Options pricing
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The document provides information and instructions for using the binomial option pricing model (BOPM) and Black-Scholes-Merton (BSM) model to value European call and put options with different underlying stock prices, strike prices, volatilities, risk free rates, and time to expiration. For each example, users are asked to use BOPM and BSM to determine the option value and in some cases the corresponding put or call value.
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Options and their Valuation
An options contract gives the holder the right, but not the obligation, to buy or sell an asset at a predetermined price on or before a specified date. There are two main types of options - calls, which give the right to buy, and puts, which give the right to sell. The Black-Scholes model provides a way to calculate the theoretical price of an option based on variables like the price of the underlying asset, strike price, time to expiration, risk-free interest rate and volatility. The model assumes markets are efficient and frictionless. Options can be combined in different ways to create positions with various risk-reward profiles.
Options and their Valuation
An options contract gives the holder the right, but not the obligation, to buy or sell an asset at a predetermined price on or before a specified date. There are two main types of options - calls, which give the right to buy, and puts, which give the right to sell. The Black-Scholes model provides a way to calculate the theoretical price of an option based on variables like the price of the underlying asset, strike price, time to expiration, risk-free interest rate and volatility. The model assumes markets are efficient and frictionless. Options can be combined in different ways to create positions with various risk-reward profiles.
Option Prib bb. Jj jcing revised.pdf
The document discusses various option pricing models, including the binomial option pricing model (BOPM) and the Black-Scholes model. It provides assumptions and explanations of how the models work, including pricing a stock that can increase or decrease at discrete time intervals for BOPM. It also gives examples of calculating call and put prices using the models.
Factor Structure in Equity Options
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2) Principal component analysis of implied volatility surfaces finds a strong common factor structure across equity options.
3) The model is estimated using a large dataset of equity and index option prices and is found to fit the cross-sectional variation in implied volatility surfaces across moneyness and maturity reasonably well.
4) The model implies that an equity's beta should be related to the level, skew, and term structure of its implied volatility, which is confirmed empirically.
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4_RealOptions.pdf
Objectives
• Know that standard NPV analysis does not account for real options
• Basic understanding of option pricing
– Black-Scholes formula
– Binomial model
• Know different types of real options and their implications
– Option to Expand
– Option to Wait
• Improve your ability to recognize valuable real options to make good business decisions
SECTION IV - CHAPTER 29 - Implied Volatility Basics
Implied volatility is the market's forecast of a likely movement in a security's price. It is used by investors to estimate future price fluctuations and is often employed to price options contracts. Implied volatility increases in bearish markets when prices are expected to decline, and decreases in bullish markets when prices are forecast to rise. Implied volatility differs from historical volatility, which measures actual past price movements.
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The document discusses upcoming changes to margin requirements for futures and options strategies in India. The key points are:
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Options and their Valuation
An options contract gives the holder the right, but not the obligation, to buy or sell an asset at a predetermined price on or before a specified date. There are two main types of options - calls, which give the right to buy, and puts, which give the right to sell. The Black-Scholes model provides a way to calculate the theoretical price of an option based on variables like the price of the underlying asset, strike price, time to expiration, risk-free interest rate and volatility. The model assumes markets are efficient and frictionless. Options can be combined in different ways to create positions with various risk-reward profiles.
Options and their Valuation
An options contract gives the holder the right, but not the obligation, to buy or sell an asset at a predetermined price on or before a specified date. There are two main types of options - calls, which give the right to buy, and puts, which give the right to sell. The Black-Scholes model provides a way to calculate the theoretical price of an option based on variables like the price of the underlying asset, strike price, time to expiration, risk-free interest rate and volatility. The model assumes markets are efficient and frictionless. Options can be combined in different ways to create positions with various risk-reward profiles.
Option Prib bb. Jj jcing revised.pdf
The document discusses various option pricing models, including the binomial option pricing model (BOPM) and the Black-Scholes model. It provides assumptions and explanations of how the models work, including pricing a stock that can increase or decrease at discrete time intervals for BOPM. It also gives examples of calculating call and put prices using the models.
