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Homework 6

Q1. Derivagem is useful for pricing options but it has some limitations. Explain why it’s impossible to solve Q12.5 in page 293 with Derivagem.

Q2. A stock price is currently $100. Over each of the next three six-month periods, it is expected to go up by 8% or down by 8%. The risk-free interest rate is 2% per annum.

a. What is dt, the length of one period?
b. What is u, the up factor? Note that the answer is not 10%.
c. What is d, the down factor?
d. Calculate p, the risk-neutral probability that the stock price will go up next period.

Hint: End of chapter 12, Q5

For Q3 and Q4, use the following information.
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A non-dividend paying stock is currently trading at $100 and its volatility is 40%. Consider a put option on this stock, with a strike price of $110, expiring in 1.5 years. The current risk-free rate is 2% per annum. We will price the put option with a 3-step binomial tree (the number of steps = 3).

Q3. First, calculate the European put option price in a spreadsheet. Then use Derivagem to price it. Confirm these 2 prices match. Include the Derivagem output (screenshot or copy paste).

Q4. Calculate the American put option price in a spreadsheet. Then use Derivagem to price it and confirm. These 2 prices must match but will be higher than Q3 answer. Include the Derivagem output.
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