Question

A call and a put are held in a diversed portfolio & they both have an exercise price of $140

The Spot price of the stock is $100

Risk free rate is 6%.

Use Put-Call Parity for A& B

A. The premium for the Call is $15.00, what is the Premium for the Put, given both options expire in 1.5 years?

B. The Premium for the Put is $3.00 and both options expire in 3.5 years, then how much is the Premium for the Call option?

(Solve using continuous compounding for A & B and show formula/steps)

Answer 1

Put call parity

X = $140

S = $100

r = 6% = 0.06

A. The premium for the Call is $15.00, what is the Premium for the Put, given both options expire in 1.5 years?

100 + P = 140 * e^(-0.06 * 1.5) + 15

P = 140 * e^(-0.09) + 15 - 100

P = $42.950365938

B. The Premium for the Put is $3.00 and both options expire in 3.5 years, then how much is the Premium for the Call option?

100 + 3 = 140 * e^(-0.06 * 3.5) + C

C = 103 - 140 * e^(-0.21)

C = -$10.4817944358

Note that it is impractical for a call option to have negative value. So, clearly the price of put option is mispriced.

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