Analytical Comparisons of Option prices in Stochastic Volatility Models
AbstractThis paper orders option prices under various well known martingale measures in an incomplete stochastic volatility model. The central result is a comparison theorem which proves convex option prices are decreasing in the market price of volatility risk, the parameter governing the choice of pricing measure. The theorem is applied to order option prices under the minimal martingale, q-optimal and minimal entropy measures. This ordering depends on the mean variance tradeoff process whilst the specifics of the volatility dynamics are not important. We illustrate our results by analyzing the Hull and White, Heston and Stein and Stein models.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf03.
Date of creation: 2002
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-08-31 (All new papers)
- NEP-ETS-2003-08-31 (Econometric Time Series)
- NEP-FIN-2003-08-31 (Finance)
- NEP-FMK-2003-08-31 (Financial Markets)
- NEP-RMG-2003-08-31 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Martin Schweizer & HuyËn Pham & (*), Thorsten RheinlÄnder, 1998. "Mean-variance hedging for continuous processes: New proofs and examples," Finance and Stochastics, Springer, vol. 2(2), pages 173-198.
- Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
- Marco Frittelli, 2000. "The Minimal Entropy Martingale Measure and the Valuation Problem in Incomplete Markets," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 39-52.
- Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
- Schweizer, Martin, 1999. "A minimality property of the minimal martingale measure," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 27-31, March.
- Martin Schweizer & Christophe Stricker & Freddy Delbaen & Pascale Monat & Walter Schachermayer, 1997. "Weighted norm inequalities and hedging in incomplete markets," Finance and Stochastics, Springer, vol. 1(3), pages 181-227.
- Gatfaoui Hayette & Chauveau Thierry, 2004.
"Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility,"
- Thierry Chauveau & Hayette Gatfaoui, 2004. "Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility," Research Paper Series 122, Quantitative Finance Research Centre, University of Technology, Sydney.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Maxine Collett).
If references are entirely missing, you can add them using this form.