 # Put-call parity and value of options with Time, RFR changes

Hi all, I am trying to get this straight in my head, and as a means of understanding the option of a. Longer Time to expiration. b. Increase in RFR on the value of Put and Call options. From the Put-Call parity S + P = C + X/((1+rf)^t) Now lets say t increases P = C + X/((1+rf)^t) - S (1+rf)^t will increase, so X/((1+rf)^t)) will reduce so P will reduce. C = S + P - X/((1+rf)^t) So C will increase rf Increases same logic So in net effect rf increases, t increases --> P reduces, C increases. Is that correct? There is a statement

cpk, the logic seems correct as long as you hold the other variables constant. P = C + X/((1+rf)^t) - S (1+rf)^t will increase, so X/((1+rf)^t)) will reduce so P will reduce… if you hold C, X, RFR and S constant -------> P will decrease C = S + P - X/((1+rf)^t) So C will increase … if you hold S, P, X and RFR constant ----------> C will increase Unfortunately, in real life as further the expiration is “away” the higher the option price for calls and puts (higher intrinsic value) due to the fact that there is a probability to end in-the-money. Or in other words, you cannot keep C and P constant when increasing t. Hope this helps.

cpk123, you are right about RFR. The effect of time is explained differently. In general, the longer the time to expiration, the more valuable the option (both put and call), b/c that means more volatility and more chance that the option will be in the money. However, we can’t be absolutely positive about that for European Puts, b/c we can’t exercise early and the lower bound is: X/(1+RFR)^T-t - St if T is greater, X/(1+RFR)^T-t decreases. This decreases the value of the pay-off @ expiration (since you can’t exercise early). The question is which effect is stronger - increase in value b/c of more time to expiration or decrease in potential payoff? The conclusion: 1)If volatility is high and int. rates low, the time effect will be dominant and the value will be larger than that of a similar shorter term E Put. 2)If volatility is low and int rates high, the int. rates are dominant factor and the value of longer term E Put can be less that a shorter term E Put

sorry needs to be time value… Unfortunately, in real life as further the expiration is “away” the higher the option price for calls and puts (higher TIME VALUE) due to the fact that there is a probability to end in-the-money. Or in other words, you cannot keep C and P constant when increasing t.

Thanks guys… helps crystallize the idea and get a hold of the concept… this discussion… CP