# Put–Call Parity

Biomian shares trade at a price (S 0) of INR295 per share. VFO is considering the purchase of a six-month put on Biomian shares at an exercise price (X ) of INR265. If VFO’s chief investment officer observes a traded six-month call option price of INR59 per share for the same INR265 exercise price, what should he expect to pay for the put option per share if the relevant risk-free rate is 4%?

Please help me to understand where is put/call/stock/forward in this question. I read and was so confused to place them into the formula to find put price.
Thanks.

This isn’t put-call forward parity; it’s simply put-call parity.

S_0 + p_0 = c_0 + \dfrac{X}{\left(1 + r_{rf}\right)^T}

Fill in the values that you know and solve for p_0.

This is solution from CFA website:

the put–call forward parity relationship is

p 0 – c 0 = [XF 0(T)](1 + r)–T.

Substituting terms and solving for F 0(T) = INR300.84 (= INR295(1.04)0.5),

p 0 – INR59 = (INR265 – INR300.84)(1.04)–0.5.

p 0 = INR23.86.

VFO should expect to pay a six-month put option premium of p 0 = INR23.86.

Their use of forward parity is a little silly:

\left[X - F_0\left(T\right)\right]\left(1 + r\right)^{-T} = \dfrac{X - F_0\left(T\right)}{\left(1 + r\right)^T} = \dfrac{X}{\left(1 + r\right)^T} - \dfrac{F_0\left(T\right)}{\left(1 + r\right)^T} = \dfrac{X}{\left(1 + r\right)^T} - S_0

so,

p_0 - c_0 = \dfrac{X}{\left(1 + r\right)^T} - S_0

or,

S_0 + p_0 = c_0 + \dfrac{X}{\left(1 + r\right)^T}

which is ordinary put-call parity.

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Many thanks. You are so helpful.

My pleasure.