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Church
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heston - piecewise constant mean reversion

April 29th, 2013, 12:36 pm

Hello,I'm looking for the characteristic function of the Heston model in case only the mean reversion level is made piecewise constant.I read that it's a relatively easy adjustment to the usual Heston function, but I cannot find the formula itself anywhere. Suggestions?Thanks.
 
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Alan
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heston - piecewise constant mean reversion

April 29th, 2013, 2:13 pm

Try to do it yourself (there are many related articles) and post questions when you get stuck. The Heston char. function has a simple form phi(T,v,x,z) = E[exp(i z X(T)) | X(0)=x, V(0)=v ] = exp{A(T) + B(T) v} (supressing some dependencies) and this still holds when the parameters are piecewise constant (or general time-varying). It is a matter of solving some ODE's for A(T) and B(T) recursively along the piecewise stretches.These ODE's are found by substitution of the soln form in the Kolmogorov backward eqn.If those ODE's can't' be solved analytically, something like Mathematica could certainly solve them easilynumerically and you would then have it.
Last edited by Alan on April 28th, 2013, 10:00 pm, edited 1 time in total.
 
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mj
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heston - piecewise constant mean reversion

May 2nd, 2013, 11:41 pm

you get Riccati equations for A and B which are solvable.