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You are right, the mean is going to be $S_0 e^{\mu t}$. You may want to increase the number of simulations by the way, 1,000 ain’t that many. Since you know $(S_t)$ analytically in closed form, simulating and averaging does not really provide you with any further information. We know all moments of $(S_t)$ in closed-form anyway and can compute probabilities ...


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If you just want a confidence interval for the sigma squared produced by the garch notice that the most popular approach is to assume that the distribution of the estimator is unknown and, as such, use non-parametric methods like bootstrapping. For more info read this answer which is also consistent with other sources like this . On bootstrapping meaning I ...


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The least bad answer would be to use local-currency bond yields. But good luck trying. Local issuance in any real size is a relative novelty of the last decade or so. There's no guarantee there's always a nice clean 10 year note live for every country, like a Treasury, Bund, JGB, Gilt etc.; and no guarantee that if it did exist 20 years ago that it was a ...


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If you check the quantlib documentation you can find, that greeks for american options are only supported if you use a numerical pricing engine and not BAW (which is the default option). Documentation: "Note that under the new pricing framework used in QuantLib, pricers do not provide analytics for all 'Greeks'. When “CrankNicolson” is selected, then at ...


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How you define things should mirror how you invest/trade. In practice, nothing is 100% risk-free. What people call risk-free rate is really what they'd earn if they don't allocate capital away from their risk-neutral position. For the vast majority of US investors, this risk-neutral position is simply USD cash, which earns T-bill rates or some USD deposit ...


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There is no such thing as a risk free rate. That is an abstract academic construct to keep their models as simple as possible. In practice, many treat the USD t-bill rate as "the risk free rate". It isn't actually risk free (eg current t-bill interest rates, even before taxes, are below CPI -- so a t-bill buyer faces a lot of inflation risk). If one ...


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The short answer us that the risk-free curve that you seek is simply the yield curve of the government bonds denominated in local fiat currency. (Nominal, not inflation-adjusted.) It is extremely unusual for governments to default on such bonds (I know of only two recent examples, Russia and Peru in the 1990s). The government can just print more currency to ...


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Result of refined search: https://rpubs.com/thierrymoudiki/33287 High quality material in R. No need to reinvent the wheel.


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As Chris already wrote in his comments: your description is not complete. But I would suggest to write a simple loop over your data matrix. There is no need for working with zoo/xts while doing these computations. I use your sample dataset and call it data0. library("xts") library("zoo") time0 <- index(data0) assets <- colnames(data0) data0 <- ...


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Preliminary Thomson Reuters Datastream is one of the most commonly used and widely accepted data-source for non-US data in empirical finance. Working with financial data is based on many filters prior to any calculations. My answer focuses especially on "data cleaning" methods for Datastream, which are published in academic journals and commonly used in ...


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