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| Type | Journal Article |
| Scope | Discipline-based scholarship |
| Title | Diffusion coefficient estimation and asset pricing when risk premia and sensitivities are time varying |
| Organization Unit | |
| Authors |
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| Item Subtype | Original Work |
| Refereed | Yes |
| Status | Published in final form |
| Language |
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| Journal Title | Mathematical Finance |
| Publisher | Wiley-Blackwell |
| Geographical Reach | international |
| ISSN | 0960-1627 |
| Volume | 3 |
| Number | 2 |
| Page Range | 85 - 99 |
| Date | 1993 |
| Abstract Text | The exponential of a scalar diffusion is considered. Point estimates of the diffusion coefficient can be obtained by considering proportional increments of different powers of the exponential. an investigation of the minimum variance estimator gives unique optimal power. |
| Zusammenfassung | Given a diffusion process it is often easier to estimate the drift coefficient than the diffusion coefficient. Log-normal diffusion processes are frequently used to model asset prices in finance and, in a recent paper, Chesney and Elliott (1992) have used the Mihlstein (1974) approximation to estimate the diffusion coefficient (known in finance as the volatility). The application they had in mind was that of an exchange rate between two currencies: if s, represents the U.S. dollar to French franc rate, then 1/S, represents the French franc to U.S. dollar rate. Their result follows by using the It6 calculus and properties of a log-normal diffusion. In this paper a general (scalar) diffusion xt is considered. By introducing the process yt = exp xt, properties of the exponential can be exploited. In the paper of Chesney and Elliott (19921, a point estimate for the diffusion coefficient is obtained by comparing expressions derived from S, and S; ; in the present paper estimates for the diffusion coefficient of X, are obtained by using the It6 calculus and Mihlstein approximations and by comparing expressions for y, and yp (a real). The minimum variance estimate gives a unique optimal value of a. A table illustrating optimal a values is also presented. The scalar diffusion estimation strategy is then extended to also allow estimation of the instantaneous variation in the predictable quadratic covariation of two diffusion processes. Such a point estimate may be used to accommodate time-varying risk sensitivities in asset pricing models that simultaneously permit time variation in risk premia as well. Applications to the capital asset pricing model (CAPM) illustrate the procedure. |
| Official URL | http://www.bf.uzh.ch/publikationen/pdf/publ_930.pdf |
| Digital Object Identifier | 10.1111/j.1467-9965.1993.tb00080.x |
| Other Identification Number | merlin-id:4686 |
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