Suppose we have an interest-free bond and a stock, both initially priced at $1. We have a two-stage, discrete-time economy where the stock (that is currently worth $1) is worth either $2 or $0.5 in the next time-step. Recall the Butler vs. K-State bet from Dr. Brunick's notes on arbitrage. 1. (40 points) What is the no-arbitrage price p of a compound-bet that pays: (1) $a if Butler wins & stock goes up; (2) $b if Butler wins & stock goes down; (3) $c if Butler looses & stock goes up; (4) $d if Butler looses & stock goes down. BUTER 2. (10 points) As a follow-on to problem 1, what is the no-arbitrage price p of the bet where ab - 2 andc-d- 1? 3. (10 points) As a follow-on to problem 1, what is the no-arbitrage price p of the bet where a c-3 and b-d- -1.5? 4. (40 points) Suppose all your friends think the price of the bet of problem 3 is worth p + a, where a > 0. Create an arbitrage-generating portfolio that will help you pocket Sa from each of your friends Suppose we have an interest-free bond and a stock, both initially priced at $1. We have a two-stage, discrete-time economy where the stock (that is currently worth $1) is worth either $2 or $0.5 in the next time-step. Recall the Butler vs. K-State bet from Dr. Brunick's notes on arbitrage. 1. (40 points) What is the no-arbitrage price p of a compound-bet that pays: (1) $a if Butler wins & stock goes up; (2) $b if Butler wins & stock goes down; (3) $c if Butler looses & stock goes up; (4) $d if Butler looses & stock goes down. BUTER 2. (10 points) As a follow-on to problem 1, what is the no-arbitrage price p of the bet where ab - 2 andc-d- 1? 3. (10 points) As a follow-on to problem 1, what is the no-arbitrage price p of the bet where a c-3 and b-d- -1.5? 4. (40 points) Suppose all your friends think the price of the bet of problem 3 is worth p + a, where a > 0. Create an arbitrage-generating portfolio that will help you pocket Sa from each of your friends