3. 3 points. Consider a stock with current price S0=$60. The value of the stock at time t=1 can take one of two values: S1,u=$100,S1,d=$40. The price of a risk-free bond that pays out $1 in period t=1 is $0.90. (a) Using a one step binomial tree, write down the possible payoffs of a put option on stock S with strike K=$60 and maturity t=1. (b) What is the price of this put option? HINT: this calculation is very similar to what we did for a call option in the lecture notes. (c) What is the price of a call option with strike K=$60 and maturity t=1 ? HINT: you can use put-call parity to find the call price. (d) Another stock S that can take the values S1,u=$200 or S1,d=$40 at time t=1 currently trades at S0=$110. Using your results from parts (b) and (c) verify whether the stock is correctly priced (hint: no-arbitrage needs to hold). Note the price of S moves with S, that is either both reach S1,u and S1,u or both reach Sd,1 and Sd,u together at time 1 . (e) If the stock is mispriced, write down a trade that takes advantage of the mispricing and results in a positive payoff for sure