# Questions tagged [geometric-brownian]

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### Equivalence of Call Option on $S_T$ and Put Option on $\frac{1}{S_T}$ in FX Markets

Part 1: I am trying to price an option in the FX world. It naturally pays in the domestic currency, but in this case the payout currency must be the foreign currency. For example, consider the payoff: ...
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### How to compute the Present Value of this path-dependent option?

I have an option whose payoff depends on its value at two times $T_1$ and $T_2$ as follows. $$V(t) = \mathbb{E}^{Q}[\mathbb{1}_{S(T_1)>B} (S(T_2)-K)^+)],$$ where the stock price follows the GBM ...
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### Deriving Law of Motion by Ito's Lemma

I've been trying to derive the law of motion for the stochastic process above using Ito's Lemma, given Geometric Brownian Motion with it's law of motion shown below: I've managed to take the partial ...
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### Do simulated values for IV need to be linked to the simulated series of underlying prices when used together in a Monte Carlo Simulation?

I've been using thousands of simulated stock price series generated with mean and standard deviation of daily returns and Geometric Brownian Motion, and then running these simulated price series ...
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### Geometric Brownian Motion simulation in Python: strange results

I am trying to simulate Geometric Brownian Motion in Python, however the results that I get seem very strange and in my opinion they can't be correct. My goal is to simulate each day of 1 year. ...
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### Copula analytic formula for $max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}}$

Consider the payoff function $$V_T = max(S_T^1 - K, 0) 1_{\{L<S_T^2<U\}} = (S_T^1 - K)1_{\{S_T^1 > K\}}1_{\{L<S_T^2<U\}}$$ where $S_T^1$ and $S_T^2$ are two GBM distributed stocks with ...
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### Volatility of a function of an asset

Suppose that $G$ is a function of the underlying asset $S$, which follows a geometric Brownian motion. Suppose that $\sigma_{S}$ and $\sigma_{G}$ are the volatilities of $S$ and $G$, ...
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