Question

Rebecca is interested in purchasing a European call on a hot new​ stock, Up, Inc. The call has a strike price of

$ 95.00

and expires in

89

days. The current price of Up stock is

$ 118.73

and the stock has a standard deviation of 45%

per year. The​ risk-free interest rate is 6.94%

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

a. Price of call option can be calculated by using Black-Scholes formula in following manner –

INPUTS		Outputs	Value
Standard deviation (Annual) (σ)	45.00%	d1	1.19071
Time until Expiration (in Years) (t)	0.2438	d2	0.96850
Risk free rates (Annual) (r)	6.94%	N(d1)	0.88312
Stock Price (S0)	$118.7300	N(d2)	0.83360
Strike price (X)	$95.00	B/S call value (C )	26.98895
Dividend yield	0.00%	B/S Put Value (P)	1.66486

Price of call option is $26.98895

Formulas used in excel calculation:

b. Now price of put option by using following put-call parity equation

P = C –S0 + X* e^ (-r*t)

Where,

C = price of the call option = $26.98895

P= price of the put option =?

S0 = spot price = $118.73

Strike price X= $95

The risk-free rate r= 6.94%

Time period t= 89/365 = 0.2438

Now putting all the values in the put-call parity equation

P = $26.98895 - $118.73 + $95 * e^ (-0.0694*0.2438)

Or P = $26.98895 - $118.73 + $93.40615 = $1.66486 (which is equal to the value of Put option using Black-Scholes formula)