: a generalization of the Geske-Johnson technique. J. Finance 52:827–40 [Google Scholar]
  81. Huang JZ, Subrahmanyam M, Yu G. 1996. Pricing and hedging American options: a recursive integration method. Rev. Financ. Stud. 9:277–330 [Google Scholar]
  82. Ibanez A, Zapatero F. 2004. Monte Carlo valuation of American options through computation of the optimal exercise frontier. J. Financ. Quant. Anal. 39:253–75 [Google Scholar]
  83. Jacka SD. 1991. Optimal stopping and the American put. Math. Finance 1:1–14 [Google Scholar]
  84. Jaillet P, Lamberton D, Lapeyre B. 1990. Variational inequalities and the pricing of American options. Acta Appl. Math. 21:263–89 [Google Scholar]
  85. Jamshidian F. 1992. An analysis of American options. Rev. Futures Mark. 11:72–80 [Google Scholar]
  86. Ju N. 1998. Pricing an American option by approximating its early exercise boundary as a multipiece exponential function. Rev. Financ. Stud. 11:627–46 [Google Scholar]
  87. Kallast S, Kivinukk A. 2003. Pricing and hedging American options using approximations by Kim integral equations. Eur. Finance Rev. 7:361–83 [Google Scholar]
  88. Kamrad B, Ritchken P. 1991. Multinomial approximating models for options with k state variables. Manag. Sci. 37:1640–52 [Google Scholar]
  89. Karatzas I. 1988. On the pricing of American options. Appl. Math. Optim. 17:37–60 [Google Scholar]
  90. Karatzas I, Shreve S. 1998. Methods of Mathematical Finance New York: Springer-Verlag
  91. Kim IJ. 1990. The analytic valuation of American options. Rev. Financ. Stud. 3:547–72 [Google Scholar]
  92. Kim IJ, Yu GG. 1996. An alternative approach to the valuation of American options and applications. Rev. Deriv. Res. 1:61–85 [Google Scholar]
  93. Kinderlehrer D, Stampacchia G. 1980. An Introduction to Variational Inequalities and their Applications New York: Academic
  94. Kovalov P, Linetsky V, Marcozzi M. 2007. Pricing multi-asset American options: a finite element method-of-lines with smooth penalty. J. Sci. Comput. 33:209–37 [Google Scholar]
  95. Kuske RA, Keller JB. 1998. Optimal exercise boundary for an American put option. Appl. Math. Finance 5:107–16 [Google Scholar]
  96. Little T, Pant V, Hou C. 2000. A new integral representation of the early exercise boundary for American put options. J. Comput. Finance 3:73–96 [Google Scholar]
  97. Longstaff FA, Schwartz ES. 2001. Valuing American options by simulation: a simple least squares approach. Rev. Financ. Stud. 14:113–48 [Google Scholar]
  98. MacMillan LW. 1986. Analytic approximation for the American put option. Adv. Futures Options Res. 1:119–39 [Google Scholar]
  99. McDonald R, Schroder M. 1998. A parity result for American options. J. Comput. Finance 1:5–13 [Google Scholar]
  100. McKean HP. 1965. A free boundary problem for the heat equation arising from a problem in mathematical economics. Ind. Manag. Rev 6:32–39 [Google Scholar]
  101. Medvedev A, Scaillet O. 2010. Pricing American options under stochastic volatility and stochastic interest rates. J. Financ. Econ. 98:145–59 [Google Scholar]
  102. Menkveld AJ, Vorst T. 2000. A pricing model for American options with Gaussian interest rates. Ann. Oper. Res. 100:211–26 [Google Scholar]
  103. Merton RC. 1973a. An intertemporal capital asset pricing model. Econometrica 41:867–87 [Google Scholar]
  104. Merton RC. 1973b. Theory of rational option pricing. Bell J. Econ. Manag. Sci. 4:141–83 [Google Scholar]
  105. Merton RC. 1976. Option pricing when underlying stock returns are discontinuous. J. Financ. Econ. 3:125–44 [Google Scholar]
  106. Meyer GH. 1998. The numerical valuation of options with underlying jumps. Acta Math. 67:69–82 [Google Scholar]
  107. Meyer GH, van der Hoek J. 1997. The valuation of American options with the method of lines. Adv. Futures Options Res. 9:265–85 [Google Scholar]
  108. Mitchell D, Goodman J, Muthuraman K. 2014. Boundary evolution equations for American options. Math. Finance 24:3505–32 [Google Scholar]
  109. Mullinaci S. 1996. An approximation of American option prices in a jump-diffusion model. Stoch. Proc. Appl. 62:1–17 [Google Scholar]
  110. Muthuraman K. 2008. A moving boundary approach to American option pricing. J. Econ. Dyn. Control 32:3520–37 [Google Scholar]
  111. Myneni R. 1992. The pricing of the American option. Ann. Appl. Probab. 2:1–23 [Google Scholar]
