Put call forward parity

CFA Level I Derivatives
#1

Forward plus risk free bond equal call plus risk free bond.

Is it correct formula ?

Why it contradicts with book ?

#2

This is not the formula. The formula for put call parity is the following:

Stock + Put = Call + X (risk free zero coupon bond payoff)/ (1+r)t

Protective put = Fiduciary call

The forward version replaces the stock value with a forward contract:

F/(1+r)t + Put = Call + X (risk free zero coupon bond payoff)/ (1+r)t

Put = Call + (X-F)/(1+r)t

#3

How can you replace So with Fo(T)/(1+r)t ? As per the curriculum

risk free bond + Forward = Asset

Would you please explain.

#4

What’s the arbitrage-free forward price?

F0(T) = S0(1 + r)T

Solve for S0:

S0 = F0(T) / (1 + r)T

#5

So, even if we are replacing S0 with the no Arbitrage forward price -

  • what does F0(T)/(1+R)^T represent because the price of forward at inception is Zero (we don’t pay anything). In the book it seems they take it as long forward but for forward we are not paying anything at inception. To me it seems like long risk free bond with FV = F0(T)
  • Also as mentioned before - In the book it is written -
    Long Asset = Long Forward + Long risk Free asset. So, Where did the risk free asset go?
#6

The present value of a liability.

It pays off the liability.

#7

Thank you. So, basically the present value of liability is the future forward obligation and hence liability. The risk free asset ensures we have the amount in future to pay off this liability. So, the equation becomes -
Long Forward + Long Put = Long Call + Long Risk Free Bond

#8

Yup.

#9

Thank you for always helping CFA candidates. I am grateful!

#10

My pleasure.