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The assumption of 100% delta for an option would give a good upper estimate for the exposure due only to the part of the option exposure that comes from the movements in the underlying price. But for example, imagine you had a portfolio which is long a long dated call and long a long dated put, such that the portfolio is overall delta neutral over a ...


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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 ...


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Overall you are not mistaken, although it is worth revisiting a few steps in your question. We assume $S$ follows the SDE $$ \dfrac{dS}{S} = \mu\:dt+ \sigma\:dW^\mathbb{P}(t) $$ under the physical measure $\mathbb{P}$. If we change to the risk neutral measure $\mathbb{Q}$ (using Girsanov's theorem) then $\mu \to r$ and we have the following SDE $$ \dfrac{dS}...


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The log-return of a stock over a period $\Delta t $ starting at $t=0$ is defined as: $$ r_{\Delta t} = \ln \left( \frac{S_{\Delta t}}{S_0} \right) $$ Thus you should compute $S_{\Delta t}$ as $$ S_{\Delta t} = S_0 \exp ( r_{\Delta t} ) $$ when you are given the $\Delta t $-period log-return i.e. the one which you sample as you propose above. Thus no ...


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You mix up several things: if you sample from Brownian motion, then $$ B_{t+\Delta t} - B_t $$ is normally distributed with variance $\Delta t$. Thus if you sample a standard normal $Z$ (with variance 1) then you can use $$ \sqrt{\Delta t} Z $$ as sample for $B_{t+\Delta t} - B_t$ in order to get the correct variance. Recall that constant factors enter ...


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There's nothing wrong with your formulation, in my opinion. If you model the rate z_30 with a fixed mean, then indeed the forward ZCB price is long vega. This means that the forward interest rate is short vega (i.e. the 30yr into 10yr forward rate goes down when vol goes up). This is self-consistent. In most textbooks, however, the forward interest ...


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Note that, under measure $Q$, the dynamics is of the form \begin{align*} dS_t = S_t \big[(r+ \sigma \theta_t) dt + \sigma dW_t^Q \big]. \end{align*} Then, for $\Delta>0$ sufficiently small, \begin{align*} S_{t+\Delta} &= S_te^{\left(r-\frac{1}{2}\sigma^2\right)\Delta + \sigma \int_t^{t+\Delta} \theta_s ds + \sigma \left(W_{t+\Delta}^Q-W_t^Q\right)}\\ &...


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in the new measure, the stock has drift $r + \sigma \theta$ so yes you just proceed with that drift as you say. If $\theta$ is time dependent, it gets more complicated.



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