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Using Put-Call Parity to Infer a Stock Forward Price

Article Quant Q&A · Author: Kirill
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Summary

The document addresses how option prices can reveal a stock’s forward price for a specified maturity. Its main method is to compare calls and puts with the same expiration and identify the strike where their prices are equal. Under put-call parity, that strike corresponds to the forward price, assuming the options and underlying are aligned in maturity and other contract terms.

It also notes that interest rates and dividend yield can help determine a forward level when those inputs are known. The discussion warns against interpreting an option premium as simply the discounted expected excess of the stock price over the strike: option value is affected by convexity. The answers are brief and provide no numerical example or treatment of market frictions, so they do not establish how to handle bid-ask spreads, discrete strikes, early exercise, or mismatched option contracts. The parity method identifies a no-arbitrage forward price; it should not be confused with an unqualified forecast of the stock’s realized future price.

Key ideas

  • For a given maturity, the strike where matched call and put prices coincide indicates the forward price under put-call parity.
  • Interest rates and dividend yield can also be used to derive a forward stock level.
  • An option premium is not simply the discounted expected stock price above the strike.
  • The parity inference assumes the options are comparable in maturity and contract terms.
  • A forward price is a no-arbitrage value, not necessarily a forecast of the realized stock price.

Tags

OptionsEquitiesDerivatives pricing
Full text
# How to compute the expected stock price from option prices?


# How to compute the expected stock price from option prices?












I need to extract expected future stock price from an option price. Could anyone please suggest me how I could do this?

## Answer by Janthelme (score 1)

https://quant.stackexchange.com/a/32198

If by "expected future stock price" you mean the stock's "forward price" for a given maturity (eg 1 year forward), F, then look at the price of all puts and all calls for this maturity, find the strike K such as the price of the put for this strike equals the price of the call for the same strike, C(K) = P(K), and K should be the forward stock price you are looking for, F = K. This comes from the Put-Call parity.

## Answer by Stefan Müller (score 1)

https://quant.stackexchange.com/a/32277

As Janthelme said the Put-Call Parity is the best approach. Nevertheless if you have enough Information you can also use the Interest Rate and the Dividend Yield to come up with an expected Future Stock level.

But remarkt the convexity of an option. Hence the todays premium is not equal the discounted value of E[S]-K.

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.