FINANCIAL ENGINEERING CLUB TRADING 201

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "FINANCIAL ENGINEERING CLUB TRADING 201"

Transcription

1 FINANCIAL ENGINEERING CLUB TRADING 201

2 GREG PASTOREK

3 OPTIONS REVIEW A call (put) option with strike K expiring on date T gives the owner the right to buy (sell) the underlying security for price K until date T. For stock options, 1 option gives the right to buy/sell 100 stock.

4 OPTIONS PRICING In order to trade options, we need to understand how they are priced The Black-Scholes equation calculates the price of an option based on a number of variables including: Stock Price Strike Time to Expiration Interest Rates Volatility

5 OPTION PRICING It s all about volatility Volatility is the measure of how much a stock moves, the true future volatility is unknown. The implied volatility (IV) of a stock is the price volatility implied from the options prices For each day into the future, we can forecast a probability distribution for a stock price

6 STOCK PRICE The change in the option price as a function of the change in the stock price is known as Delta Delta is the first derivative with respect to stock price of the Black-Scholes option pricing equation

7 STOCK PRICE Delta can be viewed as the probability of an option expiring ITM Far ITM options have ±100 deltas ATM options have ±50 deltas Far OTM options have 0 deltas

8 STOCK PRICE Gamma is the second derivative with respect to stock price of the Black-Scholes equation So Delta tells you how much the option price will change if the stock price increases by $1, c.p. Gamma tells you how Delta changes if the stock price increases by $1, c.p. Gamma is highest for ATM options

9 STOCK PRICE Note that a long gamma position favors price movement while a short gamma position favors little to no price movement If we are long gamma, the stock price increases, then our delta exposure will increase. We become increasingly long delta as the price increases

10 HEDGING WITH DELTA Hedging is the idea of reducing risk By hedging a trade, we are limiting the profitability of a trade while at the same time decreasing the amount of risk we are taking Suppose we are trading options, and we do not want to make any bets on the underlying price movement, then we would want to hedge against the underlying price risk.

11 HEDGING WITH DELTA So for example, if we sold an OTM Call in some underlying then we are short Deltas A hedge would be any trade that adds long Deltas in the same underlying so that we are (near) zero deltas. This could include buying the underlying, buying a Call at a different strike, selling a Put, etc.

12 HEDGING WITH DELTA Also note that delta hedging doesn t protect against large underlying changes because of gamma Your delta changes as price changes too!

13 TIME TO EXPIRATION Theta is the first derivative with respect to time of the Black- Scholes options pricing equation Options decrease in price over time Theta will always be given as a negative value equal to the decrease in an options price given 1 day has passed, c.p. Refer to theta position as paying theta and collecting theta.

14 TIME TO EXPIRATION If options have a lot of time till their expiration, they have a greater chance of winding up ITM If there is only 1 day left until expiration, an OTM option will be much cheaper than an option at the same strike if there were 100 days until expiration, c.p. OTM options will be worthless at expiration ITM options will converge to their intrinsic value

15 TIME TO EXPIRATION ATM options are more sensitive to time than deep ITM or far OTM options All long option position will pay Theta. A long (short) gamma position will always pay (collect) Theta.

16 VOLATILITY Vega is the first derivative with respect to volatility of the Black-Scholes options pricing equation Volatility makes options more expensive If you have limited loss and unlimited profit potential, more volatility will increase the expected profit of a long position.

17 VOLATILITY Options traders are generally trading volatility and vega is their unit of risk since delta is generally hedged Gamma and theta are closely tied with some exceptions (time-spreads) Volatility is a mean-reverting process Implied vs. Realized Volatility

18 VOLATILITY ATM options are more sensitive to changes in volatility than deep ITM or far OTM options Vega is highest for ATM options All options have positive Vega

19 SKEW Volatility skew describes how volatility risk (vega) varies from low to high strikes High skew positions are at risk of reaching large vega for large (one direction) moves in the underlying

20 SKEW For example, risk reversal:

21 KURTOSIS Volatility kurtosis describes how volatility risk (vega) varies from ITM/OTM strikes to ATM strikes High kurtosis positions are at risk of reaching large vega for large (either direction) moves in the underlying

22 KURTOSIS For example, iron condor:

23 INTEREST RATES Rho is the first derivative with respect to the risk-free rate of interest of the Black-Scholes equation Rho tells you how much an option price will change with a 1 percentage-point increase in interest rates Rho is positive for Calls and negative for Puts

24 THE GREEKS Delta, Gamma, Vega, Theta, and Rho are collectively known as the Greeks They are various derivatives of the Black-Scholes options pricing equation

25 PROBLEMS The Black-Scholes model does not agree with reality in a number of ways Assumes stock returns are log-normally distributed, ignores the fat tails that account for black swan events Black-Scholes is also used to price European options while we will typically be dealing with American options Assumes volatility is constant across all strikes, in reality we see a skew or a smile. No transactions costs, unlimited short selling, etc.

