Question

in purchasing a European call on a hot new stock, Up, Inc. The call has a strike price of $100.00 and expires in 91 days. The current nce of Up stock is S1 19.75, and the stock has a standard deviation of 42% per year. The risk-free interest rate is 6.02% per year. Up stock pays no dividends. Use a 365-day year. a. Using the Black-Scholes f o. Use out-call parity to compute the price of the nut with the same strike and e a. Using the Black-Scholes formula, compute the price of the call. compute the price of the call. exnira The price of the call is s(Round to two decimal places.)

Answer 1

The main formulas pertaining to the Black Scholes are listed below -

(a)

At first, we shall calculate d1 as follows:

d1 (Numerator) = ln(119.75/100) + {[6.02%+(0.42^2)]*(91/365)}

d1 (Denominator) = 0.42*sqrt(91/365)

This gives us d1 = 1.03587

d2 = 1.03587 - [0.42*sqrt(91/365)]

This gives us d2 = 0.826157

To calculate N(d1), use Excel function =NORM.S.DIST(D1,TRUE)

To calculate N(d2), use Excel function =NORM.S.DIST(D2,TRUE)

This gives us N(d1) = 0.84987

and N(d2) = 0.79564

Before we calculate the price of Call, let us calculate the Present Value of Strike:

PV of strike = $98.51

Substituting all the values in the Call Price formula above, we get:

Call Price = $119.74*(0.84987) - $98.51*(0.79564)

Call Price = $23.39

(b)

According to the Put Call parity, the following equation must hold true:

Put Price + Spot Price of Underline = Call Price + PV of Strike

Put Price + $119.75 = $23.39 + $98.51

Put Price = $23.39 + $98.51 - $119.75

Thus, Put Price = $2.15