# Tag Info

## Hot answers tagged stochastic-volatility

5

To recover the Black-Scholes pricing equation, you should first express the standard normal cdf in terms of its characteristic function analogous to the Heston solution: $$N(x) = \frac{1}{2} - \frac{1}{\pi} \int_0^{\infty} Re [\frac{e^{-i\phi x} f(\phi)}{i\phi}] d\phi$$ where $f(\phi)$ is the characteristic function of the standard normal distribution: $$... 2 I think a sketch of the proof would look like this Let's say you start from$$ S_t = S_t \odot (\mu_t dt + \sigma_t dW_t)  where $S$ is an vector valued process of your $n$ risky assets prices, $W$ a standard $k$-dimensionnal brownian motion under the historic probability, $\sigma_t$ an $n \times k$ matrix valued process and $\odot$ is the Hadamard ...

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