Pricing Path-Dependent Options Under the Heston Model

Summary

The document asks how to price an arithmetic-average Asian option under the Heston stochastic-volatility model. The author compares this problem with Black–Scholes pricing using forward volatilities and wonders whether Heston requires time-dependent, piecewise-constant parameters derived from an existing method, then applied in Monte Carlo simulation.

The central question is whether a single static set of Heston parameters can price a path-dependent payoff using a discrete simulation scheme such as Milstein or quadratic-exponential. No answer, derivation, numerical experiment, or pricing evidence is included. The text therefore frames a modeling question rather than teaching a resolved method. It highlights that path-dependent pricing depends on the evolution of the underlying and variance over time, but gives no guidance on calibration, discretization bias, or how static parameters compare with forward parameters.

Key ideas

• The document asks how to price an arithmetic-average Asian option under Heston dynamics.
• It contrasts static Heston parameters with piecewise-constant forward parameters.
• It proposes Monte Carlo simulation and names Milstein and quadratic-exponential schemes as possibilities.
• It does not provide an answer or evidence comparing these approaches.

Tags

# Pricing a Path-Dependent Option with Heston


# Pricing a Path-Dependent Option with Heston












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.

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