A put option that expires in six months with an exercise price of $30 sells for

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

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