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 = [X – F 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.
1 Like
Many thanks. You are so helpful.