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101 Concepts for the Level I Exam

Concept 94: Put–Call Parity for European Options


European put and call prices are related through put–call parity, which specifies that the put price plus the price of the underlying equals the call price plus the present value of the exercise price.

According to put-call parity,

Fiduciary call = Protective put

  \noindent c${}_{0}$+ ${{X}\over {{\left(1\ +\ r\right)}^T}}$ = p${}_{0 }$+ S${}_{0}$

Assume call and put options with an exercise price of $100 in which the underlying is at $90 at time t=0. The risk free rate is 10% and the options expire in 3 months. The call price is $2. Calculate the put price.

Solution:

  \noindent p${}_{0 }$= c${}_{0}$+ ${{X}\over {{\left(1\ +\ r\right)}^T}}$ - S${}_{0}$ = 2 + 100/1.1${}^{0.25}$ -- 90 = \$9.64