Assume the Black-Scholes framework. For t ≥ 0, let S(t) be the time-t price of a stock that pays dividends continuously at a rate proportional to its price.

Consider a 1-year European gap option. If the 1-year stock price is less than $150, the payoff is 120 − S(1); otherwise, the payoff is zero.

You are given:

(i) S(0) = $120.

(ii) The stock’s volatility is 35%.

(iii) The price of a 1-year 150-strike European put option on the stock is $34.022.

(iv) The delta of the put option in (iii) is −0.638.

(v) The continuously compounded risk-free interest rate is 5%.

Calculate the elasticity of the gap option.