6533b824fe1ef96bd128003e
RESEARCH PRODUCT
European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis
Marco SammartinoCarlo SgarraRussel E. CaflischGaetana Gambinosubject
Transaction costAsymptotic analysisStochastic volatilityAsymptotic AnalysisApplied MathematicsStochastic VolatilityBlack–Scholes modelDynamical Systems (math.DS)Implied volatilityTransaction CostsFOS: Economics and businessOption Pricing; Stochastic Volatility; Transaction Costs; Asymptotic AnalysisValuation of optionstransaction costEconometricsMean reversionFOS: MathematicsCall optionPricing of Securities (q-fin.PR)Mathematics - Dynamical SystemsOption PricingSettore MAT/07 - Fisica MatematicaQuantitative Finance - Pricing of SecuritiesMathematicsdescription
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-01-01 |