| 3. Assuming that a one-year call option with an exercise price of $38 is available for the stock of the DEW Corp., consider the following price tree for DEW stock over the next year: |
| Now | SI | | S2 | | One Year |
| | | | 44.1 | | 46.31 |
| | 42 | | 40.32 | | 42.34 |
| 40 | 38.4 | | 36.86 | | 38.71 |
| | | | | | 35.39 |
| RFR = | 6% |
| 1/3 year = | 0.33 |
| RFR 1/3 yr = | 1.0196 |
| a. If the sequence of stock prices that DEW stock follows over the year is $40.00, $42.00, $40.32, and $38.71, describe the composition of the initial riskless portfolio of stock and options you would form and all the subsequent adjustments you would have to make to keep this portfolio riskless. Assume the one-year risk-free rate is 6 percent. |
| U = | 1.05 | | | rf = 1.961% per period |
| D = | 0.96 |
| R = | 1.020 | | | | Pu = (R-D) / (U-D) = | 0.6623646936 |
| | S = | $ 40.32 | | | | stock price rises, option value = | $ 4.34 | = | Cudu | U-(D/R) |
| | Pu = | 0.662 | | | | stock price falls, option value = | $ 0.71 | = | Cudd | D-(D/R) |
| | | | | | | Cud = Pu * Cudu + (1-Pu)*Cudd = | $ 3.112 | = | $ 3.05 |
| | C0 = | 4.00 | | | | | 1.0196 |
| | C0 = | 0.4 | | | | hRud = (U - D) *S = | $3.63 |
| | h = | -1 | | | | hRud = Cudu - Cudd = | $ 3.63 | = | -1.00 | ≈ | -1 |
| | | | | | | hRud = Cudd - Cudu = | $ (3.63) |
| | S = | $ 42.00 | | | | stock price rises, option value = | $6.84 | = | Cuu |
| | Pu = | 0.662 | | | | stock price falls, option value = | $3.05 | = | Cud |
| | | | | | | Cud = Pu * Cuu + (1-Pu)*Cud = | $ 5.557 | = | $ 5.451 |
| | | | | | | | 1.0196 |
| | | | | | | hRu = Cuu - Cud = | $ 3.78 | = | -0.9997230929 | ≈ | -1 |
| | | | | | | hRu = (U - D) *S = | ($3.78) |
| | S = | $ 40.00 | | | | stock price rises, option value = | $5.45 | = | Cuu |
| | Pu = | 0.662 | | | | stock price falls, option value = | $2.14 | = | Cud |
| | | | | | | Cud = Pu * Cuu + (1-Pu)*Cud = | $ 4.331 | = | $ 4.248 |
| | | | | | | | 1.0196 |
| | | | | | | hRu = Cuu - Cud = | $ 3.60 | = | -1.0859898353 | ≈ | -1 |
| | | | | | | hRu = (U - D) *S = | ($3.31) |
bryjnsah87
22-3a1.xlsx
