Does anyone know a reference where I can find the pricing formulas for vanilla calls in the affine stochastic volatility jump diffusion class of models such as SVJ and SVJJ?
I am looking for something analogous to the following formulas which apply to the Heston (square root) affine stochastic volatility model:
\begin{align} c(t) & = \frac{e^{-\alpha\log K}}{\pi}\int_0^\infty dv e^{-i v \log K}\rho(v) \\ \rho(v) & = \frac{e^{-r(T-t)}\phi(v-i(\alpha+1);T)}{\alpha^2+\alpha-v^2 + i(2\alpha+1)v} \\ \phi(u;T) & = \mathbb{E}^{Q_B}_t[e^{i u \log S(T)}], \\ \phi(u;T) & = e^{i u[\log S(t)+(r-\delta)(T-t)]-\frac{1}{\sigma_v^2}\left[\bar{v}\kappa\left(a(T-t) + 2\log\beta\right)+v_0 \gamma \right]} \\ \beta & = \frac{1-ge^{-d (T-t)}}{1-g} \\ \gamma & = \frac{a(1-e^{-d (T-t)})}{1-g e^{-d (T-t)}} \\ d & = \sqrt{(i\rho \sigma_v u - \kappa)^2 + \sigma_v^2(iu + u^2)} \\ g & = a/b \\ a & = i\rho\sigma_v u-\kappa + d \\ b & = i\rho \sigma_v u-\kappa - d \end{align}
