Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation
We consider a discrete-time approximation of paths of an Ornstein–Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler–Maruyama approximation scheme is implemented. We determine the estimates for the opti...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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VTeX
2015-12-01
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| Series: | Modern Stochastics: Theory and Applications |
| Subjects: | |
| Online Access: | https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA43 |
| _version_ | 1818584216939528192 |
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| author | Sergii Kuchuk-Iatsenko Yuliya Mishura |
| author_facet | Sergii Kuchuk-Iatsenko Yuliya Mishura |
| author_sort | Sergii Kuchuk-Iatsenko |
| collection | DOAJ |
| description | We consider a discrete-time approximation of paths of an Ornstein–Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler–Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived. |
| first_indexed | 2024-12-16T08:17:39Z |
| format | Article |
| id | doaj.art-4d41638c7c3d485789339d94554ad331 |
| institution | Directory Open Access Journal |
| issn | 2351-6046 2351-6054 |
| language | English |
| last_indexed | 2024-12-16T08:17:39Z |
| publishDate | 2015-12-01 |
| publisher | VTeX |
| record_format | Article |
| series | Modern Stochastics: Theory and Applications |
| spelling | doaj.art-4d41638c7c3d485789339d94554ad3312022-12-21T22:38:12ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542015-12-012435536910.15559/15-VMSTA43Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. SimulationSergii Kuchuk-Iatsenko0Yuliya Mishura1Taras Shevchenko National University of Kyiv, Volodymyrska str. 64, 01601, Kyiv, UkraineTaras Shevchenko National University of Kyiv, Volodymyrska str. 64, 01601, Kyiv, UkraineWe consider a discrete-time approximation of paths of an Ornstein–Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler–Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived.https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA43Financial marketsstochastic volatilityOrnstein–Uhlenbeck processoption pricingdiscrete-time approximationsEuler–Maruyama scheme |
| spellingShingle | Sergii Kuchuk-Iatsenko Yuliya Mishura Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation Modern Stochastics: Theory and Applications Financial markets stochastic volatility Ornstein–Uhlenbeck process option pricing discrete-time approximations Euler–Maruyama scheme |
| title | Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation |
| title_full | Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation |
| title_fullStr | Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation |
| title_full_unstemmed | Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation |
| title_short | Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation |
| title_sort | option pricing in the model with stochastic volatility driven by ornstein uhlenbeck process simulation |
| topic | Financial markets stochastic volatility Ornstein–Uhlenbeck process option pricing discrete-time approximations Euler–Maruyama scheme |
| url | https://vmsta.vtex.vmt/doi/10.15559/15-VMSTA43 |
| work_keys_str_mv | AT sergiikuchukiatsenko optionpricinginthemodelwithstochasticvolatilitydrivenbyornsteinuhlenbeckprocesssimulation AT yuliyamishura optionpricinginthemodelwithstochasticvolatilitydrivenbyornsteinuhlenbeckprocesssimulation |