Homework-Bonus-3-answers-2000 by stariya

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									                          MGT 890-891: Corporate Finance and Options
                                        Bonus Homework Set #3
                                                 Answers

Question 1:

Days in Yr:                 365
Days of                      32
Contract:
S:                      73.9375


  Symbol          Last        Open            Strike        Symbol            Last        Open Risk Free
                             Interest                                                    Interes Rate
                                                                                            t
                                              Price
  GM-CL         16.0000         347            60          GM-OL              0.250      1243        41.9%
  GM-CM         14.7500        1088            65          GM-OM              0.500       628       164.5%
  GM-CN          6.1250         880            70          GM-ON              1.500      1061        11.9%
  GM-CO          3.2500        3663            75          GM-OO              3.500      1373        13.2%
  GM-CP          1.5625        1523            80          GM-OP              6.875      1148        11.3%
  GM-CQ          0.5625        2453            85          GM-OQ              8.000      5600        64.4%
  GM-CR          0.1875        2332            90          GM-OR             10.375       259       116.0%

The calculations show that the contracts in the 70 to 80 strike range do have relatively similar risk
free rates based on put-call parity while the extreme low and high strike contracts have ridiculous
rates. This often occurs because of a lack of trading activity on the contracts. That is, the prices
listed as "Last" are historic and likely stale. Thus, they do not reflect the true market price as
would be implied by put-call parity.


Question 2:

    S         73.9375    73.9375   73.9375     73.9375   73.9375   73.9375     73.9375    Current Asset Value

    X          60.00      65.00       70.00     75.00      80.00     85.00      90.00     Exercise (Strike) Price

    T          0.088      0.088       0.088     0.088      0.088     0.088      0.088     Time to Maturity (Years)

    rf        4.88%       4.88%    4.88%        4.88%    4.88%       4.88%      4.88%     Risk-free Interest Rate

    d         0.00%       0.00%    0.00%        0.00%    0.00%       0.00%      0.00%     Dividend Yield (% p.a.)

            84.36%     115.95%   42.70%      41.14%    41.37%    39.40%      39.03%     Volatility (% p.a.)


    d1        0.9782      0.5594   0.5299      -0.0211   -0.5472   -1.1003     -1.6062

    d2        0.7284      0.2161   0.4034      -0.1429   -0.6697   -1.2170     -1.7218
  N(d1)       0.8360    0.7120        0.7019        0.4916    0.2921          0.1356    0.0541

  N(d2)       0.7668    0.5855        0.6567        0.4432    0.2515          0.1118    0.0426



   CE       16.00000   14.75000      6.12500        3.25000   1.56250         0.56250   0.18750   European Call Value ($)

   PE          1.81       5.54         1.89          3.99      7.28            11.26     15.87    European Put Value ($)



Question 3.

Binomial Tree Valuation

                                                              Binomial Tree (One-Step)
    CALL INPUTS                              u=        1.10            0               1
                                             d=        0.91
     Current Stock 73.94            R (period)=      3.67%
             Price:
           Strike: 60.00         R(continuously        35%                                81.3
                                         comp)
  Time to Maturity 0.09                     q=         0.67            73.9               21.3
           (years):
  Riskless interest 41.89         d1=                  1.08       16.063                  67.2
        rate (p.a.)     %
  Annual Volatility: 84.36        d2=                  0.83                                7.2
                        %
   CALL PRICE= 16.06 Call Price (Black                17.22
                       292   Scholes)

                                                              Binomial Tree (One-Step)
    CALL INPUTS                  (Note Possible)    1.10               0               1
                                              u=
                                              d=    0.91
     Current Stock 73.94             R (period)= 14.42%
             Price:
           Strike: 65.00         R(continuously        97%                                81.3
                                         comp)
  Time to Maturity 0.09                     q=         1.23            73.9               16.3
           (years):
  Riskless interest 164.4         d1=                  0.80       17.129                  67.2
        rate (p.a.)    7%
  Annual Volatility: 115.9        d2=                  0.45                                2.2
                       5%
   CALL PRICE= 17.12 Call Price (Black                17.92
                        88   Scholes)

