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lovenatalya
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Re: Positive Heston European call theta

August 23rd, 2018, 6:00 pm

Sorry for the confusing notations in my paper. Thank you, Alan, for your suggestion. The link for the Broadie and Kaya paper is broke though. Is the following paper what you are referring to?
 
Broadie, M., and Kaya, O., (2004), Exact Simulation of Option Greeks under Stochastic Volatility and Jump Diffusion Models, in Proceedings of the 2004 Winter Simulation Conference, eds: R.G. Ingalls, M.D. Rossetti, J.S. Smith, and B.A. Peters, The Society for Computer Simulation


lovenatalya
 
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Alan
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Re: Positive Heston European call theta

August 23rd, 2018, 6:08 pm

You're welcome.

It's slightly different: "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes", Operations Research, 54(2), 2006, 217-231

Strange on the link. It continues to work for me, again: 
http://www.columbia.edu/~mnb2/broadie/A ... r_2006.pdf
 
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lovenatalya
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Re: Positive Heston European call theta

August 23rd, 2018, 6:41 pm

@Alan:

Now it works. Probably it was a temporary glitch. Thanks again.
 
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lovenatalya
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Re: Positive Heston European call theta

August 24th, 2018, 7:05 am

Alan:

Broadie, M., and Kaya, O., (2006), Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes", Operations Research, 54(2), 2006, 217-231 
[simulation paper thereafter]

defers to  

Broadie, M., and Kaya, O., (2004), Exact Simulation of Option Greeks under Stochastic Volatility and Jump Diffusion Models [Greeks paper thereafter]

for application of their exact simulation algorithm to the computation of Greeks. 

In their Greeks paper, they show the method to simulate Delta, Gamma and Rho but not Theta. I would say Theta is quite different from the Greeks they have calculated as it involves shifting the whole path. So my contribution is novel.
 
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Alan
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Re: Positive Heston European call theta

August 24th, 2018, 2:42 pm

Maybe so, but I think it needs discussion (in a revised write-up). 

Take the Black-Scholes model. It is trivial to differentiate the Black-Scholes formula w.r.t. "t" , holding other parameters constant, to get Theta for that model. As we have time-homogeneity, it is equally trivial to differentiate w.r.t. T, the option maturity time. What is the relationship of "shifting the whole path" to these trivial calculations? (honest question, but one for the write-up, not here).

Under stochastic vol conditioning (i.e., mixing), the Black-Scholes formula also appears -- now inside an expectation. Why can't we again differentiate that formula to find Theta, as Brodie & Kaya do for the other Greeks? Is the time-homogeneous case special? Why? 

All these questions need discussion, IMO -- again, in the write-up, not here. I am just elaborating on my earlier suggestions, assuming you want to create a more readable write-up.
 
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lovenatalya
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Re: Positive Heston European call theta

August 24th, 2018, 3:56 pm

These are good suggestions. I will address these issues in my write-up. I most likely will not be able to get to it until some time next week though. I will inform you after I have revised my paper. Thank you again, Alan.