Option pricing via maximization over uncertainty and correction of volatility smile
The paper presents a pricing rule for market models with stochastic volatility and with an uncertainty in its evolution law. It is shown that the most common stochastic volatility models allow a possibility that the option price calculated for random volatility with an error in volatility forecasts...
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| Format: | Journal Article |
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World Scientific
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/19216 |
| _version_ | 1848749969076387840 |
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| author | Dokuchaev, Nikolai |
| author_facet | Dokuchaev, Nikolai |
| author_sort | Dokuchaev, Nikolai |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The paper presents a pricing rule for market models with stochastic volatility and with an uncertainty in its evolution law. It is shown that the most common stochastic volatility models allow a possibility that the option price calculated for random volatility with an error in volatility forecasts is lower than the price for the market with zero error of volatility forecast. To eliminate this possibility, we suggest a pricing rule based on maximization of the price via a class of possible equivalent risk-neutral measures. It shown that, in a Markovian setting, this pricing rule requires to solve a parabolic Bellman equation. Some existence results and a priory estimates are obtained for this equation. |
| first_indexed | 2025-11-14T07:29:22Z |
| format | Journal Article |
| id | curtin-20.500.11937-19216 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:29:22Z |
| publishDate | 2011 |
| publisher | World Scientific |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-192162019-02-19T05:34:59Z Option pricing via maximization over uncertainty and correction of volatility smile Dokuchaev, Nikolai uncertain volatility stochastic volatility Hamilton–Jacobi–Bellman equation volatility smile Diffusion market model The paper presents a pricing rule for market models with stochastic volatility and with an uncertainty in its evolution law. It is shown that the most common stochastic volatility models allow a possibility that the option price calculated for random volatility with an error in volatility forecasts is lower than the price for the market with zero error of volatility forecast. To eliminate this possibility, we suggest a pricing rule based on maximization of the price via a class of possible equivalent risk-neutral measures. It shown that, in a Markovian setting, this pricing rule requires to solve a parabolic Bellman equation. Some existence results and a priory estimates are obtained for this equation. 2011 Journal Article http://hdl.handle.net/20.500.11937/19216 10.1142/S0219024911006711 World Scientific fulltext |
| spellingShingle | uncertain volatility stochastic volatility Hamilton–Jacobi–Bellman equation volatility smile Diffusion market model Dokuchaev, Nikolai Option pricing via maximization over uncertainty and correction of volatility smile |
| title | Option pricing via maximization over uncertainty and correction of volatility smile |
| title_full | Option pricing via maximization over uncertainty and correction of volatility smile |
| title_fullStr | Option pricing via maximization over uncertainty and correction of volatility smile |
| title_full_unstemmed | Option pricing via maximization over uncertainty and correction of volatility smile |
| title_short | Option pricing via maximization over uncertainty and correction of volatility smile |
| title_sort | option pricing via maximization over uncertainty and correction of volatility smile |
| topic | uncertain volatility stochastic volatility Hamilton–Jacobi–Bellman equation volatility smile Diffusion market model |
| url | http://hdl.handle.net/20.500.11937/19216 |