## The Fine Structure of Asset Returns: An Empirical Investigation (2000)

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Citations: | 260 - 26 self |

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@MISC{Carr00thefine,

author = {Peter Carr and Hélyette Geman and Dilip B. Madan and Marc Yor},

title = {The Fine Structure of Asset Returns: An Empirical Investigation},

year = {2000}

}

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### Abstract

We investigate the relative importance of diffusion and jumps in a new jump diffusion model for asset returns. In contrast to the standard modelling of jumps for asset returns, the jump component of our process can display finite or infinite activity, and finite or infinite variation. Empirical investigations of time series indicate that index dynamics are essentially devoid of a diffusion component, while this component may be present in the dynamics of individual stocks. This result leads to the conjecture that the risk-neutral process should be free of a diffusion component for both indices and individual stocks. Empirical investigation of options data tends to confirm this conjecture. We conclude that the statistical and risk-neutral processes for indices and stocks tend to be pure jump processes of innite activity and finite variation.

### Citations

3572 |
The pricing of options and corporate liabilities
- Black, Scholes
- 1973
(Show Context)
Citation Context ...nd stocks tend to be pure jump processes of infinite activity and finite variation. 1 Introduction Asset returns have been modeled in continuous time as di#usions by Merton [13] and Black and Scholes =-=[2]-=-, as pure jump processes by Cox and Ross [5], and as jump-di#usions by Merton [14]. The jump processes studied by the latter authors display finite activity, while some recent research has considered ... |

1242 |
Theory of Rational Option Pricing
- Merton
- 1973
(Show Context)
Citation Context ...ral processes for indices and stocks tend to be pure jump processes of infinite activity and finite variation. 1 Introduction Asset returns have been modeled in continuous time as di#usions by Merton =-=[13]-=- and Black and Scholes [2], as pure jump processes by Cox and Ross [5], and as jump-di#usions by Merton [14]. The jump processes studied by the latter authors display finite activity, while some recen... |

688 | Option Pricing When Underlying Stock Returns are Discontinuous
- Merton
- 1976
(Show Context)
Citation Context ...n. 1 Introduction Asset returns have been modeled in continuous time as di#usions by Merton [13] and Black and Scholes [2], as pure jump processes by Cox and Ross [5], and as jump-di#usions by Merton =-=[14]-=-. The jump processes studied by the latter authors display finite activity, while some recent research has considered some pure jump processes with infinite activity. Two examples of these infinite ac... |

683 |
Limit Theorems for Stochastic Processes
- Jacod, Shiryaev
- 2003
(Show Context)
Citation Context ...variant under an equivalent change of measure. For infinite variation jump processes, like the stable laws with exponent above unity, equivalence of the measure change implies (see Jacod and Shiryaev =-=[10]-=- condition 3.25 page 160) that the di#erence between the risk neutral and statistical Levy densities be of finite variation and this imposes the restriction that the two processes have the the same ex... |

517 | The Valuation of Options for Alternative Stochastic Processes
- Cox, Ross
- 1976
(Show Context)
Citation Context ...infinite activity and finite variation. 1 Introduction Asset returns have been modeled in continuous time as di#usions by Merton [13] and Black and Scholes [2], as pure jump processes by Cox and Ross =-=[5]-=-, and as jump-di#usions by Merton [14]. The jump processes studied by the latter authors display finite activity, while some recent research has considered some pure jump processes with infinite activ... |

501 | Empirical performance of alternative option pricing models
- Bakshi, Cao, et al.
- 1997
(Show Context)
Citation Context ...data on the asset prices over the period January 1, 1994 to December 31, 1998. For the risk-neutral process, we follow the traditional practice established in the literature (See Bakshi, Cao and Chen =-=[1]-=-) and estimate risk-neutral parameters on a set of days from closing option prices. We discuss the details of each of these two estimations separately in the following two subsections. The data for bo... |

254 | The Variance Gamma process and option pricing, European Finance Review
- Madan, Carr, et al.
- 1998
(Show Context)
Citation Context ...d some pure jump processes with infinite activity. Two examples of these infinite activity pure jump processes are the variance gamma model studied by Madan and Seneta [16] and Madan, Carr, and Chang =-=[15]-=-, and the hyperbolic model considered in Eberlein, Keller, and Prause [6]. The rationale usually given for describing asset returns as jump-di#usions is that di#usions capture frequent small moves whi... |

253 | Option valuation using the Fast Fourier Transform
- Carr, Madan
- 1999
(Show Context)
Citation Context ...ameters of the statistical process from time series data becomes feasible. Furthermore, similar methods may be employed to estimate riskneutral parameters from options data as shown in Carr and Madan =-=[3]-=-. We are thus able to design a probe of the data enabling one to learn about the fine structure of asset returns from discrete observations, admittedly under some maintained auxiliary hypotheses. The ... |