26 SYNTHETICS Long Call + Short Put = Long 1 Underlying Short Call + Long Put = Short 1 Underlying Try to find arbitrage relationships! Account for interest. Long 1 call + Short 1 Put is equivalent to holding 100 shares of stock, but you pay less cash to hold the option position so you have more capital to earn interest on

27 PUT-CALL PARITY For European Options For American Options C P = S Ke rt S K C P S Ke rt Using Put-Call Parity, traders can quickly identify mispricings by relative value

28 BOX SPREAD Long (lower) Call Short (higher) Call Long (higher) Put Short (lower) Put Selling box spreads is similar to taking a loan at the risk free rate

29 PIN RISK Scenario: You are short a call or put option and the option expires ATM. You don t know if the option was used until the next day, so you are unsure how to hedge your delta overnight Can turn a box spread into a high delta position! Avoid PIN risk by avoiding holding ATM options near expiration

30 NICK GARFIELD

31 OPPORTUNITIES We re going to look for places where the market gives us an edge (mispricings) We re going to look for reversion to the mean We re going to trade with probabilities, not emotions

32 SELLING THETA All option prices decrease over time, c.p. Buying a Call or a Put has the disadvantage of time decay We can take advantage of theta by short-selling options

33 SELLING THETA Selling theta is the strategy of selling OTM Calls and Puts instead of buying them By selling options, we take advantage of the theta decay in their prices Studies have shown that the fastest rate of Theta decay occurs while options are in the DTE range So, looking to selling options with 45 DTE should provide you with a slight edge

34 VOLATILITY MEAN REVERSION Volatility is a highly mean-reverting statistic We can take advantage of this by selling options with volatile underlyings Selling options in a volatile stock not only gives you a greater POP but also more profit Options are more expensive in a volatile underlying. By selling them, we take in a greater max profit

35 USE THE PROBABILITIES Find a percentage that is comfortable for your trading Selling an option with a strike 1 SD away from the current price has a POP of around 82% Selling an option with a strike 2 SD away form the current price has a POP of around 98% POP is the probability of making at least $0.01 on a trade If we are selling options, POP is the probability that the stock will not be beyond the option s strike at expiration

36 USE THE PROBABILITIES

37 POP OF 1 SD SHORT CALL

38 POP 2 SD SHORT CALL

39 USE THE PROBABILITIES Probability ITM is the probability that an option will expire in the money Probability of a touch (POT) is the probability that we will be tested at some point during our trade It is the probability that the stock will touch our short strike point sometime between now and our option s expiration date POT = 2 Prob. ITM So the 1 SD short option will be tested approximately 36% of the time

40 SPREADS A spread is the simultaneous trade of two or more options Verticals Strangles Iron Condors

41 VERTICALS A Vertical is made up of a short option and a long option at different strike prices with the same expiration This is risk-defined trade to use when you have a directional assumption about a particular stock The max loss for a short vertical is equal to the width of the strikes minus the credit received The max loss for a long vertical is equal to the debit paid for the position

42 VERTICALS Trade short verticals when there is relatively high IV and we are looking for a volatility contraction Trade long verticals when there is relatively low IV and we are looking for a volatility expansion

43 VERTICALS Verticals can be thought of as a hedge to the naked option position We are combining two positions of both long and short Deltas into the same underlying Decreases our POP but also defines our max loss

44 SHORT VERTICALS Sell an OTM strike Buy a further OTM strike Credit received is the difference between the two prices

45 SHORT CALL VERTICALS Your max loss is the difference between the strikes minus the credit received Your max profit is the total credit you received for selling the spread

46 LONG CALL VERTICALS Your max loss of buying a Long Vertical is the total premium you paid for the position Your max profit is difference between the strikes minus the premium paid

47 VERTICALS EXAMPLE Long AAPL Sept 50 Call for $2.00 Short APPL Sept 60 Call for $0.75 Total Cost? Max Loss? Max Profit?

48 STRANGLES A strangle is a position that consists of selling both a short Call and a short Put The strategy is profitable when the underlying stays above the strike of the short put and below the strike of the short call The trade will lose money when the underlying moves outside of this defined range Excellent strategy to employ with high IV

49 STRANGLES Sell an OTM Put Sell an OTM Call Credit received is the sum of the two prices

50 STRANGLES Your max loss is infinite Your max profit is the total credit you received for selling the strangle

51 STRANGLES

52 IRON CONDORS The Iron Condor is a mix of the short vertical and the strangle It is a position consisting of the selling a short Call spread and selling a short Put spread Unlike the strangle, the icon condor has a defined max loss and a lower POP Like the strangle, the iron condor is profitable when he underlying stays between the two strikes

53 IRON CONDORS Sell an OTM Put vertical Sell an OTM Call vertical Credit received is the sum of the two sales

54 IRON CONDORS Your max loss is limited and defined unlike the strangle Your max profit is the total credit you received for selling the spread

55 SPREADS Short verticals, strangles, and iron condors all of the the advantage of theta decay They tend to work best in high-vol environments and take advantage of volatility s reversion to the mean Easy to understand and calculate the POP

56 Time Spreads Short front-month ATM straddle Long back-month ATM straddle Short gamma (since the front-month gamma explodes as expiration approaches) Short gamma = Collecting theta We are long vega, front month vega is less than back month. We have gamma and vega opposite signs!

