Consider a “sad” 1-year European contingent claim on a stock. You are given:

(i) The time-0 stock price is 70.

(ii) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%.

(iii) The continuously compounded risk-free interest rate is 6%.

(iv) The time-1 payoff diagram (not drawn to scale) of the contingent claim is described by the following “sad” face:

Let C(K₁, K₂) be the time-0 price of a 1-year European gap call option on the above stock with a strike price of K₁ and a payment trigger of K₂. Let P(K₁, K₂) be the time-0 price of an otherwise identical gap put option.

Determine whether each of the following is a correct expression for the time-0 price of the contingent claim.

(A) P(70, 60) + C(70, 80) + 10e^−0.06

(B) C(70, 60) + C(70, 80) − 70e^−0.03 + 80e^−0.06

(C) C(70, 60) + C(70, 80) − 70e^−0.03 + 70e^−0.06

(D) P(70, 60) + P(70, 80) + 70e^−0.03 − 60e^−0.06

(E) P(70, 60) + P(70, 80) + 70e^−0.03 − 70e^−0.06

Transcribed Image Text:

Payoff 80 20 10 60 80 140 Time-1 stock price