I want to price a path-dependent option (let's say for example an arithmetic average Asian option) under a Heston model. In a Black-Scholes setup, I use forward volatilities to do so. I want to apply the same idea with a Heston model as I'm not only interested in the terminal state of the underlying process, but also in the path by which the final process is reached. So I assume I need to use forward parameters and the only idea I have so far is obtaining time dependent parameters ( Piecewise constant actually) using Elices's Paper (https://arxiv.org/abs/0708.2020) and then using them in a Monte Carlo scheme.

Question : Is there a way to do the same with only static parameters ( 1 set of 5 parameters) using any discrete scheme for Heston such us Milstein or QE.

Thank you.

  • $\begingroup$ When you say static parameters do you mean time independent (more akin to the BS model)? If so then you can use whatever method you want to compute volatilities and calibrate the five parameters for a Heston model (look at historic data/prices for call/put options). Then for a path dependent option you can just use a simple Euler-Maruyama scheme to simulate the paths and compute the running averages needed for an Asian option. $\endgroup$ – oliversm Aug 23 '18 at 19:31

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