57 BREAK-EVENS Short Call Verticals: Short Strike + Credit Received Short Put Verticals: Short Strike Credit Received Strangles: Call side: Short Strike + Credit Received Put side: Short Strike Credit Received Iron Condors: Same as above

58 CLOSING TRADES We can significantly improve our POP by locking in profits and taking off trades at 50% of max profit For example, if we sell a short Put vertical for $2.00, the probability that the vertical will trade for $1.00 sometime between now and expiration is significantly greater than the probability than the short Put vertical will expire worthless So if we lock in profits at 50%, we can take some risk off the table and move on to the next trade

59 THANK YOU

FINANCIAL ENGINEERING CLUB TRADING 201

FINANCIAL ENGINEERING CLUB TRADING 201 FINANCIAL ENGINEERING CLUB TRADING 201 STOCK PRICING It s all about volatility Volatility is the measure of how much a stock moves The implied volatility (IV) of a stock represents a 1 standard deviation

More information

Finance 436 Futures and Options Review Notes for Final Exam. Chapter 9

Finance 436 Futures and Options Review Notes for Final Exam. Chapter 9 Finance 436 Futures and Options Review Notes for Final Exam Chapter 9 1. Options: call options vs. put options, American options vs. European options 2. Characteristics: option premium, option type, underlying

More information

ETF Trend Trading. Option Basics Part Two The Greeks

ETF Trend Trading. Option Basics Part Two The Greeks ETF Trend Trading Option Basics Part Two The Greeks Option Basics Separate Sections 1. Option Basics 2. The Greeks 3. Pricing 4. Types of Option Trades The Greeks A simple perspective on the 5 Greeks 1.

More information

Week 13 Introduction to the Greeks and Portfolio Management:

Week 13 Introduction to the Greeks and Portfolio Management: Week 13 Introduction to the Greeks and Portfolio Management: Hull, Ch. 17; Poitras, Ch.9: I, IIA, IIB, III. 1 Introduction to the Greeks and Portfolio Management Objective: To explain how derivative portfolios

More information

Caput Derivatives: October 30, 2003

Caput Derivatives: October 30, 2003 Caput Derivatives: October 30, 2003 Exam + Answers Total time: 2 hours and 30 minutes. Note 1: You are allowed to use books, course notes, and a calculator. Question 1. [20 points] Consider an investor

More information

Trading Options MICHAEL BURKE

Trading Options MICHAEL BURKE Trading Options MICHAEL BURKE Table of Contents Important Information and Disclosures... 3 Options Risk Disclosure... 4 Prologue... 5 The Benefits of Trading Options... 6 Options Trading Primer... 8 Options

More information

Buying Call or Long Call. Unlimited Profit Potential

Buying Call or Long Call. Unlimited Profit Potential Options Basis 1 An Investor can use options to achieve a number of different things depending on the strategy the investor employs. Novice option traders will be allowed to buy calls and puts, to anticipate

More information

The equilibrium price of the call option (C; European on a non-dividend paying stock) is shown by Black and Scholes to be: are given by. p T t.

The equilibrium price of the call option (C; European on a non-dividend paying stock) is shown by Black and Scholes to be: are given by. p T t. THE GREEKS BLACK AND SCHOLES (BS) FORMULA The equilibrium price of the call option (C; European on a non-dividend paying stock) is shown by Black and Scholes to be: C t = S t N(d 1 ) Xe r(t t) N(d ); Moreover

More information

The Four Basic Options Strategies

The Four Basic Options Strategies 1 The Four Basic Options Strategies Introduction The easiest way to learn options is with pictures so that you can begin to piece together strategies step-by-step. However, first we need to understand

More information

Factors Affecting Option Prices. Ron Shonkwiler (shonkwiler@math.gatech.edu) www.math.gatech.edu/ shenk

Factors Affecting Option Prices. Ron Shonkwiler (shonkwiler@math.gatech.edu) www.math.gatech.edu/ shenk 1 Factors Affecting Option Prices Ron Shonkwiler (shonkwiler@math.gatech.edu) www.math.gatech.edu/ shenk 1 Factors Affecting Option Prices Ron Shonkwiler (shonkwiler@math.gatech.edu) www.math.gatech.edu/

More information

FINANCIAL ENGINEERING CLUB TRADING 101

FINANCIAL ENGINEERING CLUB TRADING 101 FINANCIAL ENGINEERING CLUB TRADING 101 WHAT IS TRADING TRADING/INVESTING is the act of putting capital to use, by either buying or selling securities, for the purpose of gaining profits. Buy low, sell

More information

Basics of Spreading: Butterflies and Condors

Basics of Spreading: Butterflies and Condors 1 of 31 Basics of Spreading: Butterflies and Condors What is a Spread? Review the links below for detailed information. Terms and Characterizations: Part 1 Download What is a Spread? Download: Butterflies

More information

Volatility as an indicator of Supply and Demand for the Option. the price of a stock expressed as a decimal or percentage.

