1. Assume the Black-Scholes framework. The continuously compounded

risk-free interest rate is r is unknown, but for a non-dividend paying

stock S we know:

The current stock price S₀ = 10

The stocks volatility is 10%.

The price of a 6-month European gap call option on S, with a

strike price of K₁ = 10 and a payment trigger of K₂ = 9.90, is 1.

The price of a 6-month European gap put option on S, with a

strike price of K₁ = 10 and a payment trigger of K₂ = 9:90, is

0.50.

The definition of the payoffs is then

G_GapCall(S) = (S - K₁)1_{{S > K2}}

G_GapPut(S) = (K₁ - S)1_{{S < K2}}

Calculate r.