put call parity

CFA Level II Derivatives
#1

I was hoping to get some help in remembering the formula below:

value of put= value of call + Xe^-rt - spot price

I understand the last part- the value of a put is negative if the stock price is very high…but I need a better way to conceptualize the 1st part of the formula? Why exactly is the value of a put related to the value of the call as shown above?

thnx!

#2

I wouldn’t bother to memorize anything other than the basic put-call parity formula:

p + S0 = c + X / (1 + r)

In words: a protective put is identical to a fiduciary call.

Your formula, and a lot of others, can be derived from that one using simple algebra.

#3

COX = POSO (my mnemonic)

C0 + Xe^-rt = P0 + S0

You can shuffle the above equation to your heart’s content to get the various parity relationships. As well, the sign of each term will tell you if you are long or short that item, i.e. negative = short, positive = long

#4

Careful with your notation there: _ C _0 and _ P _0 refer to American calls and puts, respectively; _ c _0 and _ p _0 refer to European calls and puts, respectively. Put-call parity applies to European options, not American options.

#5

thanks!

#6

My pleasure.

#7

If you wanna get a little lewd remembering it…

Pamela is a Sexy X-Rated Callgirl

P+S = XR + C

XR = X/(1+R)^T