Exam 18: Multiperiod Binomial Model

Consider the following exotic option whose payoff at maturity is given by the stock price squared less a strike price if it has a positive value,zero otherwise,that is: max[S(1)² - K,0]. Using the above data except for assuming a new strike price is $5,today's arbitrage-free price of this exotic option is:

Suppose a trader quotes a put price of $6.Then,you can make an immediate arbitrage profit of:

The arbitrage-free price of a put option is:

Use the following data for a two-period binomial model to answer the questions that follow. - The stock's price S is $100.After three months,it either goes up and gets multiplied by the factor U =1.13847256,or it goes down and gets multiplied by the factor D = 0.88664332. - Options mature after T = 0.5 year and have a strike price of K = $105. - The continuously compounded risk-free interest rate r is 5 percent per year. - Today's European call price is c and the put price is p.Call prices after one period are denoted by c_U in the up node and c_D in the down node.Call prices after two periods are denoted by c_UD in the "up,and then down node" and so on.Put prices are similarly defined. -The stock price tree (in dollars)is given by:

To create the arbitrage-free synthetic call today,you need to:

Which of the following statements is correct regarding a binomial option pricing model?