I would like to know what the relationship is between the time value of call/puts. From the put call parity formula

$$C-P = S_{t} - PV(K)$$

and that value of call/put options is simply the sum of the intrinsic and time values $$C=(S-K)^++TV_C$$ $$P=(K-S)^++TV_P$$

Does that then imply that the no-arbitrage relationship is that the time value of $C$, $TV_C$, is equal to the time value of $P$, $TV_P$?

  • $\begingroup$ How are your time value defined? Note that, the conditional expectation is linear. $\endgroup$ – Gordon May 14 at 15:00
  • $\begingroup$ Yes, they are the same. it is easier to see if you put your equation in terms of forward value. $\endgroup$ – Brian B May 14 at 15:27

Into the first equation we can substitute $C$ and $P$ as given by the other two equations, we get:

$(S-K)^+ -(K-S)^+ +TV_C - TV_P = S-PV(K)$



If interest rates are zero then $PV(K)=K$ and then we indeed have


Note: as suggested in the comments above a slightly different definition of Intrinsic Value and Time Value might be preferable here. If we define the "modified time values" in the following way



then we would have equality of the (modified) time values for any level of interest rates:


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