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European Put-Call Parity Applies Across Pricing Models

Article Quant Q&A · Author: Landscape
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Summary

The document answers whether the standard European put-call parity relation also applies when the underlying is modeled with Heston stochastic volatility. Its central point is that parity follows from the option contracts and the ability to construct equivalent payoffs, rather than from a particular pricing model. Thus, changing from Black-Scholes to Heston does not by itself require a different parity relation for European options.

The explanation invokes arbitrage: in a liquid market, a violation of parity among matching European options, the underlying, and the discounted strike would create an opportunity to trade the price difference. The answer is brief and does not derive the replicating positions or discuss dividends, financing details, transaction costs, or American exercise. Those contract and market assumptions matter when applying the relation in practice.

Key ideas

  • European put-call parity is determined by contract payoffs rather than the chosen pricing model.
  • The standard relation therefore applies under Heston as well as Black-Scholes, given matching contract terms.
  • A material parity violation in a liquid market would imply an arbitrage opportunity under the stated assumptions.
  • The brief answer does not address adjustments for dividends or differences in exercise style.

Tags

OptionsDerivatives pricingArbitrage
Full text
# Does the put-call-parity hold for the Heston model?


# Does the put-call-parity hold for the Heston model?












My question is quite simple: Does the Put-Call-Parity hold for the Heston model? My textbook handels the Black-Scholes model with the Put-Call-Parity being

$$p_t = Ke^{-r(T-t)}+c_t-S_t.$$

However, it is not very specific about the assumptions. Does the same formula apply directly to other models (e.g. the Heston-model) or do we need to modify the formula?

## Answer by Kermittfrog (score 2)

https://quant.stackexchange.com/a/70406

The Put-Call-Parity is a characteristic of the contract universe, not the underlying model. For European type options, the parity should always hold (in a liquid market) - else, there'd be an arbitrage opportunity.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.