Question

QUESTION 11 10 pois The stock of the Miami Tower Company (MTC) is currently worth $100. Over each of the next two years, the stock price will either move up to 115% of the beginning-of-year stock price or down to 90% of the beginning of year price. You do not know which one will happen, nor how likely these are. The risk-free interest rate is 3% per year. MTC will also pay a $2 per share dividend at the end of year 1. Assume that it is possible to observe the stock price at the end of year 1, exercise any option you might hold immediately (should you choose to do so), and still qualify for the dividend if exercise gives ownership of the underlying. What is the risk-neutral probability for the above situation? Give your answer to 2 decimal places and include a leading zero. QUESTION 12 10 poi Using the information from the previous question, find the dollar price of a European call option with strike price $95. Do not use dollar signs, and round to the nearest cent. QUESTION 13 10 poi Using the same information, find the price of an American call option with strike price $95. Use the same format as above. QUESTION 14 10 poi Using the same information, find the price of an American put option, with strike price $95. Use the same format as above. Click Save and Submit to save and submit. Click Save All Answers to save all answers, Save All Answers

Answer 1

Solution:

The risk neutral probability is given by:

Qu = (e^rt - d) / (u-d)    . . . . . .Equation A)

Where Qu -> risk neutral probability of an upmove

r -> risk free rate , t -> period , u -> size of the upmove , d -> size of the downmove

We have with us:

r = 3% (.03) u =115% (1.15) d=90% (.9) t =1 year

Putting the above values in Equation A) we get,

Qu = (e^(.03*1) - .9)/(1.15 - .9)

= (1.0304545 - .9)/(1.15 - .9)

= .130454534 / .25

=.521818136 = 52.1818136 %

The risk neutral probability of an upmove is 52.1818136% and probability of a downmove is (1-Qu) i.e.

1- .521818136 = .478181864