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## Hot answers tagged heston

6

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: $$... 1 You need to obtain a 4 \times 4 correlation matrix. As you effectively observe, you have four random processes driving the system, with i \in 1,2$$ \frac{dS_i}{S_i} = \mu_i dt + \sqrt{v_i} dW_{Si} \\ dv_i = \kappa(\bar{v}_{i}-v_i) dt + \xi \sqrt{v_i} dW_{vi}  Each of the $W_{ji},j\in\{S,v\},i\in 1,2$ is a brownian motion correlated with the others, ...

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