Introduction to Mathematical Finance - 2020

Thea, 3. August, 11:00-11:30 They let me in 15 minutes late. 1) Definition of arbitrage, arbitrage opportunity of 1st and 2nd kind 2) Explain the binomial model an its conditions to be arbitrage free 3) What if u=r, what would be an arbitrage opportunity and its associated wealth process. 3) Taking a payoff H, what would be a fair price? -> sellers and buyers price, what are you using when, you are saying that the extended market (with price \pi_b < \pi < \pi_s) is arbitrage free? -> FTAP 4) State the FTAP 1st, which are the easy implications? Prove one of the hard ones. Then he offered me to prove other directions as well. 5) Prove: a local martingale bounded from below is a super-martingale. 6) Prove: a local martingale bounded from below is a true martingale. 7) What is the trinomial model? When m = r and u>r>d, it is easy to see that the market is arbitrage free. What is the explanation? He wanted to here: q_1*u + q_2*r + q_3*d= r and r lies strictly between u and d and this is just a convex combination, so it is easy to see that there actually exists one.