In: Finance
As an analyst at Bank of America
Merrill Lynch, you are evaluating European call futures option and
European put futures options. A futures price is currently $50. It
is expected to move either to $55 or down to $45 over the next
three months. The risk-free interest rate is 8% per annum with
continuous compounding.
a. What is the probability of an up movement in a
risk-neutral world?
(sample answer: 35.0%)
b. What is the value of a three-month call option with a
strike price of $49?
(sample answer: $1.45)
c. What is the value of a three-month put option with a
strike price of $49?
(sample answer: $1.45)
Solution:-
Current price = $50.
Risk Free Rate = 8%
Lower Price = $45
Higher Pice = $55
To Find probability of an up movement in a risk-neutral world -
Probability of up Movement =
Probability of up Movement =
Probability of up Movement =
Probability of up Movement = 60%
Probability of Down Movement = 1 - Probability of up Movement
Probability of Down Movement = 1 - 60%
Probability of Down Movement = 40%
To find value of a three-month call option with a strike price of $49 -
Option Price of call as on Today | ||||
A | B | A*B | ||
Current Market Price as on Expiry | Excersice Price | Option Price as on Expiry | Probability | Expected Option price as on expiry |
55 | 49 | 6 | 0.6 | 3.60 |
45 | 49 | 0 | 0.4 | 0 |
3.60 |
Value of Three month call option as on Today =
Value of Three month call option as on Today = 3.60 * 0.9802
Value of Three month call option as on Today =$3.53
To find value of a three-month Put option with a strike price of $49 -
Option Price of put as on Today | ||||
A | B | A*B | ||
Current Market Price as on Expiry | Strike Price | Option Price as on Expiry | Probability | Expected Option price as on expiry |
55 | 49 | 0 | 0.6 | 0.00 |
45 | 49 | 4 | 0.4 | 0.833536 |
0.83 |
Value of Three month Put option as on Today =
Value of Three month Put option as on Today = 0.83 * 0.9802
Value of Three month Put option as on Today =$0.814
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