Alternative models for stock price dynamics

Alternative models for stock price dynamics This paper evaluates the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions. We use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns. We consider two broad families of models: (1) the multifactor loglinear family, and (2) the affine-jump family. Both classes of models have attracted much attention in the derivatives and econometrics literatures. There are various tradeoffs in considering such diverse specifications. If pure diffusion SV models are chosen over jump diffusions, it has important implications for hedging strategies. If logarithmic models are chosen over affine ones, it may seriously complicate option pricing. Comparing many different specifications of pure diffusion multifactor models and jump diffusion models, we find that (1) log linear models have to be extended to two factors with feedback in the mean reverting factor, (2) affine models have to have a jump in returns, stochastic volatility or probably both. Models (1) and (2) are observationally equivalent on the data set in hand. In either (1) or (2) the key is that the volatility can move violently. As we obtain models with comparable empirical fit, one must make a choice based on arguments other than statistical goodness-of-fit criteria. The considerations include facility to price options, to hedge and parsimony. The affine specification with jumps in volatility might therefore be preferred because of the closed-form derivatives prices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Econometrics Elsevier

Alternative models for stock price dynamics

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Publisher
Elsevier
Copyright
Copyright © 2003 Elsevier B.V.
ISSN
0304-4076
eISSN
1872-6895
D.O.I.
10.1016/S0304-4076(03)00108-8
Publisher site
See Article on Publisher Site

Abstract

This paper evaluates the role of various volatility specifications, such as multiple stochastic volatility (SV) factors and jump components, in appropriate modeling of equity return distributions. We use estimation technology that facilitates nonnested model comparisons and use a long data set which provides rich information about the conditional and unconditional distribution of returns. We consider two broad families of models: (1) the multifactor loglinear family, and (2) the affine-jump family. Both classes of models have attracted much attention in the derivatives and econometrics literatures. There are various tradeoffs in considering such diverse specifications. If pure diffusion SV models are chosen over jump diffusions, it has important implications for hedging strategies. If logarithmic models are chosen over affine ones, it may seriously complicate option pricing. Comparing many different specifications of pure diffusion multifactor models and jump diffusion models, we find that (1) log linear models have to be extended to two factors with feedback in the mean reverting factor, (2) affine models have to have a jump in returns, stochastic volatility or probably both. Models (1) and (2) are observationally equivalent on the data set in hand. In either (1) or (2) the key is that the volatility can move violently. As we obtain models with comparable empirical fit, one must make a choice based on arguments other than statistical goodness-of-fit criteria. The considerations include facility to price options, to hedge and parsimony. The affine specification with jumps in volatility might therefore be preferred because of the closed-form derivatives prices.

Journal

Journal of EconometricsElsevier

Published: Sep 1, 2003

References

  • The market model of interest rate dynamics
    Brace, A.; Gatarek, D.; Musiela, M.
  • A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation
    Chernov, M.; Ghysels, E.
  • Estimation of stochastic volatility models with diagnostics
    Gallant, A.R.; Hsieh, D.; Tauchen, G.
  • The jump-risk premia implicit in options: evidence from an integrated time-series study
    Pan, J.

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