valuing a put option

CFA Level I Derivatives
#1

When using put-call parity to value a put, why is it that we add the value of the call + the value of the strike P discounted + the value of the stock’s CFs discounted - spot P of the stock?

Can someone help me make sense of the formula as whole? I thought we started with S+P=B+C so where do the doicounted CFs of the underlying stock come into play?

Thanks,

#2

The put call-parity consists of two parts:

  1. Protective Put: put option § + stock long investment (S0) = P + S0 2. Fiduciary Call: call option + zero coupon bond with maturity equal to both options and a par value also equal to the strike price of both options (X) = C + X /(1+r)^T Note that you need to discount the zero bond with the risk-free rate r (no default assumption) by the years to maturity T.

You have now:

P + S0 = C + X /(1+r)^T

This is the fomula before maturity of the options/bonds. Note that at maturity T= 0 and (1+r)^T becomes 1 so that you just get:

P + S0 = C + X

With both formulas you can assume different stock prices for a given excercise price (e.g. 100) and you’ll see that you get the same payment streams on both sides of the equation, i.e. you can derive the price of a call out of a put and vice versa,

Best, Oscar