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The Feller condition applies without modification. That is under the assumption that $v$ is square-root process with poisson-arrival jumps (as you wrote), and assuming the jump distribution is strictly positive and initial level $v_0>0$. The reason is, conditional on no jumps occuring, the process is just a square root process, for which the references ...


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Mark Joshi has pretty much solved it. To add to it, you can see that from Feynamn Kac (see remarks in http://en.wikipedia.org/wiki/Feynman–Kac_formula ) it follows that $$ F(t,S,v) = B_t \mathbf{E}\left[ \frac{ \sqrt{ S_T } }{ B_T } \big \vert S_t = S, v_t = v \right], $$ where the expectation is taken with respect to a measure where $W$ and $Z$ are ...


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Show that the discounted expectation price of the new security is the same as the solution of the PDE. Once this is done all three assets have discounted price processes which are martingales so there can be no arbitrage.


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Actually BS model is still applicable in the market where the upwards/downwards move is much more probable than move in the opposite direction. The Black-Scholes price process model has the form: $\frac{dS}{S} = \mu dt + \sigma dW$ And with significantly non-zero $\mu$ (called drift) it will capture just what you are talking about. Quite surprisingly, the ...


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Well if you think that this model represents reality more accurately than the Black-Scholes assumptions. A lot of people do indeed think so. But I wouldn't say you're "tweaking" Black-Scholes... you're just assuming another model altogether and you will use risk-neutral pricing to compute the fair value of the option at time $t$, just like BS. Frankly, I'm ...


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There is a qualitative shift in the shape of the density. When V is small it is monotone decaying. When V is large it looks more like a Gaussian. Another reason he uses two schemes is that he wants match two moments of the density. When V is small, the moment matching equations for the quadratic Gaussian are unsolvable. When V is large they are unsolvable ...



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