Question

# An investor is very bullish about the stock market but does not want to take too...

An investor is very bullish about the stock market but does not want to take too much
risk. He decides to buy four American call options on one particular stock. Each option is
for 100 shares with exercise price at \$65 per share and maturity of eight months. He is told
that the expected return from the stock is 20% per annum with annual volatility of 30%.
The current stock price is \$61. The risk{free rate is 6% per annum. Calculate the price of
one call option, assuming the stock will not pay any dividends before maturity of the option.

Input Data
Stock Price now (P) 61
Exercise Price of Option (EX) 65
Number of periods to Exercise in years (t) 0.67
Compounded Risk-Free Interest Rate (rf) 6.00%
Standard Deviation (annualized s) 30.00%
Output Data
Present Value of Exercise Price (PV(EX)) 62.4513
s*t^.5 0.2449
d1 0.0265
d2 -0.2185
Delta N(d1) Normal Cumulative Density Function 0.5106
Bank Loan N(d2)*PV(EX) 25.8256
Value of Call 5.3187
Value of Put 6.7700
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