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What is AJD option pricing? - Mathematical finance
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Define the Fourier transform inversion of the conditional expectation \begin{align*} G(a,b,y) &= EQ\left[\exp\left(-\int_0^{T}R(X_s)ds\right)e^{a^TX_T}\mathbb{1}_{bX_T\leq y}\right]\\ &=\frac{\psi(a,X_0,T)}{2}-\frac{1}{\pi}\int_0^{\infty}\frac{\Im(\psi(a+ivb,X_0,T)e^{-ivy})}{v}dv \end{align*} The $i$th entry in $X$ is the log asset price and $k=log(K)$, the log strike. $d$ is a vector whose $i$th element is $1$, else zero. The corresponding call option price is \begin{equation*} C=G(d,-d,-k)-KG(0,-d,-k) \end{equation*}
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