Volatility as an indicator of Supply and Demand for the Option. the price of a stock expressed as a decimal or percentage. Option Greeks - Evaluating Option Price Sensitivity to: Price Changes to the Stock Time to Expiration Alterations in Interest Rates Volatility as an indicator of Supply and Demand for the Option Different

More information

Arbitrage spreads. Arbitrage spreads refer to standard option strategies like vanilla spreads to

Arbitrage spreads. Arbitrage spreads refer to standard option strategies like vanilla spreads to Arbitrage spreads Arbitrage spreads refer to standard option strategies like vanilla spreads to lock up some arbitrage in case of mispricing of options. Although arbitrage used to exist in the early days

More information

Option Values. Option Valuation. Call Option Value before Expiration. Determinants of Call Option Values

Option Values. Option Valuation. Call Option Value before Expiration. Determinants of Call Option Values Option Values Option Valuation Intrinsic value profit that could be made if the option was immediately exercised Call: stock price exercise price : S T X i i k i X S Put: exercise price stock price : X

More information

VANILLA OPTIONS MANUAL

VANILLA OPTIONS MANUAL VANILLA OPTIONS MANUAL BALANCE YOUR RISK WITH OPTIONS Blue Capital Markets Limited 2013. All rights reserved. Content Part A The what and why of options 1 Types of options: Profit and loss scenarios 2

More information

CHAPTER 20 Understanding Options

CHAPTER 20 Understanding Options CHAPTER 20 Understanding Options Answers to Practice Questions 1. a. The put places a floor on value of investment, i.e., less risky than buying stock. The risk reduction comes at the cost of the option

More information

9 Basics of options, including trading strategies

9 Basics of options, including trading strategies ECG590I Asset Pricing. Lecture 9: Basics of options, including trading strategies 1 9 Basics of options, including trading strategies Option: The option of buying (call) or selling (put) an asset. European

More information

Swing Trade Warrior Chapter 1. Introduction to swing trading and how to understand and use options How does Swing Trading Work? The idea behind swing trading is to capitalize on short term moves of stocks

More information

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION

CHAPTER 20: OPTIONS MARKETS: INTRODUCTION CHAPTER 20: OPTIONS MARKETS: INTRODUCTION 1. Cost Profit Call option, X = 95 12.20 10 2.20 Put option, X = 95 1.65 0 1.65 Call option, X = 105 4.70 0 4.70 Put option, X = 105 4.40 0 4.40 Call option, X

More information

How to Trade Options: Strategy Building Blocks

How to Trade Options: Strategy Building Blocks How to Trade Options: Strategy Building Blocks MICHAEL BURKE Important Information and Disclosures This course is provided by TradeStation, a U.S.-based multi-asset brokerage company that seeks to serve

More information

Week 1: Futures, Forwards and Options derivative three Hedge: Speculation: Futures Contract: buy or sell

Week 1: Futures, Forwards and Options derivative three Hedge: Speculation: Futures Contract: buy or sell Week 1: Futures, Forwards and Options - A derivative is a financial instrument which has a value which is determined by the price of something else (or an underlying instrument) E.g. energy like coal/electricity

More information

Options Markets: Introduction

Options Markets: Introduction Options Markets: Introduction Chapter 20 Option Contracts call option = contract that gives the holder the right to purchase an asset at a specified price, on or before a certain date put option = contract

More information

Clear and Simple Option Strategy PRESENTED BY: DENNIS W. WILBORN

Clear and Simple Option Strategy PRESENTED BY: DENNIS W. WILBORN Clear and Simple Option Strategy PRESENTED BY: DENNIS W. WILBORN Disclaimer U.S. GOVERNMENT REQUIRED DISCLAIMER COMMODITY FUTURES TRADING COMMISSION FUTURES AND OPTIONS TRADING HAS LARGE POTENTIAL REWARDS,

More information

Session X: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics. Department of Economics, City University, London

Session X: Lecturer: Dr. Jose Olmo. Module: Economics of Financial Markets. MSc. Financial Economics. Department of Economics, City University, London Session X: Options: Hedging, Insurance and Trading Strategies Lecturer: Dr. Jose Olmo Module: Economics of Financial Markets MSc. Financial Economics Department of Economics, City University, London Option

More information

Hedging. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan Hedging

Hedging. An Undergraduate Introduction to Financial Mathematics. J. Robert Buchanan. J. Robert Buchanan Hedging Hedging An Undergraduate Introduction to Financial Mathematics J. Robert Buchanan 2010 Introduction Definition Hedging is the practice of making a portfolio of investments less sensitive to changes in

More information

Factors Affecting Option Prices

Factors Affecting Option Prices Factors Affecting Option Prices 1. The current stock price S 0. 2. The option strike price K. 3. The time to expiration T. 4. The volatility of the stock price σ. 5. The risk-free interest rate r. 6. The

More information

OPTIONS. FINANCE TRAINER International Options / Page 1 of 38

OPTIONS. FINANCE TRAINER International Options / Page 1 of 38 OPTIONS 1. FX Options... 3 1.1 Terminology... 4 1.2 The Four Basic Positions... 5 1.3 Standard Options... 7 1.4 Exotic Options... 7 1.4.1 Asian Option (Average Rate Option, ARO)... 7 1.4.2 Compound Option...

