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 stock0s 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 denition of the payos is then GGapCall(S) = (S -K1)1{S>K2}
GGapPut(S) = (K1 -S)1{S
Calculate r