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could you please answer this question and give

step-by-step calculations, thank you !

Q5.png

Question 5
Given the inputs r = 0.045, So = $45 and T = 1/4, consider the following
European call option schedule
Strike $X |Option Price Co
40
6.3718
42
4.6538
44
2.9886
46
1.7042
48
1.1859
50
0.9591
Part A
Find the implied volatilities for each of these options and hence derive a volatility
smile
Part B
What does the volatility smile tell you? How can we relate this to Black Scholes
Merton. Thus, what are the limitations of BSM? How might this be corrected?

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