More information

Properties of Stock Options. Chapter 10

Properties of Stock Options. Chapter 10 Properties of Stock Options Chapter 10 1 Notation c : European call option price C : American Call option price p : European put option price P : American Put option price S 0 : Stock price today K : Strike

More information

Contents. iii. MFE/3F Study Manual 9th edition Copyright 2011 ASM

Contents. iii. MFE/3F Study Manual 9th edition Copyright 2011 ASM Contents 1 Put-Call Parity 1 1.1 Review of derivative instruments................................................ 1 1.1.1 Forwards............................................................ 1 1.1.2 Call

More information

Lecture 5: Put - Call Parity

Lecture 5: Put - Call Parity Lecture 5: Put - Call Parity Reading: J.C.Hull, Chapter 9 Reminder: basic assumptions 1. There are no arbitrage opportunities, i.e. no party can get a riskless profit. 2. Borrowing and lending are possible

More information

Lecture 11: The Greeks and Risk Management

Lecture 11: The Greeks and Risk Management Lecture 11: The Greeks and Risk Management This lecture studies market risk management from the perspective of an options trader. First, we show how to describe the risk characteristics of derivatives.

More information

Market Risk for Single Trading Positions

Market Risk for Single Trading Positions Chapter 6 Market Risk for Single Trading Positions Market risk is the risk that the market value of trading positions will be adversely influenced by changes in prices and/or interest rates. For banks,

More information

Option Spreads Continued

Option Spreads Continued Option Spreads Continued 3/4/2015 Option Boot Camp by Sunset Partners Capital Management Questions/Comments/Suggestions: info@sunsetpartnerscapital.com Disclosure This presentation is for educational purposes

More information

Return to Risk Limited website: www.risklimited.com. Overview of Options An Introduction

Return to Risk Limited website: www.risklimited.com. Overview of Options An Introduction Return to Risk Limited website: www.risklimited.com Overview of Options An Introduction Options Definition The right, but not the obligation, to enter into a transaction [buy or sell] at a pre-agreed price,

More information

Options: How About Wealth & Income? I Really Don t Care Which Way the Market Goes!

Options: How About Wealth & Income? I Really Don t Care Which Way the Market Goes! Options: How About Wealth & Income? I Really Don t Care Which Way the Market Goes! Disclaimer U.S. GOVERNMENT REQUIRED DISCLAIMER COMMODITY FUTURES TRADING COMMISSION FUTURES AND OPTIONS TRADING HAS LARGE

More information

Underlying (S) The asset, which the option buyer has the right to buy or sell. Notation: S or S t = S(t)

Underlying (S) The asset, which the option buyer has the right to buy or sell. Notation: S or S t = S(t) INTRODUCTION TO OPTIONS Readings: Hull, Chapters 8, 9, and 10 Part I. Options Basics Options Lexicon Options Payoffs (Payoff diagrams) Calls and Puts as two halves of a forward contract: the Put-Call-Forward

More information

Underlier Filters Category Data Field Description

Underlier Filters Category Data Field Description Price//Capitalization Market Capitalization The market price of an entire company, calculated by multiplying the number of shares outstanding by the price per share. Market Capitalization is not applicable

More information

Example 1. Consider the following two portfolios: 2. Buy one c(s(t), 20, τ, r) and sell one c(s(t), 10, τ, r).

Example 1. Consider the following two portfolios: 2. Buy one c(s(t), 20, τ, r) and sell one c(s(t), 10, τ, r). Chapter 4 Put-Call Parity 1 Bull and Bear Financial analysts use words such as bull and bear to describe the trend in stock markets. Generally speaking, a bull market is characterized by rising prices.

More information

Chapter 5 Financial Forwards and Futures

Chapter 5 Financial Forwards and Futures Chapter 5 Financial Forwards and Futures Question 5.1. Four different ways to sell a share of stock that has a price S(0) at time 0. Question 5.2. Description Get Paid at Lose Ownership of Receive Payment

More information

INTRODUCTION TO WEEKLY OPTIONS

INTRODUCTION TO WEEKLY OPTIONS INTRODUCTION TO WEEKLY OPTIONS Kerry W. Given, Ph.D. (Dr. Duke) Parkwood Capital, LLC Weekly options have grown dramatically in popularity over the past year or two. In one sense, you could say weekly

More information

Steve Meizinger. FX Options Pricing, what does it Mean?

Steve Meizinger. FX Options Pricing, what does it Mean? Steve Meizinger FX Options Pricing, what does it Mean? For the sake of simplicity, the examples that follow do not take into consideration commissions and other transaction fees, tax considerations, or

More information

On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price

On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price On Black-Scholes Equation, Black- Scholes Formula and Binary Option Price Abstract: Chi Gao 12/15/2013 I. Black-Scholes Equation is derived using two methods: (1) risk-neutral measure; (2) - hedge. II.

