Let's add some dividends to the binomial model. We will have three times t = 0,...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Let's add some dividends to the binomial model. We will have three times t = 0, 1, 2. Time periods are of length At = 1, the stock starts at So = $100, and risk-free zero rates are always r = 0.02. At each time, the stock goes up by a factor of u = 1.1 or down by a factor of d = 1.1-1, with probability 65% of it going up and 35% of it going down. Att = 1 we will have a dividend payout of $5. We will be pricing a call option, so we will want to allow the investor to exercise before the dividend is paid out, which is the only time they would ever consider early exercise in reality. We will model this with the following timing at t = 1. If the investor exercises their option at t = 1, then exercise happens before the stock goes ex-dividend. For example, in the up state, they would exercise while the stock is still worth uSo = $110. The stock goes ex-dividend right after the time when investors can do early exercise, and it is the ex-dividend prices that are multiplied by u and d to get the time t = 2 prices. For example, the price of the stock in the up-up state at t = 2 is Suu = u($110 - $5) = $115.50. This is the ex-dividend price of $110 - $5 multiplied by u. (a) (5 points) Draw the binomial tree corresponding to this setup. Include the stock, savings, and probabilities. At t = 1, write down the stock price both before and after it goes ex-dividend. Note: it will not be a recombinant tree, even though u and d are the same each period. If you did things correctly, you will get 4 different values of the stock at t = 2. (b) (3 points) As a warmup, price a European call option that expires at t = 2 with strike price K = $100. (c) (7 points) Now, price an American call option that expires at t = 2 with strike price K = $100. (d) (5 points) Briefly (a few sentences at most!) explain why you obtained a higher price in (c) than (b). let's look at put options in the binomial model with dividends. We again have three times t = 0, 1, 2, and the setup for the stock price and risk free rates is the same as before: So = $100, u = 1.1, d = 1.1-1, r=0.02, and At = 1. Again, the stock is going to pay a $5 dividend at t = 1. As before, between time 1 and 2 the multiplicative factors u and d apply In this problem, we'll consider two different timings. above (a) (7 points) Consider exactly the same timing as in question. That is, at t = 1, if you exercise your option early, you exercise it before the stock goes ex-dividend. For example, in the up state, if an investor exercises early they do so while the stock is still worth uSo = $110. With this timing, price an American put option that expires at t = 2 with a strike price of $100. (b) (8 points) Now, let's change the timing. At t = 1, if you exercise your option, it is immediately after the stock goes ex-dividend. For example, in the up state, that means that if they exercise they will exercise it when the stock is worth $110 - $5 = $105. With this timing, price the same American put option (expires at t = 2 with strike $100). (c) (5 points) Briefly (a few sentences at most!) explain the relationship between the two prices. Let's add some dividends to the binomial model. We will have three times t = 0, 1, 2. Time periods are of length At = 1, the stock starts at So = $100, and risk-free zero rates are always r = 0.02. At each time, the stock goes up by a factor of u = 1.1 or down by a factor of d = 1.1-1, with probability 65% of it going up and 35% of it going down. Att = 1 we will have a dividend payout of $5. We will be pricing a call option, so we will want to allow the investor to exercise before the dividend is paid out, which is the only time they would ever consider early exercise in reality. We will model this with the following timing at t = 1. If the investor exercises their option at t = 1, then exercise happens before the stock goes ex-dividend. For example, in the up state, they would exercise while the stock is still worth uSo = $110. The stock goes ex-dividend right after the time when investors can do early exercise, and it is the ex-dividend prices that are multiplied by u and d to get the time t = 2 prices. For example, the price of the stock in the up-up state at t = 2 is Suu = u($110 - $5) = $115.50. This is the ex-dividend price of $110 - $5 multiplied by u. (a) (5 points) Draw the binomial tree corresponding to this setup. Include the stock, savings, and probabilities. At t = 1, write down the stock price both before and after it goes ex-dividend. Note: it will not be a recombinant tree, even though u and d are the same each period. If you did things correctly, you will get 4 different values of the stock at t = 2. (b) (3 points) As a warmup, price a European call option that expires at t = 2 with strike price K = $100. (c) (7 points) Now, price an American call option that expires at t = 2 with strike price K = $100. (d) (5 points) Briefly (a few sentences at most!) explain why you obtained a higher price in (c) than (b). let's look at put options in the binomial model with dividends. We again have three times t = 0, 1, 2, and the setup for the stock price and risk free rates is the same as before: So = $100, u = 1.1, d = 1.1-1, r=0.02, and At = 1. Again, the stock is going to pay a $5 dividend at t = 1. As before, between time 1 and 2 the multiplicative factors u and d apply In this problem, we'll consider two different timings. above (a) (7 points) Consider exactly the same timing as in question. That is, at t = 1, if you exercise your option early, you exercise it before the stock goes ex-dividend. For example, in the up state, if an investor exercises early they do so while the stock is still worth uSo = $110. With this timing, price an American put option that expires at t = 2 with a strike price of $100. (b) (8 points) Now, let's change the timing. At t = 1, if you exercise your option, it is immediately after the stock goes ex-dividend. For example, in the up state, that means that if they exercise they will exercise it when the stock is worth $110 - $5 = $105. With this timing, price the same American put option (expires at t = 2 with strike $100). (c) (5 points) Briefly (a few sentences at most!) explain the relationship between the two prices.
