Question

Find the price of a call option with an exercise price of $30 if a put option with the same strike price and maturity sells for $3.00. The options expire in 1 year. The current stock price is $31 and the risk-free rate is 3% compunded continuously.

O $1.64
O $0.84
O $4.89
O $4.87
O $1.72

Answer 1

The price of the call option with the given parameters is $4.87. The correct answer is option d.

Step-by-step explanation:

To find the price of a call option with an exercise price of $30, we can use the put-call parity relationship. According to put-call parity, the price of a call option (C) and a put option (P) with the same strike price and expiration date can be related as:

C + P = S + X / (1 + r)T

where S is the current stock price, X is the exercise price, r is the risk-free rate, and T is the time to expiration. Plugging in the given values, we have:

C + $3.00 = $31 + $30 / (1 + 0.03)1

C + $3.00 = $31 + $30 / (1.03)

C + $3.00 = $31 + $29.13

C = $4.87