Reference no: EM13831745
Q1. Derivagem is useful for pricing options but it cannot be used all the time. Explain why one should not use Derivagem to solve Q12.5 in page 293.
Q2. A stock price is currently $100. Over each of the next three 2-month periods, it is expected to go up by 4% or down by 4%. (That means in the first 2 months, price may go up or down by 4%. The next 2 months, price may go up or down again by 4%. Again in the final 6 months. So, if the price goes up 3 consecutive times, the price will become $100 * (1+4%) * (1+4%) * (1+4%). Don’t forget the compounding.) The risk-free interest rate is 1% per annum.
a. What is dt, the length of one period?
b. What is u, the up factor?
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 (answer in the back of textbook)
For Q3 and Q4, use the following information.
A non-dividend paying stock is currently trading at $100 and its volatility is 45%. Consider a put option on this stock, with a strike price of $115, expiring in 6 months. The current risk-free rate is 1% 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).
Hint: The put pricing exercise in class was a 2-step tree. You can extend 1 more step to that example to create a 3-step tree
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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