More information

Steve Meizinger. Understanding the FX Option Greeks

Steve Meizinger. Understanding the FX Option Greeks Steve Meizinger Understanding the FX Option Greeks For the sake of simplicity, the examples that follow do not take into consideration commissions and other transaction fees, tax considerations, or margin

More information

Chapters 15. Delta Hedging with Black-Scholes Model. Joel R. Barber. Department of Finance. Florida International University.

Chapters 15. Delta Hedging with Black-Scholes Model. Joel R. Barber. Department of Finance. Florida International University. Chapters 15 Delta Hedging with Black-Scholes Model Joel R. Barber Department of Finance Florida International University Miami, FL 33199 1 Hedging Example A bank has sold for $300,000 a European call option

More information

Options: Valuation and (No) Arbitrage

Options: Valuation and (No) Arbitrage Prof. Alex Shapiro Lecture Notes 15 Options: Valuation and (No) Arbitrage I. Readings and Suggested Practice Problems II. Introduction: Objectives and Notation III. No Arbitrage Pricing Bound IV. The Binomial

More information

Credit Spreads and Iron Condors

Credit Spreads and Iron Condors Credit Spreads and Iron Condors Marty Kearney Senior Instructor The Options Institute at CBOE Disclosures In order to simplify the computations, commissions have not been included in the examples used

More information

Options/1. Prof. Ian Giddy

Options/1. Prof. Ian Giddy Options/1 New York University Stern School of Business Options Prof. Ian Giddy New York University Options Puts and Calls Put-Call Parity Combinations and Trading Strategies Valuation Hedging Options2

More information

Covered Call Option Strategy

Covered Call Option Strategy The covered call option strategy, also known as a buy write strategy, is implemented by writing (selling) a call option contract while owning an equivalent number of shares of the underlying stock. This

More information

Implied Volatility Surface

Implied Volatility Surface Implied Volatility Surface Liuren Wu Zicklin School of Business, Baruch College Options Markets (Hull chapter: 16) Liuren Wu Implied Volatility Surface Options Markets 1 / 18 Implied volatility Recall

More information

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald)

Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs. Binomial Option Pricing: Basics (Chapter 10 of McDonald) Copyright 2003 Pearson Education, Inc. Slide 08-1 Institutional Finance 08: Dynamic Arbitrage to Replicate Non-linear Payoffs Binomial Option Pricing: Basics (Chapter 10 of McDonald) Originally prepared

More information

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008

FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 Options These notes consider the way put and call options and the underlying can be combined to create hedges, spreads and combinations. We will consider the

More information

Chapter 11 Properties of Stock Options. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull

Chapter 11 Properties of Stock Options. Options, Futures, and Other Derivatives, 9th Edition, Copyright John C. Hull Chapter 11 Properties of Stock Options 1 Notation c: European call option price p: European put option price S 0 : Stock price today K: Strike price T: Life of option σ: Volatility of stock price C: American

More information

INTRODUCTION TO OPTIONS MARKETS QUESTIONS

INTRODUCTION TO OPTIONS MARKETS QUESTIONS INTRODUCTION TO OPTIONS MARKETS QUESTIONS 1. What is the difference between a put option and a call option? 2. What is the difference between an American option and a European option? 3. Why does an option

More information

OPTIONS EDUCATION GLOBAL

OPTIONS EDUCATION GLOBAL OPTIONS EDUCATION GLOBAL TABLE OF CONTENTS Introduction What are FX Options? Trading 101 ITM, ATM and OTM Options Trading Strategies Glossary Contact Information 3 5 6 8 9 10 16 HIGH RISK WARNING: Before

More information

Vertical Spread Design

Vertical Spread Design Vertical Spread Design J. Scott Chaput* Louis H. Ederington** November 2004 initial draft: June 2002 * Lecturer in Finance ** Michael F. Price Professor of Finance University of Otago Michael F. Price

More information

Trading Strategies Involving Options. Chapter 11

Trading Strategies Involving Options. Chapter 11 Trading Strategies Involving Options Chapter 11 1 Strategies to be Considered A risk-free bond and an option to create a principal-protected note A stock and an option Two or more options of the same type

More information

The Call Option. Options Boot Camp Part 2

The Call Option. Options Boot Camp Part 2 Options Boot Camp Part 2 About Sunset Partners Our Presenters Today Robert Hamer, Principal Chief Investment Strategist & Portfolio Manager Experience Trader Chicago Board Options Exchange: 1983-1998 Senior

More information

b. June expiration: 95-23 = 95 + 23/32 % = 95.71875% or.9571875.9571875 X $100,000 = $95,718.75.

b. June expiration: 95-23 = 95 + 23/32 % = 95.71875% or.9571875.9571875 X $100,000 = $95,718.75. ANSWERS FOR FINANCIAL RISK MANAGEMENT A. 2-4 Value of T-bond Futures Contracts a. March expiration: The settle price is stated as a percentage of the face value of the bond with the final "27" being read

More information

Put-Call Parity and Synthetics

Put-Call Parity and Synthetics Courtesy of Market Taker Mentoring LLC TM Excerpt from Trading Option Greeks, by Dan Passarelli Chapter 6 Put-Call Parity and Synthetics In order to understand more-complex spread strategies involving

