Security price process models : do these have the correct properties for understanding options values?
Tompkins, Robert G. (1997) Security price process models : do these have the correct properties for understanding options values? PhD thesis, University of Warwick.
WRAP_THESIS_Tompkins_1997.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://webcat.warwick.ac.uk/record=b1354472~S15
It is well known that the market price of options are inconsistent with option
pricing models that assume the innovation of the underlying price follows Geometric
Brownian Motion. What is not clear is why this occurs.
The testing of option pricing models requires a joint hypothesis to be tested
that the options pricing models are correct and that the options markets are efficient.
To test the option pricing models, we will examine the relationship between the
objective and risk neutral dispersion processes for twelve financial futures markets.
These markets have been selected so that we can investigate the dynamics of equity,
fixed income and foreign exchange asset classes.
Our analysis of the objective dispersion processes allows us to reject the
hypothesis that the prices of these twelve markets follow Geometric Brownian
motion. For all twelve markets and for various sub-periods of analysis, we find that
the optimal models for capturing the dynamics of the objective dispersion process
include jump diffusion and stochastic volatility.
For the risk neutral dispersion process, we chose to examine the implied
volatility surfaces from the closing prices of options (on these same futures markets).
It appears that both within and between markets similar dynamics determine the
shapes of the implied volatility surfaces. By employing an Analysis of Covariance
approach, we found that important consistencies exist within asset classes and
between markets. The first order strike price effect (skewness) differs widely among
markets but is fairly consistent within the same asset class. The second order strike
price effect (kurtosis) is consistent among all markets. The dependency of both strike
price effects on the time to expiration is also similar across all markets and suggests
that both jump diffusion and stochastic volatility play a role.
A comparison of option prices, which are consistent with the objective
dispersion process, with actual options prices suggests that significant divergences
exist. The actual smile patterns display greater variation in the amplitude compared to
those from the objective function. The least degree of discrepancy exists for the
foreign exchange markets. Both the stock index and fixed income options dispersion
processes display behaviours that diverge considerably. This divergence is primarily
due to the existence of negative skews that are not justified by the objective dispersion
processes. This suggests that other mechanisms are at work for the risk neutral
dispersion processes for these asset classes. The most likely explanations are the
existence of risk premia associated with stochastic volatility and non-diversifiable
jumps or that transaction costs are relevant.
|Item Type:||Thesis or Dissertation (PhD)|
|Subjects:||H Social Sciences > HB Economic Theory|
|Library of Congress Subject Headings (LCSH):||Options (Finance) -- Prices -- Mathematical models, Futures market , Brownian motion processes|
|Official Date:||December 1997|
|Institution:||University of Warwick|
|Theses Department:||School of Industrial and Business Studies|
|Supervisor(s)/Advisor:||Selby, Michael ; Hodges, Stewart D.|
|Extent:||xxxii, 438, 173 leaves|
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