Question

Rebecca is interested in purchasing a European call on a hot new​ stock, Up, Inc. The call has a strike price of $ 96.00 and expires in 91 days. The current price of Up stock is $ 117.65​, and the stock has a standard deviation of 40% per year. The​ risk-free interest rate is 6.53 % per year. Up stock pays no dividends. Use a​ 365-day year.

a. Using the​ Black-Scholes formula, compute the price of the call.

b. Use​ put-call parity to compute the price of the put with the same strike and expiration date. ​(Note​: Make sure to round all intermediate calculations to at least five decimal places.​) ​

Answer 1

C=S *N(d1​) − Ke− rt N(d2​)

where: d1​ = [​ln (S/K) ​​+ {(r + (SD2/2)​)*t}] / (SD*SQRT t )​ and

d2​=d1​− (SD*SQRT t )​

where:

C=Call option price

S=Current stock (or other underlying) price

K=Strike price

r=Risk-free interest rate

t=Time to maturity

N=A normal distribution​

SD= STSANDARD DEVIATION

d1 = [ln(117.65/96) + { 6.53% + (40%2 / 2) * 91/365} ] / (40% * sqrt(91/365) )
= (0.20336 + 0.03622) / 0.19972
=1.19957
d2= 1.19957 - (0.4 * sqrt(91/365))
= 0.99984

C = Rs1.969827
THEREFORE,price of put using call-put parity is C-P=S-Xe-rt    IS Rs21.71996