Factor Structure in Equity Options
1) The document presents a factor model for equity option pricing where the underlying stock price follows a factor structure linked to a stochastic volatility index.
2) Principal component analysis of implied volatility surfaces finds a strong common factor structure across equity options.
3) The model is estimated using a large dataset of equity and index option prices and is found to fit the cross-sectional variation in implied volatility surfaces across moneyness and maturity reasonably well.
4) The model implies that an equity's beta should be related to the level, skew, and term structure of its implied volatility, which is confirmed empirically.
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The document discusses various metrics and indicators that can be used to determine bear markets and market tops. It presents four ways to identify market tops: the Tsunami Indicator sell everything signal, the Fifty New Lows Rule sell everything signal, accelerating new lows sell everything signal, and a series of tops sell everything signal. It also discusses signals that can be used to identify market bottoms and determine when to reenter the market, including the All Clear signal, intermediate buy signal, and Pep Indicator. The document provides definitions of the indicators and signals and examples of how they are calculated and interpreted.
4_RealOptions.pdf
Objectives
• Know that standard NPV analysis does not account for real options
• Basic understanding of option pricing
– Black-Scholes formula
– Binomial model
• Know different types of real options and their implications
– Option to Expand
– Option to Wait
• Improve your ability to recognize valuable real options to make good business decisions
SECTION IV - CHAPTER 29 - Implied Volatility Basics
Implied volatility is the market's forecast of a likely movement in a security's price. It is used by investors to estimate future price fluctuations and is often employed to price options contracts. Implied volatility increases in bearish markets when prices are expected to decline, and decreases in bullish markets when prices are forecast to rise. Implied volatility differs from historical volatility, which measures actual past price movements.
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The document discusses upcoming changes to margin requirements for futures and options strategies in India. The key points are:
1) Margin requirements for hedged futures and options strategies are expected to be reduced by 60-75% under the new framework.
2) Margins on naked futures positions will increase slightly, from the current 16.7% to the new requirement of 18.5%.
3) The changes aim to reduce margins for limited-risk strategies while increasing margins for uncovered positions, making margins more dynamic based on market volatility.
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2) It provides a step-by-step example of using a single-period model to value a European call and put. The steps include creating an asset price lattice, determining terminal option values, calculating probabilities, and determining the option and hedge ratios.
3) It then demonstrates a two-period binomial model example to value a European put option, extending the process over two periods rather than one.
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2. Choose a program location, semester, and courses that fit your degree requirements. Programs are available in Europe, Australia, and other regions.
3. Apply directly to the study abroad program provider by their application deadline, typically one semester in advance.
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2. Choose a program, location, and semester. Programs are available in Europe, Australia, and elsewhere for summer, spring break, and semester-long study.
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1) The document describes how to use a single-period and two-period binomial option pricing model to value European call and put options.
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4) Finally, it notes that an American option would be valued differently than a European option using binomial modeling, as the early exercise feature has additional value.
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This document contains announcements and information about upcoming events for the Cameron School of Business, including:
1) A lecture on "The Myth of the Robber Barons" to be given by Dr. Burton Folsom on March 27th in room CH 105.
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This document provides information for applying to the Cameron School of Business. It outlines the class standing requirements to apply, noting that freshmen must have less than 30 credit hours, sophomores 30-59 hours, and juniors 60-89 hours plus credits in progress to equal 60 or more. It encourages applying even if the requirements are not yet met and directs the reader to the last page for tips, including what the prerequisite course and admission codes refer to.
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This document contains practice questions and answers about options strategies. It includes 17 multiple choice questions that test understanding of concepts like being long or short different options positions, determining if an option is in, at, or out of the money, and the maximum profit and loss scenarios for options buyers and writers. The document also includes examples of how the payoff and profit is calculated at expiration for long and short positions in stocks, bonds, calls and puts.
