A put option that expires in six months with an exercise price of $30 sells for
ID: 2761728 • Letter: A
Question
A put option that expires in six months with an exercise price of $30 sells for $4.10. The stock is currently priced at $27, and the risk-free rate is 3.2 percent per year, compounded continuously.
What is the price of a call option with the same exercise price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
A put option that expires in six months with an exercise price of $30 sells for $4.10. The stock is currently priced at $27, and the risk-free rate is 3.2 percent per year, compounded continuously.
Explanation / Answer
As per Put Call Parity Theory:
-Vc + Vp = - VS +PV( E )
where Vc =Value of Call option.
Vp = Value of put option.
VS = Current value of Stock
PV( E ) = Present Value of Strike / Exercise Price. = Excercise price *( 1+ rate*time)
- Vc + 4.10 = -27 + 30 * ( 1+ 0.032 *.0.5)
Vc = $0.62