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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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Given the well-known stylised facts of equity markets, I would go for a generic stochastic volatility model where log-asset prices, hence geometric returns, are driven by a standard Brownian motion (although this would explain the lack of returns' auto-correlation, it would also boil down to assuming their independence, which is a stronger assumption). ...


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I presume you talk about local time. I hope it can help you : http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511662980&cid=CBO9780511662980A011


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Let $X^h$ be your hourly process Let $X^d$ be your daily process Let $\delta$ be one day you have $$X^d_t=\frac{1}{\delta}\int_{t-\delta}^{t}X^h_s ds$$ $$dX^h_t = a(b-X^h_t)dt + \sigma dB_t$$ $$\Delta X^d_t := X^d_{t+\delta}-X^d_t =\frac{1}{\delta}\int_{t-\delta}^t\left(X^h_{u+\delta}-X^h_{u}\right)du$$ so it is a gaussian random variable by knowns ...


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You can aggregate your starting hourly data to obtain daily data and re-estimate the parameters, then simulate. Alternatvely, with your parameters already obtained, you can simulate hourly data and make a post-simulation aggregation to have daily data.



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