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## Randomization and the American Put (1998)

Venue: | The Review of Financial Studies |

Citations: | 105 - 1 self |

### Citations

5044 |
M.: The pricing of options and corporate liabilities
- Black
- 1973
(Show Context)
Citation Context ... the approximation is both accurate and computationally e cient. 1I Introduction Closed-form solutions for the value of European-style options have been known since the seminal papers of BlackScholes=-=[2]-=- and Merton[26]. Since American calls on non-dividend paying stocks are not rationally exercised early, they can be valued in closed form. Unfortunately, the vast majority of listed options are Americ... |

1724 | Theory of rational option pricing - Merton - 1973 |

1323 | Optimum consumption and portfolio rules in a continuous-time model - Merton - 1971 |

1014 | Option pricing: A simplified approach, - Cox, Ross, et al. - 1979 |

280 | E cient Analytic Approximation of American Option Values
- Barone-Adesi, Whaley
- 1987
(Show Context)
Citation Context ... comprise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula=-=[1]-=-,[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approx... |

166 | 1965], ‘Rational theory of warrant pricing - Samuelson |

152 |
American option valuation: New bounds, approximations, and a comparison of existing methods, Review of Financial Studies 9
- Broadie, Detemple
- 1996
(Show Context)
Citation Context ... those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds=-=[6]-=-,[19]. The purpose of this paper is to develop a new analytic approximation for American option values and exercise boundaries based on a novel technique called randomization. procedure which can be u... |

129 |
The Valuation of American Put Options
- Brennan, Schwartz
- 1977
(Show Context)
Citation Context ...s and exercise boundaries may be classi ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,[10],[20],[31],[33], nite di erences=-=[5]-=-[39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integra... |

129 |
Appendix: A Free Boundary Problem for the Heat Equation Arising from a
- McKean
- 1965
(Show Context)
Citation Context ...ely be valued as: P (0;S;T)= sup B(t);t2[0;T ] E0;Sfe r( B^T ) [K S B^T ] + + e rT [K ST ] + 1( B T )g; S>S(0); (2) where B is the rst passage time1 from S to an exercise boundary B(t);t2[0;T]. McKean=-=[22]-=- showed that an application of It^o's lemma to (1) implies that the alive American put value and exercise boundary jointly solve afree boundary problem, consisting of the Black-Scholes partial di eren... |

108 |
The American Put Options Valued Analytically
- Geske, Johnson
- 1984
(Show Context)
Citation Context ...ods for valuing American options comprise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],=-=[12]-=-,[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is t... |

99 | Valuing American Options in a Path Simulation Model,
- Tilley
- 1993
(Show Context)
Citation Context ...ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],=-=[38]-=-. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21]... |

82 | Optimal stopping and American put. - Jacka - 1991 |

80 | Alternative characterizations of American put options, Mathematical Finance 2 - Carr, Jarrow, et al. - 1992 |

75 |
Numerical evaluation of multivariate contingent claims
- Boyle, Evnine, et al.
- 1989
(Show Context)
Citation Context ...durov[25], p. 24, an N point Richardson extrapolation is the following weighted 12 average of N Canadian put values: ^P 1:N (0) NX n=1 ( 1) N n n N n!(N n)! ^ P (T=n): (30) 11 Boyle, Evnine, and Gibbs=-=[3]-=- also use the approach tovalue multivariate options. 12 The weights always sum to unity and alternate in sign. In general, higher order approximations involve weights with greater absolute value. As a... |

60 |
Multinomial Approximating Models for Options with k
- Kamrad, Ritchken
- 1991
(Show Context)
Citation Context ...termining American option values and exercise boundaries may be classi ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,[10],=-=[20]-=-,[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exerci... |

58 | Pricing an American option by approximating its early exercise boundary as a multipiece exponential function, Review of Financial Studies 11 - Ju - 1998 |

57 | Pricing and hedging American options: a recursive integration method.
- Huang, Subrahmanyam, et al.
- 1996
(Show Context)
Citation Context ...o simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], =-=[16]-=-,[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximation for American option values and exercise boundaries based on a novel tec... |

49 |
An analytical approximation for the American put option
- MacMillan
- 1986
(Show Context)
Citation Context ...prise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],=-=[23]-=-, exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximati... |

46 | Difference Methods and Their Extrapolations; - Marchuk, Shaidurov - 1983 |

46 |
An analytical valuation formula for unprotected American options on stocks with known dividends.
- Roll
- 1977
(Show Context)
Citation Context ...rresponding results for call options. We thus assume that the underlying stock pays dividends continuously until the xed maturity T .To obtain a truly xed component of this dividend ow, we follow Roll=-=[34]-=- in assuming that this component has been escrowed out of the stock price. In other words, the time t stock price St decomposes into: St = r [1 e r(T t) ]+st; t2[0;T]; (32) where the rst term is the p... |

