Figure 1 illustrates how a barrier option works. The stock price starts at $100, ends at...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Figure 1 illustrates how a barrier option works. The stock price starts at $100, ends at $80, and hits the barrier of $75 about halfway through the year. If the option were a 95-strike down-and-in put, the option would knock in and pay $15 (= max(0, 895-880)) at expiration. If the option were a down-and-out put, it would be worthless at expiration because the barrier was hit. If the option were a down-and-in call, it would knock in at $75 but still be worthless at expiration because the stock price is below the strike price. Stock Price ($) 105 100 95 90 85 80 75 70 65- 0 Barrier Stock hits barrier 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (years) Strike price 0.8 0.9 1.0 FIG. 1 - Illustration of a price path where the initial stock price is $100 and the barrier is $75. At t = 0.5, the stock hits the barrier. Now we value a down-and-in put option with European style using Monte Carlo simula- tions. Assume that stock prices are lognormally distributed. Stock price today is $100. Annual Trial (k) 2 (1) Zk (2) Zk (3) Zk (4) Zk (5) S (1) Sk (2) Sk (3) Sk (4) Sk (5) TABLE 1 SIMULATING DOWN-AND-OUT PUT OPTION WITH EUROPEAN STYLE. 1 -0.030 1.254 -0.645 0.167 -0.944 2 0.192 0.819 0.085 -0.477 -2.166 3 0.763 1.500 -1.259 -0.313 -0.428 4 -0.157 -0.439 -2.596 -0.683 0.006 continuously compounded risk-free rate is r = 0.05, annual volatility of return o = 0.25. Strike price K = 895. The barrier is $75. This barrier option expires in 1 year. We split the time till maturity date into 5 intervals and simulate stock prices at the end of each interval. We only consider whether the barrier is hit or not based on these 5 stock prices. Compute the Monte Carlo price of this barrier option based on 4 simulations. Table 1 gives the simulated standard normal shocks in each period in each trial. Complete the table by calculating stock prices and terminal payoff of the option in each trial. Then find the Monte Carlo price. Figure 1 illustrates how a barrier option works. The stock price starts at $100, ends at $80, and hits the barrier of $75 about halfway through the year. If the option were a 95-strike down-and-in put, the option would knock in and pay $15 (= max(0, 895-880)) at expiration. If the option were a down-and-out put, it would be worthless at expiration because the barrier was hit. If the option were a down-and-in call, it would knock in at $75 but still be worthless at expiration because the stock price is below the strike price. Stock Price ($) 105 100 95 90 85 80 75 70 65- 0 Barrier Stock hits barrier 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Time (years) Strike price 0.8 0.9 1.0 FIG. 1 - Illustration of a price path where the initial stock price is $100 and the barrier is $75. At t = 0.5, the stock hits the barrier. Now we value a down-and-in put option with European style using Monte Carlo simula- tions. Assume that stock prices are lognormally distributed. Stock price today is $100. Annual Trial (k) 2 (1) Zk (2) Zk (3) Zk (4) Zk (5) S (1) Sk (2) Sk (3) Sk (4) Sk (5) TABLE 1 SIMULATING DOWN-AND-OUT PUT OPTION WITH EUROPEAN STYLE. 1 -0.030 1.254 -0.645 0.167 -0.944 2 0.192 0.819 0.085 -0.477 -2.166 3 0.763 1.500 -1.259 -0.313 -0.428 4 -0.157 -0.439 -2.596 -0.683 0.006 continuously compounded risk-free rate is r = 0.05, annual volatility of return o = 0.25. Strike price K = 895. The barrier is $75. This barrier option expires in 1 year. We split the time till maturity date into 5 intervals and simulate stock prices at the end of each interval. We only consider whether the barrier is hit or not based on these 5 stock prices. Compute the Monte Carlo price of this barrier option based on 4 simulations. Table 1 gives the simulated standard normal shocks in each period in each trial. Complete the table by calculating stock prices and terminal payoff of the option in each trial. Then find the Monte Carlo price.
Expert Answer:
Answer rating: 100% (QA)
To complete Table 1 and calculate the stock prices and terminal payoff for the downandin put option ... 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
-
Memorial Hospital is evaluating two different computer system for handling provider claims. There are no incremental revenues attached to the project, so the decision will be made on the basis of the...
-
Examine Treas. Reg. 1.183-2. What Code section and language within that Code section does the Treasury Regulation interpret? What does the Treasury Regulation state are the nine relevant factors?
-
Consider the furniture manufacturing problem discussed in this section. Suppose that the company manufactures only sofas. What is the maximum number of sofas that could be manufactured?
-
Why must every society choose some manner in which to allocate its scarce resources?
-
University Health Center has three divisions: Real Estate, with an 8 percent cost of capital; Health Services, with a 10 percent cost of capital; and Managed Care, with a 12 percent cost of capital....
-
The Black Knights Inc., a manufacturer of high-sugar, low-sodium, low cholesterol TV dinners, would like to increase its market share in the Sunbelt. In order to do so, Black Knights has decided to...
-
23. A convex mirror used for rear view on an automobile has a radius of curvature of 3m. If a bus is located at 5m from this mirror, find the position, nature and magnification of the image. 24. An...
-
A mechanical engineer at Anode Metals is considering five equivalent projects, some of which have different life expectations. Salvage value is nil for all alternatives. Assuming that the companys...
-
How might free cash flow impact financing and investing decisions for a company like Bath & Body Works?
-
Instruction Create a native application for Android that allows the user to store and manage tasks. Your application should allow user to create tasks by category that user chooses (work, school,...
-
How to overcome barriers while determination of base pay .Explain in detail
-
Exercise #4 of 4: A company, which uses a job cost system, has provided you with the following: Job Cost Sheet JOB NO. 64 FOR Bendix Quantity 1,500 Date Completed 5/31 Date Direct Materials Direct...
-
Explain as fully as possible the difference between the most important information provided in a company's statement of comprehensive income compared with its statement of financial position
-
Assume that Firm A is an all-equity firm with total assets of $5,000 and the following distribution of EBIT for the coming year: Firm A Unlevered Bad Economy Average Good Probability 30.00% 40.00%...
-
In many applications, some variables evolve over time in a random (stochastic) way in that even if you know everything up to time t, it is still impossible to know for sure which values the variables...
-
a. Show that the expansion of q(x) in ascending powers of x can be approximated to 10 2x + Bx 2 + Cx 3 where B and C are constants to be found. b. Find the percentage error made in using the series...
-
William sold Section 1245 property for $25,000 in 2012. The property cost $35,000 when it was purchased 5 years ago. The depreciation claimed on the property was $16,000. a. Calculate the adjusted...
-
Ann hires a nanny to watch her two children while she works at a local hospital. She pays the 19-year-old nanny $125 per week for 48 weeks during the current year. a. What is the employer's portion...
-
Walter, a single taxpayer, purchased a limited partnership interest in a tax shelter in 1985. He also acquired a rental house in 2012, which he actively manages. During 2012, Walter's share of the...
-
Yolanda wants to know how much time she typically spends on her cell phone. She goes to her phones website and records the call length for a random sample of 12 calls, shown in Table 3. Find the mean...
-
Find the median score of the data in Table 1. Approach Follow the steps listed on the previous page. Table 1 Student Score 1. Michelle 82 2. Ryanne 77 3. Bilal 90 4. Pam 71 5. Jennifer 62 6. Dave 68...
-
The data in Table 5 represent the birth weights (in pounds) of 50 randomly sampled babies. (a) Find the mean and the median birth weight. (b) Describe the shape of the distribution. (c) Which measure...
Study smarter with the SolutionInn App