Explore BrainMass

Explore BrainMass

    Upper and Lower Bounds of Options

    Because options confer rights, but not obligations, to the party that holds the option, this party is willing to pay an "option premium" to the writer of the option. This premium reflects the value of the option's rights. But how much is an option worth? We start to explore the value of options by looking at the most amount, and the least amount, investors would be willing to buy a call or a put.  

    Upper Bounds

    Upper Bound of a Call Option

    Both American and European call options give investors the right to buy a stock for a specified price. As a result, if a call option costs more than the underlying stock, an investor would simply buy the stock itself. 

    Upper Bound of an American Put Option

    American put options give investors the right to sell a stock for a specified price (the strike price) at any time up until the expiry date. As a result, an investor will not buy a put option that is priced higher than the strike price of the option. For example, an investor would not pay $60 for an option that gives her the right to sell a stock for only $50. 

    Upper Bound of European Put Options

    European put options can only be exercised at the expiry date. As a result, we calculate the upper bound of the option price equal to the present value of the strike price (found using the risk-free rate). If the strike price was higher than the present value of the strike price, an arbitrageur would sell a put, invest the proceeds, use the payoff at the expiry date to pay the contract, and keep the additional proceeds as profit. 

    Lower Bounds

    Lower Bound of a Call Option

    An American call option can be exercised at any time during the life of the option. In this case, the value of the call option cannot be less than the difference between the stock price and the strike price (for options in the money) and zero (for options out of the money). For example, consider a call option with a strike price of $50 is being sold on a stock worth $60. If the option price was less than $10, an arbitrageur would buy the option (for example, at $8), and immediately exercise the option and purchase the stock (at the strike price $50) for a total cost of $58. They could then sell this stock at the market price of $60 and make a risk-free profit of $2.

    In fact, we do not have to exercise an American call today. We can also exercise an American call at the expiry date. If we do this, we imagine that the strike price represents a risk-free asset, and we discount this value to find it's present value. If we write the call option today, but do not receive the value of the strike price until a future date, we miss out on investing the proceeds from the call (in, for example, a risk-free bond). For example, consider same stock option with an exercise price of $50 and a current stock price of $60. Wiith a 10% discount rate, that $50 strike price is worth $45 today. If the call option was priced at $10, an arbitrageur would buy the stock option today and invest $45 at the risk-free rate (a total cost of $55). He could also short the stock for $60 today, knowing he will be able to repurchase it, or "cover" it one year from now. This would yield an immediate profit of $5.  

    Therefore, the lower bound of both an American and a European call option can be found as the difference between the current stock price and the present value of the strike price. 

    Lower Bound of an American Put Option

    American put options have a minimum value of the current strike price less the current stock price. We do not discount the exercise price like we do with American call options. When you exercise a put, you are receiving, rather than paying, the strike price. If you exercised the put today, you could receive $50 and invest it; otherwise, you would just receive $50 at the maturity. Because of the time value of money, exercising a put sooner, rather than later, confers additional benefits to the owner. Therefore, we assume the put is exercised today. 

    Lower Bound of a European Put Option

    European put options must be exercised at the expiry date, so they have a minimum value of the present value of the strike price less the current stock price. 

    Other Considerations
    1. All options cannot have a negative value.
    2. American call and put options are always at least as valuable as European ones. 
    3. American options with more time to maturity are equally or more valuable as corresponding american options with a shorter time to maturity. 

    Photo by Fabrice Villard on Unsplash

    © BrainMass Inc. brainmass.com April 13, 2024, 9:39 am ad1c9bdddf

    BrainMass Solutions Available for Instant Download

    Sports Movement and Lower Extremity Movement

    I need to find a YouTube video that displays a sports movement and analyze the lower extremity movement and explain how the joints move, what muscles are involved, and how could the movement have been more efficient. Please give me some pointers.

    Upper and Lower Limits

    A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of 6 (n = 6) customer calls are measured for time. Results from the last eight samples are shown in the following table. Observation (seconds) S 1 2 3 4 5 6 1 425 4

    Lower of Cost or Market: Oheto Company

    E9-1 (Lower of Cost or Market) The inventory of Oheto Company on December 31, 2011, consists of the following items: Part No. Quantity Cost per Unit Cost to Replace per Unit 110 600 $95 $100 111 1,000 $60 $52 11

    Calculating the lower control limit

    The manager of an assembly line took 5 samples each with 6 observation under ideal conditions to develop control limits for an X bar chart The mean and range of each sample is shown in the table below: What would be the 3 standard deviation lower control limit? Number Mean Range 1

    Proving the properties of a real number and a function

    Let E be a subset of the real numbers R, and suppose that E has a least upper bound M which is a real number, i.e. M = sup(E). Let - E be the set - E := { - x : x belongs to E }. Show that - M is the greatest lower bound of - E i.e. - M = inf ( - E)

    Lower of Cost or Market

    E9-1 (Lower-of-Cost-or-Market) The inventory of 3T Company on December 31, 2008, consists of the following items. Part No. Quantity Cost per Unit Cost to Replace per Unit 110 600 $90 $100 111 1,0

    Find lower salary range, given 2 higher ranges.