143 |
The Variance Gamma (VG) model for share market returns
- Madan, Seneta
- 1990
(Show Context)
Citation Context ...me recent research has considered some pure jump processes with infinite activity. Two examples of these infinite activity pure jump processes are the variance gamma model studied by Madan and Seneta =-=[16]-=- and Madan, Carr, and Chang [15], and the hyperbolic model considered in Eberlein, Keller, and Prause [6]. The rationale usually given for describing asset returns as jump-di#usions is that di#usions ... |

100 | New insights into smile, mispricing, and value at risk: The hyperbolic model
- Eberlein, Keller, et al.
- 1998
(Show Context)
Citation Context ...nfinite activity pure jump processes are the variance gamma model studied by Madan and Seneta [16] and Madan, Carr, and Chang [15], and the hyperbolic model considered in Eberlein, Keller, and Prause =-=[6]-=-. The rationale usually given for describing asset returns as jump-di#usions is that di#usions capture frequent small moves while jumps capture rare large moves. Given the ability of infinite activity... |

67 |
Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process
- Koponen
- 1995
(Show Context)
Citation Context ...vy measure is symmetric and in this case, Madan, Carr, and Chang [15] show that the parameter C provides control over the kurtosis of the distribution of X(t). The case G = M has also been studied by =-=[9]-=- who gives an alternative expression for the characteristic function. The parameters G and M respectively control the rate of exponential decay on the right and left of the Levy density, leading to sk... |

60 |
Option pricing with vg martingale components
- Madan, Milne
- 1991
(Show Context)
Citation Context ...sis by considering pure jump processes. The next subsection presents the details of the variance gamma model developed by Madan and Seneta [16], and extended to incorporate skewness by Madan and Milne=-=[12]-=-, and Madan, Carr, and Chang [15]. The latter paper shows that this model permits a parsimonious description of the volatility smile observed in option prices at all maturities and for a wide variety ... |

26 | Who buys and who sells options: the role of options in an economy with background risk
- Franke, Stapleton, et al.
- 1998
(Show Context)
Citation Context ...hange function Y (x). In a two person equilibrium with heterogeneous beliefs and preferences, investors take a non-zero position in options, as shown for example in Franke, Stapleton and Subrahmanyam =-=[7]-=- or Carr and Madan [4]. Hence, one may infer the measure change if one has data on preferences and investor positions. It is well known that the measure change is given by the marginal utility of the ... |

21 | Optimal positioning in derivatives securities. Quantitative Finance 1 - Carr, Madan - 2001 |

13 |
Multiplicativité du processus gamma et étude asymptotique des lois stables d’indice α, lorsque α tend vers 0. Prépublication 289, Laboratoire de Probabilités
- Vershik, Yor
- 1995
(Show Context)
Citation Context ...ents for the process X(t). As we typically construct a process at the return level, it is reasonable to enforce finiteness of the moments at this level. The parameter Y was studied in Vershik and Yor =-=[17]-=- and it arises in the process for the stable law. The parameter Y is particularly useful in characterizing the fine structure of the stochastic process. For example, one may ask whether the up jumps a... |

6 |
Locally Optimal One–Sided Tests for Multiparameter Hypothese
- King, Wu
- 1997
(Show Context)
Citation Context ... the null hypothesis that the di#usion coe#cient is zero, which is a test on the boundary of the parameter space, we employ a locally mean most powerful (LMMP) test statistic developed by King and Wu =-=[11]-=-. The statistic is normal with mean zero and unit variance under the null hypothesis and is reported when it is positive. It is based on the score function computed at the null. The results of the est... |

4 |
Optimal Positioning in Derivative Securities," Working Paper
- Carr, Madan
- 1998
(Show Context)
Citation Context ...In a two person equilibrium with heterogeneous beliefs and preferences, investors take a non-zero position in options, as shown for example in Franke, Stapleton and Subrahmanyam [7] or Carr and Madan =-=[4]-=-. Hence, one may infer the measure change if one has data on preferences and investor positions. It is well known that the measure change is given by the marginal utility of the position times the rat... |

4 | Time changes for Lévy processes. Mathematical Finance 11:79–96 - Geman, Madan, et al. - 2001 |

2 |
Time Changes for L¶evy Processes," forthcoming
- Geman, Madan, et al.
- 2000
(Show Context)
Citation Context ...ing the class of pure jump models one may entertain, and the condition is intuitively a reasonable one. For a variety of other models along these lines the reader is referred to Geman, Madan, and Yor =-=[8]-=-. 2.2.2 Finite Variation Process From the perspective of option pricing theory, processes of finite variation (FV ) or finite activity (FA) are potentially more useful in explaining the measure change... |