Question

A put option and a call option with an exercise price of $65 and three months to expiration sells for $2.87 and $4.08, respectively. If the risk-free rate is 4.8 percent per year, compounded monthly , what should the stock sell for?

Answer 1

Put Call Parity Equation : C + X(1+r)^t= S₀ +P

C= Call Option Price=$4.08

P= Put Option Price=$2.87

X= Exercise Price =$65

T= time =3 months

r= risk free rate per month =4.8/12=0.4 i. e 0.004

S₀₌ Spot stock selling price=?

Let us put in equation

$4.08 + $65(1+0.004)³= S₀ +$2.87

$4.08 +$65(1.004)³= S₀ +$2.87

$4.08 + $65 x 1.012048= S₀ +$2.87

$4.08 + $    65.78 = S₀ +$2.87

S₀ +$2.87= $    69.86

S₀ =$69.86-$2.87

S_o=$66.99

The stock selling price should be $66.99