                                                              Binomial Tree (One-Step)
    CALL INPUTS                              u=        1.11            0               1
                                             d=        0.90
     Current Stock 73.94            R (period)=      1.04%
             Price:
           Strike: 70.00         R(continuously        11%                                81.7
                                         comp)
   Time to Maturity 0.09                    q=         0.53            73.9               11.7
            (years):
   Riskless interest 11.92                    d1=      0.57        6.125                  66.9
      rate (p.a.)     %
Annual Volatility: 42.70        d2=       0.45                           0.0
                      %
 CALL PRICE= 6.125 Call Price (Black     6.383
                       0   Scholes)

                                                  Binomial Tree (One-Step)
 CALL INPUTS                        u=     1.10            0               1
                                    d=     0.91
  Current Stock 73.94      R (period)=   1.16%
          Price:
        Strike: 75.00   R(continuously    12%                           81.1
                                comp)
Time to Maturity 0.09              q=     0.54          73.9             6.1
         (years):
Riskless interest 13.23         d1=       0.03        3.250             67.4
      rate (p.a.)     %
Annual Volatility: 41.14        d2=       -0.09                          0.0
                      %
 CALL PRICE= 3.250 Call Price (Black      3.47
                       0   Scholes)

                                                  Binomial Tree (One-Step)
 CALL INPUTS                        u=     1.12            0               1
                                    d=     0.89
  Current Stock 73.94      R (period)=   0.99%
          Price:
        Strike: 80.00   R(continuously    11%                           83.1
                                comp)
Time to Maturity 0.09              q=   0.51            73.9             3.1
         (years):
Riskless interest 11.34         d1=    -0.51          1.563             65.8
      rate (p.a.)     %
Annual Volatility: 41.37        d2=    -0.63                             0.0
                      %
 CALL PRICE= 1.562 Call Price (Black 1.6680
                       5   Scholes)

                                                  Binomial Tree (One-Step)
 CALL INPUTS                        u=     1.16            0               1
                                    d=     0.86
  Current Stock 73.94      R (period)=   5.65%
          Price:
        Strike: 85.00   R(continuously    50%                           85.9
                                comp)
Time to Maturity 0.09              q=   0.65            73.9             0.9
         (years):
Riskless interest 64.40         d1=    -0.76          0.562             63.6
      rate (p.a.)     %
Annual Volatility: 39.40        d2=    -0.88                             0.0
                      %
 CALL PRICE= 0.562 Call Price (Black 1.0456
                       5   Scholes)

                                                  Binomial Tree (One-Step)
 CALL INPUTS                        u=    1.22             0               1
                                    d=    0.82
  Current Stock 73.94      R (period)= 10.17%
          Price:
             Strike: 90.00     R(continuously   77%                            90.3
                                       comp)
   Time to Maturity 0.09                   0.70
                                          q=                  73.9              0.3
            (years):
   Riskless interest 115.9         d1=    -1.06             0.188              60.5
         rate (p.a.)    7%
   Annual Volatility: 39.03        d2=    -1.17                                 0.0
                         %
    CALL PRICE= 0.187 Call Price (Black 0.6042
                          5   Scholes)




Question 4

a) If Price of land > $111
   Buyer of put will not exercise the put, since it's an out of the money put as K<ST.
   BBA will exercise the call option since it is an in the money call as S T>K.
   BBA will have bought the land using its call option at $111.
If Price <$111
   Buyer of put option will exercise the put and sell the land for $111to BBA, since it is an in the
money put as K>ST.
   BBA will not exercise the call, since it is an out of the money call as K>ST.
   BBA will have bought back the land from the buyer who exercised his put at $111.

b) BBA           payoff
                                                      buy a call

                                                            FV of $111 received in 1990



                                111

                           Sell a put




                                                            portfolio




                                 111

                          111-FV ($111 received in 1990)




c) When BBA sold the land they got cash for $111. At the same time they bought a call for $20,
their net cash in was $91 in 1990. When the options expire (both the put and the call will expire at
the same time) BBA will for sure buy back the land for $111 (either through the put or through the
call) regardless of the land value at expiration. However, they will have paid out that $111 in the
future so the present value of $111 is lower. If the present value of $111 is lower than $91 then
they would have made a gain on the sale, if the present value of $111 is higher than $91 than
they would have made a loss. Time to maturity of the options and the risk free rate for that period
will determine the profit/loss. They record a gain of $75 in 1990 but they will record a loss in the
future if the price of land decreases. So it is misleading to record this boost in profits. This
allowed them to write off the land at book value, realizing a gain, that they will take on to the
books back at $111.

								
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