More information

CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS

CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS CHAPTER 8: TRADING STRATEGES INVOLVING OPTIONS Unless otherwise stated the options we consider are all European. Toward the end of this chapter, we will argue that if European options were available with

More information

A Report On Pricing and Technical Analysis of Derivatives

A Report On Pricing and Technical Analysis of Derivatives A Report On Pricing and Technical Analysis of Derivatives THE INDIAN INSTITUTE OF PLANNING AND MANAGEMENT EXECUTIVE SUMMARY The emergence of Derivatives market especially Futures and Options can be traced

More information

FX, Derivatives and DCM workshop I. Introduction to Options

FX, Derivatives and DCM workshop I. Introduction to Options Introduction to Options What is a Currency Option Contract? A financial agreement giving the buyer the right (but not the obligation) to buy/sell a specified amount of currency at a specified rate on a

More information

Dimensions Trading Lab. 2004. Sean Tseng. Trading Greeks. Greeks based trading strategies. Sean Tseng s presentation

Dimensions Trading Lab. 2004. Sean Tseng. Trading Greeks. Greeks based trading strategies. Sean Tseng s presentation Trading Greeks Greeks based trading strategies Position and Greeks position Delta Gamma Theta Vega Long + 0 0 0 Short - 0 0 0 Long call + (0 to 1) + - + Long put Short call - (-1 to 0) + - + - (0 to 1)

More information

One Period Binomial Model

One Period Binomial Model FIN-40008 FINANCIAL INSTRUMENTS SPRING 2008 One Period Binomial Model These notes consider the one period binomial model to exactly price an option. We will consider three different methods of pricing

More information

WHS FX options guide. Getting started with FX options. Predict the trend in currency markets or hedge your positions with FX options.

WHS FX options guide. Getting started with FX options. Predict the trend in currency markets or hedge your positions with FX options. Getting started with FX options WHS FX options guide Predict the trend in currency markets or hedge your positions with FX options. Refine your trading style and your market outlook. Learn how FX options

More information

Option pricing. Vinod Kothari

Option pricing. Vinod Kothari Option pricing Vinod Kothari Notation we use this Chapter will be as follows: S o : Price of the share at time 0 S T : Price of the share at time T T : time to maturity of the option r : risk free rate

More information

Hedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies

Hedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies Hedging Illiquid FX Options: An Empirical Analysis of Alternative Hedging Strategies Drazen Pesjak Supervised by A.A. Tsvetkov 1, D. Posthuma 2 and S.A. Borovkova 3 MSc. Thesis Finance HONOURS TRACK Quantitative

More information

WHAT ARE OPTIONS OPTIONS TRADING

WHAT ARE OPTIONS OPTIONS TRADING OPTIONS TRADING WHAT ARE OPTIONS Options are openly traded contracts that give the buyer a right to a futures position at a specific price within a specified time period Designed as more of a protective

More information

CHAPTER 21: OPTION VALUATION

CHAPTER 21: OPTION VALUATION CHAPTER 21: OPTION VALUATION 1. Put values also must increase as the volatility of the underlying stock increases. We see this from the parity relation as follows: P = C + PV(X) S 0 + PV(Dividends). Given

More information

Introduction to Options -- The Basics

Introduction to Options -- The Basics Introduction to Options -- The Basics Dec. 8 th, 2015 Fidelity Brokerage Services, Member NYSE, SIPC, 900 Salem Street, Smithfield, RI 02917. 2015 FMR LLC. All rights reserved. 744692.1.0 Disclosures Options

More information

Options Pricing. This is sometimes referred to as the intrinsic value of the option.

Options Pricing. This is sometimes referred to as the intrinsic value of the option. Options Pricing We will use the example of a call option in discussing the pricing issue. Later, we will turn our attention to the Put-Call Parity Relationship. I. Preliminary Material Recall the payoff

More information

14 Greeks Letters and Hedging

14 Greeks Letters and Hedging ECG590I Asset Pricing. Lecture 14: Greeks Letters and Hedging 1 14 Greeks Letters and Hedging 14.1 Illustration We consider the following example through out this section. A financial institution sold

More information

Fundamentals of Futures and Options (a summary)

Fundamentals of Futures and Options (a summary) Fundamentals of Futures and Options (a summary) Roger G. Clarke, Harindra de Silva, CFA, and Steven Thorley, CFA Published 2013 by the Research Foundation of CFA Institute Summary prepared by Roger G.

More information

Understanding Volatility and Making It Work for You. The Options Industry Council

Understanding Volatility and Making It Work for You. The Options Industry Council Understanding Volatility and Making It Work for You December 16, 2013 Joe Burgoyne, OIC www.optionseducation.org 2 The Options Industry Council Options involve risks and are not suitable for everyone.

