# Heston Model Maximum Return Distribution

What is the joint probability distribution of the maximum of the return between time $0$ and $t$ and the return at $t$, for the Heston model, when the return drift is $0$ and the correlation between the equity factor and the variance factor is nonzero?

• quant.stackexchange.com/q/24970/59 doesn't answer your question, but may help. Essentially, you're asking for the chance a limit order at a given price will be filled. – user59 Apr 15 '16 at 14:38
• Thank you, @barrycarter. Though it does not answer my particular question, your answer has a lot of information. I will research it later. By the way, at one glance, for the probability of touch you should note that the accepted answer is wrong and my answer is correct. – Hans Apr 21 '16 at 19:02
• Hmmm, hadn't read that one carefully, you might be right. – user59 Apr 21 '16 at 20:17