Consider the GOOG example from the extra problem of HW 1, assuming risk-free rate is 3%. You purchase a 1-year GOOG butterfly involving calls with strike 750, 870 and 990, whose individual premiums are 60, 20 and 0 respectively. Describe how likely it will be for your butterfly PROFIT function to assume the different values, under the model assumptions stated in HW 1.

HW1 for reference:

• Let S_t denote price of GOOG stock in year t. Today the spot price is S_0=871. S_1 has 40% chance of being 971 and 60% chance of being 771. Find the range of risk-free rates r (recall Math 537 default that risk-free interest rate is per annum with continuous compounding) such that you do NOT create an arbitrage opportunities when you initially take long OR short GOOG stock position at t=0 and then close out your position at t=1. (Note: this is only an arbitrage opportunity due to the model assumptions about S_1. In general, S_1 might reach $10^{100000} or $10^{-100000} and so there is no bound on the range of r)