Assume that on April 20 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.

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. Data is provided below.

b) Assume that the price of the call option on April 20 is $2.12. Back out the implied volatility from the Black and Scholes formula.

c) 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.

d) 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.

e) 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.

Data:

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