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.
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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)
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- 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.
- Gatfaoui Hayette & Chauveau Thierry, 2004. "Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility," Finance 0404002, EconWPA.
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