Sandwiched Volterra Volatility (SVV) models are a class of models able to capture both the long memory and the rough aspects of volatility as well as complying with many of the stylised features typical of volatilities. We present the model and its properties. We then discuss questions of quadratic hedging. Particularly, while the theoretical solution is characterised in terms of the non-anticipating derivative for all square integrable claims, the fact that these models are typically non-Markovian provides a concrete difficulty in the direct computation of conditional expectations at the core of the explicit hedging strategy. To overcome this difficulty, we propose a Markovian approximation of the model which stems from an adequate approximation of the kernel in the Volterra noise.
The presentation is based on joint work with Anton Yurchenko-Tytarenko (UiO, Statkraft)
Stochastic optimal control for quadratic hedging in presence of memory
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