Test by fanzhongqing


									                       Math 7780: Financial Derivatives

                                     Test, March 21, 2011
Throughout the exam we will presume the following parameters for an underlying stock:
                                      S 0 =200,   50% , r  6%
 1.   Inflation:
          a.   suppose that inflation for all of 2006 ran 4.2%, for 2007 2.4%, for 2008 5.8%, for 2009
               negative 2.1% and for 2010 1.2%. Suppose the actual oil price at the beginning of 2006 was
               $60 per barrel. What is this price adjusted for inflation in terms of (end of) 2010 dollars?
          b.   According to government statistics, the Consumer Price Index in July 1990 stood at 390.7,
               while on July 2010 it stood at 653.066. Calculate the average annual inflation rate in the US
               over these 20 years. At that rate, how long does it take for prices to double?
          c.   What would an annual income of $30,000 in 1990 correspond to in 2010?
 2.   Loan Stuff:
          a.   Suppose you need to borrow $10,000, and you can afford to pay back $200 a month. You find
               a friend who is willing to loan it to you. You agree that you pay 5% interest, compounded
               monthly. How long will it take you to pay the loan back? How much will the last payment be?
               How much will your total payments come to?
          b.   I need the same loan, can afford the same monthly payment, but I don’t have friends to loan
               me anything. So I use my credit card, which charges 20%, compounded monthly. How long
               will it take me to pay back the loan? How much will I have paid the credit card company
               when I am done?
          c.   A Car dealer loans you $10,000, and gives you a choice:
                    i. pay back $350 a month for 36 months
                   ii. or pay nothing for the first year, then $550 a month for 24 months.
                       What is the better deal and why? Think of the implied interest rate.
 3.   Expected Pay-off Pricing:
          a.   With the parameters above, price a call-option with strike $200, maturing in 4 months.
          b.   price a put-option with strike $200, maturing in 4 months.
 4.   Monte Carlo:
          a.   with Fathom, price the call-option of problem 3a. Use 84 cases (periods) and 10,000
               measures. Please copy into the blue book your formula for the random walk, and for the
               measure. (Obviously, the price should be very close to the price you got in 3, so credit is
               given mostly for the formulas.)
          b.   Add to the option of (a) that the stock price has to have fallen below $190, before the option
               becomes active. Price this `knock-in option’. (Again, please tell me what formula you used for
               the measure.)
 5.   Strategies:
          a.   Suppose I buy two shares at $200 each, buy one put with strike $150, and sell one call at
               strike $250. Create the payoff-diagram for this portfolio.
          b.   Suppose I want to create a portfolio consisting of puts and calls, (possibly short), so that the
               payoff-diagram has this shape. How is this accomplished?

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