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Put-Call Parity and the Forward-Value Difference Between Options

Article Quant Q&A · Author: quantum
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Summary

The exchange explains how put-call parity links a call, a put, the underlying share, and the discounted strike. Rearranging the parity relation shows that the call premium minus the put premium equals the share price less the present value of the strike. This difference is the value of a forward position with that delivery price, rather than the call’s conventional intrinsic value, which is based on the immediate exercise payoff and cannot be negative.

The answers also clarify that a call and put with identical terms cannot both be in the money or both out of the money at once; their exercise payoffs differ according to the relationship between spot and strike. The exchange offers a concise algebraic and economic interpretation, but does not develop a full option-pricing model or discuss adjustments such as dividends, funding conventions, or exercise style. Its notation uses “IV” in a nonstandard way, so readers should distinguish the forward-value difference from implied volatility and standard intrinsic value.

Key ideas

  • Put-call parity equates a share plus a put with a call plus the discounted strike.
  • The call-put premium difference is the spot price minus the present value of the strike.
  • That difference represents the value of a forward position with the strike as delivery price.
  • Standard intrinsic value is an immediate exercise payoff and differs from the forward-value expression.

Tags

OptionsDerivatives pricing
Full text
# Put-Call Parity; Time Value of Money


# Put-Call Parity; Time Value of Money












The intrinsic value of a call option is found by subtracting the discounted strike price from the current share price:

$IV = S - X/e^{rT}$

Put-Call parity:

$S + p = c + X/e^{rT}$

$c = p + (S - X/e^{rT})$

Since the second term is literally the definition of the intrinsic value of a call, should the time value of the call option $(c-IV)$ be equal to the value of a put with the same strike price???

What is the economic intuition?

## Answer by KaiSqDist (score 1)

https://quant.stackexchange.com/a/77463

Mathematically (not economically) speaking, an ITM (OTM) call option should be worth more (less) than the OTM (ITM) put option by a value equal to your "IV" (spot minus strike). Also, IV in quant finance is more commonly used to abbreviate implied volatility IMO.

Edit. My point is that it is not possible for a call and put with same option characteristics to be both ITM or OTM, they must differ by an amount, which is the "IV" in this case.

## Answer by Thomas Hausdorff (score 1)

https://quant.stackexchange.com/a/84029

Economically the intinsic value of a strike is the value of a forward of that stike which is the difference in the option premiums.

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.