Derivatives Analytics with Python by Yves Hilpisch

Author:Yves Hilpisch
Language: eng
Format: epub
ISBN: 9781119038009
Publisher: Wiley
Published: 2015-06-08T00:00:00+00:00

In addition, the general framework allows these special cases to be enriched by stochastic, instead of constant, short rates.

BCC97 conduct a number of empirical analyses for different parametrizations of their general model. Some major findings are:

quality of calibration: “Our empirical evidence indicates that regardless of performance yardstick, taking stochastic volatility into account is of the first-order importance in improving upon the BS[M] formula.”

quality of valuation: “According to the out-of-sample pricing measures, adding the random jump feature to the [stochastic volatility] model can further improve its performance, especially in pricing short-term options; whereas modeling stochastic interest rates can enhance the fit of long-term options.”

hedging performance: “For hedging purposes, however, incorporating either the jump or the [stochastic interest rate] feature does not seem to improve the [stochastic volatility] model’s performance further. The [stochastic volatility model] achieves the best hedging results among all the models studied, and its remaining hedging errors are generally quite small.”1

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