I seem to remember the implied volatility skew of European options decreases as the expiry increases. It is true for the Huston model under some approximation. What are the good references that prove this property in general, or at least asymptotically?
I understand that the [$]v(t)[$] integrated over a time period can be plugged into some model, say Black-Scholes formula to obtain an option price. I was told that some effective variance-time can be obtained from this variance distribution. How is that used?
Let [$]v(t)[$] be the function of the instantaneous variance of an underlying stock or index between the open and close of an exchange, normalized by the total variance. I think this is called variance schedule. How is [$]v(t)[$] used, particularly in options pricing/trading/market making?
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.
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 Stochast...
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 ...
@Alan: I am coming back to this problem after having been tied up elsewhere for a long while. I am now posting the full formula/algorithm which I derived a while ago for computing the theta of the European option under a stochastic volatility process prescribed by Equation (1). It is to avoid taki...
It doesn't make sense to reason with him, ISayMoo. He cannot even calculate a continuous fraction - vide Brainteaser forum. Hahahaa, the desperation! Again, instead of saying anything of substance, you choose to throw yet another tantrum because you do not understand the question and the answer whe...
I know, but nevertheless I am happy that I prodded him to be a bit more rigorous this time. Keep it up like that, young friend, and we'll make something out of you. I do not know whether to laugh or sneer. "Prodded" me to be more rigorous? The irony is written all over the place. And you ...
The [$]\sqrt 7[$] identity is wrong. The continued fraction should be the golden ratio with the only radical being [$]\sqrt 5[$]. So the two side cannot be equal. Could you explain what you mean by that? I posted a derivation of the continuous fraction (something they teach children at primary scho...
You are funny. How did I attack everyone, by pointing out something is wrong? Just point out the specific part of my last post that you think is wrong if you say I have made a mistake. As for the "missing" part, do you see the 4 in your calculator? Do you see a 4 in the painting? Yes or no?
[$]\sqrt{7}=2+\overline{1,1,1,4}[$] where the number under the bar is the periodic integer sequence in the continued fraction. ppauper's calculator confirms this. ppauper missed the 4. So if the continued fraction is indeed for [$]\sqrt{7}[$], there should have been a [$]4[$] below and to the right...