This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be th...This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be the rate at which local volatility will revert to the mean.Then,a B-spline method with proper knot control is applied to interpolate the local volatility matrix.The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix.Finally,empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.展开更多
We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations an...We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.展开更多
文摘This paper studies the traditional local volatility model and proposes:A novel local volatility model with mean-reversion process.The larger is the gap between local volatility and its mean level,the higher will be the rate at which local volatility will revert to the mean.Then,a B-spline method with proper knot control is applied to interpolate the local volatility matrix.The bi-cubic B-spline is used to recover the local volatility surface from this local volatility matrix.Finally,empirical tests show that the proposed mean-reversion local volatility model offers better prediction performance than the traditional local volatility model.
基金support by Deutsche Forschungsgemeinschaft through the Research Training Group RTG 1953.
文摘We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.