2016 fall finance requirements
The document outlines the requirements and core curriculum for admission to and graduation from the Cameron School of Business at UNCW, including a list of prerequisite and required courses, information on applying for graduation, and a chart showing the course schedule and semester each course is offered. It also provides details on international study opportunities through the business school and when students should apply for graduation.
2016 fall economics requirements
1. Meet with the CSB study abroad advisor to discuss options for business courses that can be taken abroad.
2. Choose a program location, semester, and courses that fit your degree requirements. Programs are available in Europe, Australia, and other regions.
3. Apply directly to the study abroad program provider by their application deadline, typically one semester in advance.
4. Course credits earned abroad will transfer back to UNCW to count towards your business degree.
2016 fall inb requirements
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Fall 2016 economics requirements
1. Meet with the CSB study abroad advisor to discuss options for business courses abroad.
2. Choose a program, location, and semester. Programs are available in Europe, Australia, and elsewhere for summer, spring break, and semester-long study.
3. Register for pre-approved CSB courses to count towards your degree while abroad. Business courses like marketing, management, and international business are offered.
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Fall 2016 finance requirements
The document outlines the requirements and core curriculum for admission to and graduation from the Cameron School of Business at UNCW, including prerequisite and required courses, minimum GPA and credit requirements, and course schedules. It also provides information on studying abroad opportunities, applying to graduate, and a chart of the subset of core courses required for admission to the business school.
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The document outlines the thesis process for an IMBA program at UNC Wilmington. It discusses selecting a thesis committee, developing a topic and research question, scheduling a proposal defense, conducting research and data collection, writing drafts, scheduling a final defense, and submitting the final thesis. It provides details on the roles of the committee chair and readers in guiding the process and approving the thesis. Key steps in the research process are also summarized.
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বিসিএস ও ব্যাংক এর লিখিত পরীক্ষা ...+এছাড়া মাধ্যমিক ও উচ্চমাধ্যমিকের স্টুডেন্টদের জন্য অনেক কাজে আসবে ...
How to Setup Warehouse & Location in Odoo 17 Inventory
In this slide, we'll explore how to set up warehouses and locations in Odoo 17 Inventory. This will help us manage our stock effectively, track inventory levels, and streamline warehouse operations.
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www.StokeNewingtonHistory.com
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Options pricing
- 1. © 2018 Dr. N. Richie, UNCW 1 Options Pricing BOPM and BSM Models
- 2. © 2018 Dr. N. Richie, UNCW 2 Use the binomial option pricing model to determine the value of the call and the appropriate hedge ratios given the following information • Stock currently trading at $20 per share • European call strike price is $20 • Standard deviation of stock returns is 25% • Risk free rate is 5% • Option expires in 85 days (using 365 day year) • BOPM using 2 nodes
- 3. 3 Use the Black-Scholes-Merton model to determine the value of the call given the following information • Stock currently trading at $20 per share • European call strike price is $20 • Standard deviation of stock returns is 25% • Risk free rate is 5% • Option expires in 85 days (using 365 day year) What is the value of the corresponding put?
- 4. © 2018 Dr. N. Richie, UNCW 4 Use the binomial option pricing model to determine the value of the call and the appropriate hedge ratios given the following information • Stock currently trading at $45 per share • European call strike price is $40 • Standard deviation of stock returns is 35% • Risk free rate is 5% • Option expires in 150 days (using 365 day year) • BOPM using 3 nodes
- 5. 5 Use the Black-Scholes-Merton model to determine the value of the call given the following information • Stock currently trading at $45 per share • European call strike price is $40 • Standard deviation of stock returns is 35% • Risk free rate is 5% • Option expires in 150 days (using 365 day year) What is the value of the corresponding put?
- 6. © 2018 Dr. N. Richie, UNCW 6 Use the binomial option pricing model to determine the value of the put and the appropriate hedge ratios given the following information • Stock currently trading at $45 per share • European put strike price is $48 • Standard deviation of stock returns is 25% • Risk free rate is 6% • Option expires in 200 days (using 365 day year) • BOPM using 4 nodes