Heston model can be used to find prices of options under stochastic volatility. How do I include jumps in the model, so that I end up with a different stochastic volatility curve? References to literature would be helpful.
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3 Answers
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Yes!
But if you don't know the black-scholes basics well consider to read the book "Paul Wilmott in Quantitative Finance" before to go to Stochastic Volatility models and models with jumps.
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don't know If I understand well your question, but If you want to have a rather complete perspective about the affine class of models (to which Heston's model belongs), you better study Duffie et al. (2000). In this very important contribution you'll find many examples of jump specifications
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You can start with Wilmott:
$dS_t = \mu S_t dt +\sigma S_t dZ_t + (J-1)S_t dq_t$
where the Poisson Process
\begin{equation} dq_t =\begin{cases} 0, & \text{with prob $1-\lambda(t)dt$}\\ 1, & \text{with prob $\lambda(t)dt$} \end{cases} \end{equation} Also assume that jump arrival rate $\lambda(t)$ is independent of stock price
Assuming a known jump size $J$ is simple but somewhat unrealistic, one can assume some distribution of jump size. For example, Merton's jump diffusion models assumes $J$ to be lognormally distributed.
Note however, that in the case of random jump size, there's no replicating portfolio so there is no self-financing hedge.