  112. Nielsen BF, Skavhaug O, Tveito A. 2002. Penalty and front-fixing methods for the numerical solution of American option problems. J. Comput. Finance 5:69–97 [Google Scholar]
  113. Omberg E. 1987. The valuation of American put options with exponential exercise policies. Adv. Futures Options Res. 2:117–42 [Google Scholar]
  114. Parkinson M. 1977. Option pricing: the American put. J. Bus. 50:21–36 [Google Scholar]
  115. Peskir G. 2005. On the American option problem. Math. Finance 15:169–81 [Google Scholar]
  116. Pham H. 1997. Optimal stopping, free boundary, and American option in a jump-diffusion model. Appl. Math. Optim. 35:145–64 [Google Scholar]
  117. Ramaswamy K, Sundaresan SM. 1985. The valuation of options on futures contracts. J. Finance 40:1319–40 [Google Scholar]
  118. Raymar S, Zwecher M. 1997. A Monte Carlo valuation of American call options on the maximum of several stocks. J. Deriv. 5:7–23 [Google Scholar]
  119. Reimer M, Sandmann K. 1995. A discrete time approach for European and American barrier options. Work. Pap., Dep. Stat., Rheinische Friedrich-Wilhelms-Univ
  120. Rendleman RJ, Bartter BJ. 1979. Two-state option pricing. J. Finance 34:1093–110 [Google Scholar]
  121. Ritchken P. 1995. On pricing barrier options. J. Deriv. 3:19–28 [Google Scholar]
  122. Rogers C. 2002. Monte Carlo valuation of American options. Math. Finance 12:271–86 [Google Scholar]
  123. Rogers C. 2010. Dual valuation and hedging of Bermudan options. SIAM J. Financ. Math 1:604–8 [Google Scholar]
  124. Rubinstein M, Reiner E. 1991. Breaking down the barriers. Risk 4:28–35 [Google Scholar]
  125. Rutkowski M. 1994. The early exercise premium representation of foreign market American options. Math. Finance 4:313–25 [Google Scholar]
  126. Samuelson PA. 1965. Rational theory of warrant pricing. Ind. Manag. Rev 6:13–32 [Google Scholar]
  127. Schroder M. 1999. Changes of numeraire for pricing futures, forwards and options. Rev. Financ. Stud. 12:1143–63 [Google Scholar]
  128. Schwartz ES. 1977. The valuation of warrants: implementing a new approach. J. Financ. Econ. 4:79–94 [Google Scholar]
  129. Shiryaev AN. 1978. Optimal Stopping Rules New York: Springer-Verlag
  130. Simonato JG. 2011. Computing American option prices in the lognormal jump–diffusion framework with a Markov chain. Finance Res. Lett. 8:220–26 [Google Scholar]
  131. Sullivan M. 2000. Valuing American put options using Gaussian quadrature. Rev. Financ. Stud. 13:75–94 [Google Scholar]
  132. Tan KS, Vetzal KR. 1995. Early exercise region for exotic options. J. Deriv. 3:42–55 [Google Scholar]
  133. Tilley JA. 1993. Valuing American options in a path simulation model. Trans. Soc. Actuar. 45:83–104 [Google Scholar]
  134. Tsitsiklis JN, Van Roy B. 1999. Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing high-dimensional financial derivatives. IEEE Trans. Automat. Contr. 44:1840–51 [Google Scholar]
  135. Tsitsiklis JN, Van Roy B. 2001. Regression methods for pricing complex American-style options. IEEE Trans. Neural Netw. 12:694–703 [Google Scholar]
  136. Van Moerbeke P. 1976. On optimal stopping and free boundary problems. Arch. Ration. Mech. Anal. 60:101–48 [Google Scholar]
  137. Vasicek OA. 1977. An equilibrium characterization of the term structure. J. Financ. Econ. 5:177–88 [Google Scholar]
  138. Villeneuve S. 1999. Exercise regions of American options on several assets. Finance Stoch. 3:295–322 [Google Scholar]
  139. Wu L, Dai M. 2009. Pricing jump risk with utility indifference. Quant. Finance 9:177–86 [Google Scholar]
  140. Wu L, Kwok Y. 1997. A front-fixing finite difference method for the valuation of American options. J. Financ. Eng. 6:83–97 [Google Scholar]
  141. Zhang X. 1994. Analyse numérique des options américaines dans un modèle de diffusion avec des sauts. PhD Thesis, Ecole Nationale des Ponts et Chaussées Paris
  142. Zhang XL. 1997. Numerical analysis of American option pricing in a jump-diffusion model. Math. Oper. Res. 22:668–90 [Google Scholar]
  143. Zvan R, Vetzal KR, Forsyth PA. 2000. PDE methods for pricing barrier options. J. Econ. Dyn. Control 24:1563–90 [Google Scholar]
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Optimal Exercise for Derivative Securities
Annual Review of Financial Economics 6, 459 (2014); https://doi.org/10.1146/annurev-financial-110613-034241
/content/journals/10.1146/annurev-financial-110613-034241
/content/journals/10.1146/annurev-financial-110613-034241
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