37 |
Option pricing: the American put.
- Parkinson
- 1977
(Show Context)
Citation Context ...ning American option values and exercise boundaries may be classi ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,[10],[20],=-=[31]-=-,[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise bo... |

34 |
Option Pricing: A Simpli ed Approach
- Cox, Ross, et al.
- 1979
(Show Context)
Citation Context ...or determining American option values and exercise boundaries may be classi ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,=-=[10]-=-,[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential e... |

33 |
Zweidimensionaee parabolische Randwertaufgabe als Grenzfall eindimensionaler Randwertaufgaben
- Rothe
- 1930
(Show Context)
Citation Context ...emes or the binomial model4 . The notion of discretizing time while leaving space continuous is known in the numerical methods literature as the method of horizontal lines or Rothe's method (see Rothe=-=[35]-=- and Rektorys[32]). Its application to free boundary problems has been promulgated in Meyer[27],[28] and in Meyer &van der Hoek[29], who use it to numerically value American options. Goldenberg and Sc... |

32 |
The Accelerated Binomial Option Pricing Model
- Breen
- 1991
(Show Context)
Citation Context ...accelerate valuation schemes for American 11 options. Geske and Johnson[12] rst used Richardson extrapolation in a nancial context to speed up and simplify their compound option valuation model. Breen=-=[4]-=- applied this idea to accelerate the binomial model of Cox, Ross, and Rubinstein[10]. Broadie and Detemple[6] use it to accelerate a hybrid of the binomial and Black-Scholes models. Finally, Huang, Su... |

30 |
Two-state option pricing.
- Rendleman, Bartter
- 1979
(Show Context)
Citation Context ...American option values and exercise boundaries may be classi ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,[10],[20],[31],=-=[33]-=-, nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundar... |

30 |
Weeks: Path-Dependent Options: Extending the Monte Carlo Simulation
- Grant, Vora, et al.
- 1997
(Show Context)
Citation Context ...assi ed as either numerical methods or analytic approximations. Numerical methods for valuing American options comprise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation=-=[14]-=-,[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18],... |

29 |
Optimal Stopping and the
- Jacka
- 1991
(Show Context)
Citation Context ...ulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],=-=[17]-=-, [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximation for American option values and exercise boundaries based on a novel techniqu... |

25 |
An Analytical Approximation for the American Put Price
- Johnson
- 1983
(Show Context)
Citation Context ...se based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],=-=[19]-=-. The purpose of this paper is to develop a new analytic approximation for American option values and exercise boundaries based on a novel technique called randomization. procedure which can be used t... |

20 | An Introduction to Partial Differential Equations, - Pinchover, Rubinstein - 2007 |

18 | Individual saving, aggregate capital accumulation, and efficient growth. In - Cass, Yaari - 1967 |

15 | Theory of rational option pricing. - ERTON, C - 1973 |

11 |
The Valuation of American Puts with Exponential Exercise Policies
- Omberg
- 1987
(Show Context)
Citation Context ...di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],=-=[30]-=-, integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximation for American option values and exercis... |

8 |
A Simple and Numerically E cient Valuation Method for American Puts Using a Modi ed Geske-Johnson Approach
- Bunch, Johnson
- 1992
(Show Context)
Citation Context ...methods for valuing American options comprise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options=-=[7]-=-,[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper... |

7 | Alternative - Carr, Jarrow, et al. - 1992 |

6 |
The analytic valuation of American puts
- Kim
- 1990
(Show Context)
Citation Context ...[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], =-=[21]-=-, or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximation for American option values and exercise boundaries based on a novel technique called ran... |

6 | The Method of Discretization in Time, D - Rektorys - 1982 |

6 |
Volatility Smiles, Skewness Premia and Risk Metrics: Applications of a four Parameter Closed form Generalization of Geometric Brownian Motion to the Pricing of Options
- Madan, Chang
- 1996
(Show Context)
Citation Context ...ormal proof of convergence remains an open question. 7 Note that (22) is closely related to the value of a xed maturity American option when the variance rate is gamma distributed. See Madan and Chang=-=[24]-=- for a closed form solution for European options. 8 See (61) and (60) in Appendix 2 for the randomized values of European calls and in-the-money European puts respectively. 12and nally, A (n) i (S; 1... |

6 |
Dierence methods and their extrapolations
- Marchuk, Shaidurov
(Show Context)
Citation Context ...s that the 3 point extrapolation is given by: ^P 1:3 (0) 1 2 ^ P (T ) 4 ^ P (T=2) + 9 2 ^ P (T=3): (29) Figures 10 and 11 illustrate the idea behind a 3 point extrapolation. From Marchuk and Shaidurov=-=[25]-=-, p. 24, an N point Richardson extrapolation is the following weighted 12 average of N Canadian put values: ^P 1:N (0) NX n=1 ( 1) N n n N n!(N n)! ^ P (T=n): (30) 11 Boyle, Evnine, and Gibbs[3] also ... |

