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4

Assume that your stationary time series (here a daily close-to-close log-returns' series) is modelled as follows $\forall t \in \mathcal{T}=\{1,...,N\}$ \begin{align} r_t &= E_{t-1}[r_t] + \epsilon_t \\ &= E_{t-1}[r_t] + \sigma_t z_t \end{align} with $z_t \sim N(0,1)$ and $\{z_t\}_{t \in \mathcal{T}}$ are IID. The above equations suggest that, ...


1

This reference price is also sometimes called intrinsic price. One of the simplest ways to improve it in regards to the mid-price (assuming you have the depth data) is the following: define a parameter: the size of a hypothetical market order. Let's say it's about the typical sum of first 3-10 order book levels of the instrument; execute a Buy order with ...


0

When you are solving for the local vol in the non mean reverting model, you will find that it also depends on strike. Thus, you can only match vanilla options prices between the two models for a single strike. Let's say that you pick a strike K>0 for which you match the vanilla option price. The you will find that for strike B, where B>K, the mean ...


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Kalman filter (or similar methods) are quite well suited to deal with observations that are of different sampling frequencies and/or asynchronous.



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