    I am trying to figure out the missing pay range (min, mid, max) below. I do not know if the job level number has any correlation to anything, but included it anyway. Job Level Min Mid Max 90 ? ? ? 104 ? ? ? 120 4504 5630 6756 138 5069 6336 7603

    Firm Size and Top-Level Managers' Compensation

    Some evidence suggests that there is a direct and positive relationship between a firm's size and its top-level managers' compensation. Explain what inducement you think that relationship provides to upper-level executives. Recommend what can be done to influence the relationship so that it serves shareholders' interests.

    Case: Bounds v Smith (1977)

    United States Supreme Court opinion in Bounds, Correction Commissioner et al v Smith et al. Please read this case and prepare a brief.

    How higher quality can lead to lower costs Using Malcolm Gladwel

    I read an interesting article in "The New Yorker" magazine, "The Treatment", by Malcolm Gladwell. In it he talks about two approaches to finding a working cancer drug: "rational design" and "mass screening". The first is the norm and involves starting with the disease and working backward to find or create a drug. The seco

    Choosing Between Two Financing Options

    1) (Comparing borrowing costs) Stephens Security has two financing alternatives: (1) A publicly placed $50 million bond issue. Issuance costs are $1 million, the bond has a 9% coupon paid semiannually, and the bond has a 20-year life. (2) A $50 million private placement with a large pension fund. Issuance costs are $500,000, th

    Discuss why employees steal and discuss the theft triangle. People will steal if they desire to possess an item which they long for, or to sell off at a lower price and pocket it. If any opportunity presents itself they do not mind lifting an un-attended item or there is no or lack of detection.

    The Insider Threat: Why do employees steal? Discuss the Theft triangle. Write a 2 page paper, double spaced response to this question. Address the three sides of the theft triangle and the significance of each. In addition to motivation, opportunity and lack of detection other things that contribute to theft are prevention li

    Control limits problem

    (Problem attached in excel file) Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour for the past 24 hours has produced the following results: Hour X in " R in " 1 3.25 0.71 2 3.1 1.18 3 3.22 1.43 4 3.39 1.26 5 3.07 1.17 6 2.86 0.32 7 3.05 0.53 8 2.65 1.13 9 3.02 0.71 10 2.85

    Computing Lower of Cost or Market Values

    Please see the attached. Sedato Company follows the practice of pricing its inventory at the lower-of-cost-or-market, on an individual-item basis. Item No. Quantity Cost per Unit Cost to Replace Estimated Selling Price Cost of Completion and Disposal Normal Profit 1320 1,200 $3.20 $3.00 $4.50 $0.35 $1.25 1333 900 2.70

    Lower of Cost or Market Value - Grace Company

    Can you help me understand this question? Data for Grace Company relative to the 12/31/09 inventory record Units in Original Cost Total Original Current Unit Item Inventory Per Unit Cost Replacement Cost A 2,000

    Lower Level Employee and Certified Safety Professional Review

    A certified Safety Professional has many of the key elements a safety professional should bring to an organization. Would you consider hiring lower level employees that have the potential to become certified Safety Professionals? If yes, why? If no, why not?

    Lower Control Limits

    To guarantee that cans of soda are properly filled, some cans are sampled and the amounts measured. The overall average for the samples is 12 ounces. Each sample contains 10 cans. The average range is 0.4 ounces. The lower control chart limit for the average would be?

    Plant Assets, Cost Floors and Ceilings

    1) What are the major characteristics of plant assets. 2) Explain the rationale for the ceiling and floor in the lower-of-cost-or-market method of valuing inventories.

    Analyze scenario to lower price for their FiOS Internet service

    Resources: University Library, Internet Develop a paper in which you examine the applicability of different marketing research tools to Verizon and the scenario of lowering the price for their FiOS Internet service. I selected for my Market Research Implementation Plan: Problem Identification and Project Outline. Address t

    Lower-of-Cost-or-Market: Garcia Home Improvement Company

    I need help on this...please put in excel..Thank you.. ------------- Garcia Home Improvement Company installs replacement siding, windows, and louvered glass doors for single family homes and condominium complexes in northern New Jersey and southern New York. The company is in the process of preparing its annual financial st

    Budgeting process, bias adjustment by upper level managers

    7-6 Explain the cycle of bias by lower-level managers and bias-adjustment by upper-level managers that can spiral out of control and result in meaningless budgets. 7-11 "Budgeting is an unnecessary burden on many managers. It takes time away from important day-to-day problems." Do you agree? Explain

    Lower of cost or market

    I3-1: A company carries 5 products in its inventory. It uses the FIFO method of valuing inventory under the perpetual method. Data at the end of the month is as follows: Product FIFO Value Replacement Cost Estimated Selling Price A $68,000 $64,000 $75,000 B 36,000 40,000 45,000 C 42,000 40,000 65,000 D 33,000 37,000

    Price Discrimination - Lower Prices for the Poor

    I am asked to do a presentation on whether or not companies should lower their prices for the poor. Can you please help me get started with a few important points. I am required to critically think all points and sides objectivly. Thank You