Question

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 month. 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)

Answer 1

Solution 5.>

Part a)

The probabilty of up movement in the risk neutral world, will be calculated by:

p = e^rt - d / u - d

p = e^ (0.08 * 0.25) - (45/50) / (55/50) - (45/50)

p = 60.1%

Part b) The price of the 3-month European Call option is $3.535

I have solved this question in Excel. The formula used are shown in another excel file. If you still have any doubt, kindly ask in the comment section.

The formula used are:

Part c) The price of the 3-month European Put option is $1.564

I have solved this question in Excel. The formula used are shown in another excel file. If you still have any doubt, kindly ask in the comment section.

The formula used are:

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