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## A Jump-Diffusion Model for Option Pricing (2002)

Venue: | Management Science |

Citations: | 237 - 9 self |

### Citations

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Citation Context ...r, lookback, and perpetual American options, are feasible under the double exponential jump-diffusion model while it seems impossible for many other models, including the normal jump-diffusion model (=-=Merton 1976-=-); see §2.3 for details. 2.2. Evaluating the Model Because essentially all models are “wrong” and rough approximations of reality, instead of arguing the “correctness” of the proposed model I shall ev... |

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Citation Context ...ack–Scholes model. 1088 Management Science/Vol. 48, No. 8, August 2002KOU A Jump-Diffusion Model for Option Pricing both overreaction and underreaction to various good or bad news (see, for example, =-=Fama 1998-=- and Barberis et al. 1998, and references therein). One may interpret the jump part of the model as the market response to outside news. More precisely, in the absence of outside news the asset price ... |

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Citation Context ...del. 1088 Management Science/Vol. 48, No. 8, August 2002KOU A Jump-Diffusion Model for Option Pricing both overreaction and underreaction to various good or bad news (see, for example, Fama 1998 and =-=Barberis et al. 1998-=-, and references therein). One may interpret the jump part of the model as the market response to outside news. More precisely, in the absence of outside news the asset price simply follows a geometri... |

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Citation Context ...opportunity to invest in a security (with a finite liquidation date T0, although T0 can be very large) which pays no dividends. If ��t� is Markovian, it can be shown (see, for example, pp. 484–485 in =-=Stokey and Lucas 1989-=-) that, under mild conditions, the rational expectations equilibrium price (also called the 7 The density 1 − ��t g�x� = � √ �t � ( x − ��t � √ ) �t { + ��t p� 1e ��2 � 2 1 �t�/2 e −�x−��t�� 1 � + q�2... |

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Citation Context ...becomes more pronounced if either 1/� i (the jump size expectations) or � (the jump rate) increases. 4. Equilibrium for General Jump-Diffusion Models Consider a typical rational expectations economy (=-=Lucas 1978-=-) in which a representative investor tries to solve a utility maximization problem maxc E� ∫ � U�c�t��t�dt�, where U�c�t��t� is the util0 ity function of the consumption process c�t�. There is an exog... |

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Citation Context ...ives, such as swaptions, caps, floors, and bond options (see §5.3 and Glasserman and Kou 1999); path-dependent options, such as perpetual American options, barrier, and lookback options (see §2.3 and =-=Kou and Wang 2000-=-, 2001). (c) It can be embedded into a rational expectations equilibrium framework (see §4). (d) It has a psychological interpretation (see §2.2). The model is very simple. The logarithm of the asset ... |

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Citation Context ...�� S�T� � ℱ t� U c���t�� t� = e −rT E ∗ �� S�T� � ℱ t�� □ ∏ i=1 ∏ i=1 ˜V �−1 i � ˜V �−1 i = e −rT { Z�T� E Z�t� � } S�T� � ℱt Proof of Theorem 1. The Girsanovtheorem for jump-diffusion processes (see =-=Björk et al. 1997-=-) tells us that under P∗�W ′ 1�t� �= W1�t� − �1�� − 1�t is a new Brownian motion, and under P∗ the jump rate of N�t�is �∗ = �E�˜ V �−1 i � = ��� ��−1� 1 +1�� and ˜ Vi has a new Management Science/Vol.... |

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Citation Context ...options are not easy, as the convergence rates of binomial trees and Monte Carlo simulation for path-dependent options are typically much slower than those for call and put options (for a survey, see =-=Boyle et al. 1997-=-). 5 Interestingly enough, the double exponential distribution has been widely used in mathematical psychology literature, particularly in vision cognitive studies; see, for example, the list of paper... |

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Citation Context ...�1+ 2n� −x 1F1� 1 2 3 1 n+1� � 2 �� 1 2 + 1 2 n� 2 x2 � where 1F1 is the confluent hypergeometric function. A three-term recursion is also available for the Hh function (see pp. 299–300 and p. 691 of =-=Abramowitz and Stegun 1972-=-): nHh n�x� = Hh n−2�x� − xHh n−1�x�� n ≥ 1� (19) Therefore, one can compute all Hh n�x�� n ≥ 1, by using the normal density function and normal distribution function. The Hh function is illustrated i... |

4 | Maximum likelihood estimation of asymmetric jump-diffusion models. Working paper. http://cyrus.cob.calpoly.edu/JUMPMLE/Ramezani-Zeng-PBJD.pdf - Ramezani, Zeng - 1998 |

4 |
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Citation Context ...rage-free and can be embedded in an equilibrium setting. Note that some of the alternative models may have arbitrage opportunities, and thus are not selfconsistent (to give an example, it is shown by =-=Rogers 1997-=- that models using fractal Brownian motion may lead to arbitrage opportunities). The double exponential jump-diffusion model can be embedded in a rational expectations equilibrium setting; see §4. 2. ... |

2 |
The term structure of simple interest rates with jump risk. Working paper
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(Show Context)
Citation Context ...s to analytical solutions to many option-pricing problems, including European call and put options (see §5); interest rate derivatives, such as swaptions, caps, floors, and bond options (see §5.3 and =-=Glasserman and Kou 1999-=-); path-dependent options, such as perpetual American options, barrier, and lookback options (see §2.3 and Kou and Wang 2000, 2001). (c) It can be embedded into a rational expectations equilibrium fra... |

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1 | Option hedging in the presence of jump risk - Grünewald, Trautmann - 1996 |