Rough path theory provides a rigorous framework to analyse differential equations driven by highly irregular signals, such as those encountered in stochastic differential equations (SDEs). By ...
We study the small time path behavior of double stochastic integrals of the form $\int_{0}^{t} (\int_{0}^{r} b(u) dW(u))^{T} dW(r)$, where W is a d-dimensional Brownian motion and b is an integrable ...
Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options
In this paper, we consider a large class of continuous semi-martingale models and propose a generic framework for their simultaneous calibration to vanilla and no-touch options. The method builds on ...
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