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Assume that on April 13 the ABC stock price was $20.69. Assume that the option on ABC stock expires in 1 month and the risk-free
Assume that on April 13 the ABC stock price was $20.69. Assume that the option on ABC stock expires in 1 month and the risk-free rate is 2.7% p.a.
- Compute European call price with strike X=19 using Black Scholes closed form solution. To compute the call price you will need the estimate of volatility. Calculate historical volatility based on two months of data.
- Assume that the price of the call option on April 13 is $2.12. Back out the implied volatility from the Black and Scholes formula.
- Compute European put price with strike X=19 using Black Scholes closed form solution. For the estimate of volatility use implied volatility from part b.
- Approximate prices of European put option with X=19 and European call option with X=19 using 5-step binomial trees. For the estimate of volatility use implied volatility from part b. Please, provide your u, d, p, stock tree, and option trees.
- Approximate prices of American put option with X=19 and American call option with X=19 using 5-step binomial trees. For the estimate of volatility use implied volatility from part b. Please, provide your u, d, p, stock tree, and option trees.
Day | Close |
1 | 20.69 |
2 | 21.24 |
3 | 22.08 |
4 | 21.42 |
5 | 21.08 |
6 | 21.75 |
7 | 21.87 |
8 | 21.93 |
9 | 21.85 |
10 | 21.97 |
11 | 21.18 |
12 | 20.79 |
13 | 21.09 |
14 | 21.86 |
15 | 22.27 |
16 | 22.13 |
17 | 21.75 |
18 | 21.09 |
19 | 21.75 |
20 | 20.85 |
21 | 20.66 |
22 | 21.28 |
23 | 21.12 |
24 | 21.2 |
25 | 20.12 |
26 | 20.07 |
27 | 19.87 |
28 | 20.2 |
29 | 20 |
30 | 20.01 |
31 | 19.97 |
32 | 20.49 |
33 | 20.77 |
34 | 20.69 |
35 | 19.94 |
36 | 19.82 |
37 | 20.3 |
38 | 20.38 |
39 | 20.16 |
40 | 20.11 |
41 | 20.46 |
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