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### delta-gamma-vega VaR approximation: how to calculate the delta volatility?

If you use historical VaR, i.e. reprice the portfolio under many historical market move scenarios, then you need not assume anything about the distributions of the market factors. But you need ...
1 vote

In the original Black-Scholes-Merton model, with the interest rate $r$ and the dividend yield $q$ constant, you have $$c = S e^{-q \left(T - t\right)} \Phi \left(d_1\right) - Ke^{-r \left(T - t\right)... 1 vote ### Derivation of Call Theta from Black Scholes Model You have a great website that show the derivation, step by step. It involves both the chain rule and product rule. https://quantpie.co.uk/bsm_formula/bs_theta.php If there is a step you don't ... 1 vote ### Dollar gamma formula and its derivation The correct formula is:$$ \Gamma_{DV\$} = { 1 \over 2 } \Gamma (S * 1 \%)^2 $$Gamma dollars is the change in the delta dollars for a 1% change in underlying around price S. Depending on what you're ... 1 vote ### Derive vega for Black-Scholes call from this formula? The answer by @Gordon is pretty complete, but let me add one more point. Let n(x) = N'(x) be the PDF of standard normal distribution. In the derivation, note that$$ e^{d_+^2/2 - d_-^2/2} = \frac{n(...

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