5 | Estimating the Early Exercise Boundary and Pricing American Options, working paper - Goldenberg, Schmidt - 1995 |

5 | The evaluation of American options with the method of lines
- Meyer, Hoek
- 1997
(Show Context)
Citation Context ...rature as the method of horizontal lines or Rothe's method (see Rothe[35] and Rektorys[32]). Its application to free boundary problems has been promulgated in Meyer[27],[28] and in Meyer &van der Hoek=-=[29]-=-, who use it to numerically value American options. Goldenberg and Schmidt[13] test this numerical scheme against other approaches and nd that it is highly accurate, although slightly slower 5 than so... |

5 |
The Method of Discretization in Time and Partial Di erential Equations
- Rektorys
- 1982
(Show Context)
Citation Context ...ial model4 . The notion of discretizing time while leaving space continuous is known in the numerical methods literature as the method of horizontal lines or Rothe's method (see Rothe[35] and Rektorys=-=[32]-=-). Its application to free boundary problems has been promulgated in Meyer[27],[28] and in Meyer &van der Hoek[29], who use it to numerically value American options. Goldenberg and Schmidt[13] test th... |

4 | An extension of the Black±Scholes model of security valuation - Du, D - 1988 |

4 |
Formulas for American Options," Merrill Lynch Capital Markets working paper
- Jamshidian
- 1989
(Show Context)
Citation Context ...n[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], =-=[18]-=-, [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximation for American option values and exercise boundaries based on a novel technique call... |

3 | Fast Accurate Valuation of American Options," working paper - Carr, Faguet - 1997 |

3 | The Variance Gamma Option Pricing Model," European Finance Review, forthcoming - Madan, Carr, et al. - 1996 |

3 | Pricing and Hedging American Options: A Recursive Integration Method - J, Yu - 1996 |

2 |
On a Free Boundary Problem for Linear Ordinary Di erential Equations and the One-Phase Stephan Problem
- Meyer
- 1970
(Show Context)
Citation Context ... known in the numerical methods literature as the method of horizontal lines or Rothe's method (see Rothe[35] and Rektorys[32]). Its application to free boundary problems has been promulgated in Meyer=-=[27]-=-,[28] and in Meyer &van der Hoek[29], who use it to numerically value American options. Goldenberg and Schmidt[13] test this numerical scheme against other approaches and nd that it is highly accurate... |

2 |
One-Dimensional Free Boundary Problems
- Meyer
- 1979
(Show Context)
Citation Context ...n in the numerical methods literature as the method of horizontal lines or Rothe's method (see Rothe[35] and Rektorys[32]). Its application to free boundary problems has been promulgated in Meyer[27],=-=[28]-=- and in Meyer &van der Hoek[29], who use it to numerically value American options. Goldenberg and Schmidt[13] test this numerical scheme against other approaches and nd that it is highly accurate, alt... |

2 |
Pricing American Currency Options: An Analytical Approach, HEC working paper
- Chesney
- 1989
(Show Context)
Citation Context ...ite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],[15], the quadratic formula[1],[23], exponential exercise boundaries=-=[9]-=-,[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to develop a new analytic approximation for American option values and ex... |

2 |
A Simple Technique for the Valuation and Hedging
- Ho, Stapleton, et al.
- 1994
(Show Context)
Citation Context ...or valuing American options comprise lattices,[10],[20],[31],[33], nite di erences[5][39], and Monte Carlo simulation[14],[38]. Analytic approximations include those based on compound options[7],[12],=-=[15]-=-, the quadratic formula[1],[23], exponential exercise boundaries[9],[30], integral formulations,[8], [16],[17], [18], [21], or tight lower and upper bounds[6],[19]. The purpose of this paper is to dev... |

2 | A Parity Result for American Options, Northwestern University working paper - McDonald, Schroder - 1990 |

1 | American Put Call Symmetry," forthcoming - Carr, Chesney - 1997 |

1 | Formulas for American Options," Merrill Lynch Capital Markets working paper - Jamshidian - 1989 |

1 | The Random-Time Binomial Model," University of Bonn working paper - Leisen - 1997 |

1 | A Parity Result for American Options," Northwestern University working paper - McDonald, Schroder - 1990 |

1 | Fast Accurate Binomial Pricing," forthcoming in Finance and Stochastics - Rogers, Stapleton - 1997 |

1 | American Put Call Symmetry," forthcoming - Carr, Chesney - 1997 |

1 | Fast Accurate Valuation of American Options," Cornell University working paper - Carr, Faguet - 1997 |

1 | The Random-Time Binomial Model," University ofBonnworking paper - Leisen - 1997 |

1 | The Variance Gamma Option Pricing Model," University of Maryland working paper - Madan, Chang - 1997 |

1 | Fast Accurate Binomial Pricing," forthcoming in Finance and Stochastics - Rogers, Stapleton - 1997 |

1 | Partial Di erential Equations - Rubinstein, Rubinstein - 1993 |