Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%.

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Asked Nov 27, 2019
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Question 2. (a) Use the Black-Scholes formula to find the current price of a European call option on a stock paying no income with strike 60 and maturity 18 months from now. Assume the current stock price is 50, the lognormal volatility of the stock is σ = 20%, and the constant continuously compounded interest rate is r = 10%.

 

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Expert Answer

Step 1

Calculation of Price of European Call Option:

The price of European call option is $4.18.

Excel Spreadsheet:

...
A
B
1 Stock Price
$50
2 Exercise Price
$60
3 Period
1.5
4 Riskfree Rate
10.00%
5 Standard Deviation
20%
6 PV of Exercise Price 51.64247859
7 Square of Time
0.244948974
-0.00947772
8 d1
-0.25442669
9 d2
0.496218995
10 N(dl)
11 N(d2)
20.6354548
Value of Call
$4.18
12
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A B 1 Stock Price $50 2 Exercise Price $60 3 Period 1.5 4 Riskfree Rate 10.00% 5 Standard Deviation 20% 6 PV of Exercise Price 51.64247859 7 Square of Time 0.244948974 -0.00947772 8 d1 -0.25442669 9 d2 0.496218995 10 N(dl) 11 N(d2) 20.6354548 Value of Call $4.18 12

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