2
$\begingroup$

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}

$\endgroup$
2
$\begingroup$

Do these work for you?

P34 of http://web.mit.edu/junpan/www/SVJ.pdf

P1360 of http://www.darrellduffie.com/uploads/pubs/DuffiePanSingleton2000.pdf

P2045 of http://www.math.ku.dk/~rolf/bakshi.pdf

$\endgroup$
1
$\begingroup$

One of these two books may help you:

They are both from the same author. Both price European vanilla options under various stochastic processes.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.