Question

A stock price is currently $40. It is known that at the end of one month it will be either $42 or $38. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a one-month European call option with a strike price of $39

Answer 1

Answer:

$1.70

Explanation:

Given that,

Current stock price= $40

Strike price= $39

After a period of one month, two states will be achievable.

- First state

Stock price=$42

Option value= 42-39

=$3

- Second state

Stock price= $38

Option value= 0

Upmove size of first state is

U= 42/40 =1.05

Downmove size of the second state is

D=38/40=0.95

The values given for the upside probability is given as:

Rf= 0.08

t= 1/12

πu = 0.567

The downside probability is equal to:

= 1 - 0.567

= 0.433

Therefore, the present value of option is:

(0.567 × 3) + (0.43 × 0) / e^0.08 × 1/12

= 1.70

Thus, the value of a one-month European call option is $1.70