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Tagged with normal-distribution options
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In Black-Scholes, why is $\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t)}$?
I don't understand why in the formula
$$\log{\frac{S_{t+\triangle t}}{S_t}} \sim \phi{\left((\mu - \frac{1}{2}\sigma^2)\triangle t, \sigma^2 \triangle t\right)}$$
the mean is $(\mu - \frac{1}{2}\sigma^...
- 73
4
votes
1
answer
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How to use the Feymann-Kac formula to solve the Black-Scholes equation
I have the Black-Scholes equation for European option with maturity $T$ and strike $K$
$$\begin{cases}\frac{\partial u}{\partial t} = ru - \frac{1}{2} \sigma^2 x^2 \frac{\partial^2 u}{\partial x^2}-r ...
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