Use the Following Data for a Single-Period Binomial Model to Answer

question 10

Multiple Choice

Use the following data for a single-period binomial model to answer the questions that follow.
- The stock's price S is $50.After three months,it either goes up by the factor U = 1.16038286 or it goes down by the factor D = 0.85963276.
- Options mature after T =0 0.25 years.
- The continuously compounded risk-free interest rate r is 4 percent per year.
-Given the above data,consider an exotic option whose payoff at expiration is given by the stock price S(1) squared less a strike price (K= $2,500) if it has a positive value,zero otherwise,that is: max[S(1) ²- 2500,0].
Suppose a trader quotes a price of $450 for this option.Then you can make an immediate arbitrage profit of:

• A) $21.08 by selling the traded call and buying the synthetic call involving buying 57.60 shares of stock and selling 2,451.28 units of the money market account
• B) $226.50 by buying the traded call and selling the synthetic call involving selling 90.85 shares of stock and buying 3,866.21 units of the money market account
• C) $50 by buying the traded call and selling the synthetic call involving selling 60.54 shares of stock and buying 2,321.21 units of the money market account
• D) $337.76 by selling the traded call and buying the synthetic call involving buying 16.74 shares of stock and selling 641.35 units of the money market account
• E) None of these answers are correct.

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