Put–Call Parity and Implied Volatility Differences in Option Strategies

Summary

The document compares a covered call with a cash-secured put on the same underlying, strike, and expiration. Their similar payoff profiles can still show different displayed maximum gains when the call and put have different prices or implied volatilities. The response points to put–call parity: for European options, call and put prices are linked by the underlying price, strike, and the present value of the strike. Given an assumed spot and strike, it uses this relationship to explain the expected price difference when the options share a consistent implied volatility.

The explanation is tentative because the prompt does not provide full contract details or market data. It flags American exercise as a reason parity may not hold in the same form, and supply-demand or liquidity effects as possible sources of observed pricing discrepancies. It does not establish that liquidity alone explains the screenshots, and the parity calculation depends on assumptions about rates, timing, and the quoted prices.

Key ideas

• Put–call parity links call and put prices for matching European options.
• The underlying price and discounted strike determine the parity relationship.
• A covered call and a cash-secured put can have different quoted implied volatilities when prices depart from parity.
• American exercise and market supply-demand can affect observed deviations.
• The example offers an intuition rather than a complete diagnosis of the screenshots.

Tags

# What accounts for the difference between these two option strategies?


# What accounts for the difference between these two option strategies?












Same underlying, same strike, same expiration. One is a covered call, the other is cash secured put.

These are screenshots taken from a website. As you can see, they are similar, but the max win levels are different.

The implied vols seem to be different. Is this simply due to the two options having slightly different liquidity?

## Answer by KaiSqDist (score 1)

https://quant.stackexchange.com/a/78092

In theory, Calls and Puts should have the same IV via Put-Call Parity. However, sometimes they do not exactly obey:

- Are the options American? American options do not obey PCP (Why is IV different between put and call of same strike)

- Perhaps just due to demand and supply they do not obey PCP. In this case, I see that the prices of the two strats are the same? But via PCP (I guess the current spot price is 136.8):

\begin{equation} C - P = S_0 - Ke^{-r(T-t)} = 136.8 - 130.0 = 6.8 \end{equation}

Therefore, the call should be above the price of the put by 6.8 to have the same IV. That's just my intuition on your problem, please feel free to correct/clarify/add more details/inquiries.

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.