Expert Answer:
Answer rating: 100% (QA)
SOLUTION a Binomial Tree The binomial tree for this setup is shown below t S savings prob stock 0 10... View the full answer
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these finance questions
-
Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
???????Need answer for below questionWoolworth Ltd, After Pay Ltd, and Santos Ltd for the years 2021,2020 and 2019. Examine the consolidated Cash Flow Statements foreach companies acr f) If the firm...
-
Sudz'N'Bubbles Company owns and operates 10 car washes in Ontario. The general manager of each location reports to the company president, Christopher O'Donnell. At the end of each quarter,...
-
For each of the situations listed, identify the primary standard from the IMA Statement of Ethical Professional Practice that is violated (competence, confidentiality, integrity, or credibility.) 1....
-
Complete the second half of the proof of the "forward price formula with carrying cost". To construct the arbitrage, go long one unit of a forward and short one unit spot. To execute the short, it is...
-
High correlation between two variables means that one is the cause and the other is the effect. Do you agree? Explain.
-
1. Let be the vector : err =[0.5671; 0.4328%; 0.4555e-01; 0.3305e-02; 0.2707e-04; 0.1660e-7]; In PYTHON, we want to calculate the values of the ratios : errn+1 errn errn+1 errn errn+1 et err 1+5...
-
Suppose you are a bank lending officer at the Midtown National Bank considering a loan request from Miller Manufacturing company for $1.05 million. The firm currently has $1 million in equity and its...
-
Identify a SMB of your choice in US. In a paper, examine risk management approaches the organization may consider deploying for mobile device management and provide rationale for the prerequisites...
-
A manufacturing company operating a system of budgetary control finds that their production capacity during the year varies between 75 per cent and 90 per cent as against the budgeted capacity of 80...
-
Lufthansa hedges the purchase of 20 Boeing jets (A). In January 1985, Lufthansa German Airlines purchased 20 Boeing 737 long-distance aircraft for US$500 million payable to Boeing exactly one year...
-
Suppose a firm is considering replacing an old machine with a new one. The firm does not anticipate that any new revenues will be created by the replacement since demand for the product generation by...
-
In a move toward becoming a major car producer in Eastern Europe, Renault in 2004 purchased the Romanian firm Dacia for 200 million to build Logans in Romania. The pact calls for Renault to start...
-
Referring to information provided in problem 8, Cardiexs sales in the European Union are projected to remain stable at 100 million for the next 5 years. Show pro-form income and cash-flow statements...
-
The solid beam shown in Figure 2 is subjected to a concentrated load P at its center. Assume that El is constant for the bear. (a) Determine the support reaction and internal forces from equation of...
-
Velshi Printers has contracts to complete weekly supplements required by fortysix customers. For the year 2018, manufacturing overhead cost estimates total $600,000 for an annual production capacity...
-
Mallory Corporation has a calendar year-end. The corporation has paid estimated payments of $10,000 during 2012 but still owes an additional $5,000 for its 2012 tax year. a. When is the 2012 tax...
-
Indicate, in each of the following situations, the number of exemptions the taxpayers are entitled to claim on their 2012 income tax returns. Number of Exemptions a. Donna, a 20-year-old single...
-
In 2012, Margaret and John Murphy are married taxpayers who file a joint tax return with AGl of $25,000. During the year they incurred the following expenses: Hospitalization insurance...
-
Using a financial calculator, solve for the unknowns in each of the following situations. a. On June 1, 2024, Holly Golightly purchases lakefront property from her neighbor, George Peppard, and...
-
Ed owns Oak Knoll Apartments. During the year, Fred, a tenant, moved to another state. Fred paid Ed \($1,000\) to cancel the two-year lease he had signed. Ed subsequently began renting the unit to...
-
In 2017, Harry and Mary purchased Series EE bonds, and in 2023 redeemed the bonds, receiving \($500\) of interest and \($1,500\) of principal. Their income from other sources totaled \($30,000.\)...
Study smarter with the SolutionInn App