Question

In: Finance

As an analyst at Bank of America Merrill Lynch, you are evaluating European call futures option...

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)

Solutions

Expert Solution

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

If you have any query related to question then feel free to ask me in a comment. Thanks.


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