Title : Approximation of the local time of a sticky diffusion and applications
Abstract : We show that the local time of a sticky diffusion can be approximated by certain kind of high-frequency path statistics. This generalizes results of Jacod for smooth diffusions. We prove various form of the result that depend on the type of normalizing sequence we use. We then use the result to:
1. devise a consistent stickiness parameter estimator,
2. assess the behavior of number of crossing statistics,
3. (if time allows) assess the convergence rate of discrete-time hedging strategies in a "sticky Black-Scholes model".
Approximation of the local time of a sticky diffusion and applications
Abstract : We show that the local time of a sticky diffusion can be approximated by certain kind of high-frequency path statistics. This generalizes results of Jacod for smooth diffusions. We prove various form of the result that depend on the type of normalizing sequence we use. We then use the result to:
1. devise a consistent stickiness parameter estimator,
2. assess the behavior of number of crossing statistics,
3. (if time allows) assess the convergence rate of discrete-time hedging strategies in a "sticky Black-Scholes model".
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