Much asset and derivative pricing theory is based on diffusion models for primary securities, including equities. In contrast, there are hardly any empirical estimates of satisfactory continuous-time models for equity returns. For daily observations on the S&P 500 index, the obstacles facing empirical work are perhaps best illustrated by the striking rejections of the standard discrete-time stochastic volatility (SV) models and the corresponding strong rejections of standard diffusion models.
This research extends the class of stochastic volatility diffusions explored in the literature to allow for Poisson jumps in returns. Estimation is performed via a careful implementation of the efficient method of moments, generating powerful model diagnostics and specification tests. Every variant of the stochastic volatility diffusions without jumps fails to jointly accommodate all prominent features of the daily S&P 500 returns, while the SV jump diffusions provide an overall acceptable characterization.
It can then be inferred that satisfactory continuous-time models for equity returns must incorporate both stochastic volatility and discrete jumps in order to provide a relatively accurate empirical representation. Results so far point towards an average of five jumps per year, with a jump of 3% not being uncommon. Alternative specifications of the stochastic volatility factor are being explored, and implications for derivative pricing are being illustrated.
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URL: http://www.msi.umn.edu/about/publications/annualreport/ar2000/depts/CSOM/Finance/benzoni.html |
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