More information

THETA AS AN ASSET CLASS By Dominik von Eynern, Swiss Alpha Asset Management GMBH

THETA AS AN ASSET CLASS By Dominik von Eynern, Swiss Alpha Asset Management GMBH THETA AS AN ASSET CLASS By Dominik von Eynern, Swiss Alpha Asset Management GMBH It is essential to find new ways or asset classes to deliver consistent and uncorrelated returns within the asset management

More information

Earnings Plays. Profiting Around This Key Quarterly Event July 21, 2016

Earnings Plays. Profiting Around This Key Quarterly Event July 21, 2016 Earnings Plays Profiting Around This Key Quarterly Event July 21, 2016 1 How to Get the Most Out of This Class In a nutshell... Kick back and listen. This is a well laid out presentation. You don t have

More information

Lecture 12. Options Strategies

Lecture 12. Options Strategies Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same

More information

Beyond Black- Scholes: Smile & Exo6c op6ons. Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles

Beyond Black- Scholes: Smile & Exo6c op6ons. Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles Beyond Black- Scholes: Smile & Exo6c op6ons Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles 1 What is a Vola6lity Smile? Rela6onship between implied

More information

Copyright 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA

Copyright 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA Copyright 2009 by National Stock Exchange of India Ltd. (NSE) Exchange Plaza, Bandra Kurla Complex, Bandra (East), Mumbai 400 051 INDIA All content included in this book, such as text, graphics, logos,

More information

The Greeks Vega. Outline: Explanation of the greeks. Using greeks for short term prediction. How to find vega. Factors influencing vega.

The Greeks Vega. Outline: Explanation of the greeks. Using greeks for short term prediction. How to find vega. Factors influencing vega. The Greeks Vega 1 1 The Greeks Vega Outline: Explanation of the greeks. Using greeks for short term prediction. How to find vega. Factors influencing vega. 2 Outline continued: Using greeks to shield your

More information

Valuation, Pricing of Options / Use of MATLAB

Valuation, Pricing of Options / Use of MATLAB CS-5 Computational Tools and Methods in Finance Tom Coleman Valuation, Pricing of Options / Use of MATLAB 1.0 Put-Call Parity (review) Given a European option with no dividends, let t current time T exercise

More information

2. Exercising the option - buying or selling asset by using option. 3. Strike (or exercise) price - price at which asset may be bought or sold

2. Exercising the option - buying or selling asset by using option. 3. Strike (or exercise) price - price at which asset may be bought or sold Chapter 21 : Options-1 CHAPTER 21. OPTIONS Contents I. INTRODUCTION BASIC TERMS II. VALUATION OF OPTIONS A. Minimum Values of Options B. Maximum Values of Options C. Determinants of Call Value D. Black-Scholes

More information

Overview. Option Basics. Options and Derivatives. Professor Lasse H. Pedersen. Option basics and option strategies

Overview. Option Basics. Options and Derivatives. Professor Lasse H. Pedersen. Option basics and option strategies Options and Derivatives Professor Lasse H. Pedersen Prof. Lasse H. Pedersen 1 Overview Option basics and option strategies No-arbitrage bounds on option prices Binomial option pricing Black-Scholes-Merton

More information

CHAPTER 22 Options and Corporate Finance

CHAPTER 22 Options and Corporate Finance CHAPTER 22 Options and Corporate Finance Multiple Choice Questions: I. DEFINITIONS OPTIONS a 1. A financial contract that gives its owner the right, but not the obligation, to buy or sell a specified asset

More information

Option Spread and Combination Trading

Option Spread and Combination Trading Option Spread and Combination Trading J. Scott Chaput* Louis H. Ederington** January 2002 Initial Draft: January 2000 * University of Otago ** Until 31 January, 2002: Department of Finance Visiting Professor,

More information

The Terms and Conditions govern use of this website and use of this website will be deemed acceptance of those Terms and Conditions.

The Terms and Conditions govern use of this website and use of this website will be deemed acceptance of those Terms and Conditions. Options involve risk and are not suitable for all investors. Prior to buying or selling an option, a person must receive a copy of Characteristics and Risks of Standardized Options. Copies of the ODD are

More information

Journal of Business & Economics Research Volume 2, Number 8

Journal of Business & Economics Research Volume 2, Number 8 Long-Term Capital Gains Tax Strategies: Correlated Protective Put Strategy John R. Aulerich, (E-Mail: aulericj@uww.edu), University of Wisconsin-Whitewater James Molloy, University of Wisconsin-Whitewater

More information

Economics 1723: Capital Markets Lecture 20

Economics 1723: Capital Markets Lecture 20 Economics 1723: Capital Markets Lecture 20 John Y. Campbell Ec1723 November 14, 2013 John Y. Campbell (Ec1723) Lecture 20 November 14, 2013 1 / 43 Key questions What is a CDS? What information do we get

More information

Don t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC

Don t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC Don t be Intimidated by the Greeks, Part 2 August 29, 2013 Joe Burgoyne, OIC www.optionseducation.org 2 The Options Industry Council Options involve risks and are not suitable for everyone. Prior to buying

More information

Put-Call Parity. chris bemis

Put-Call Parity. chris bemis Put-Call Parity chris bemis May 22, 2006 Recall that a replicating portfolio of a contingent claim determines the claim s price. This was justified by the no arbitrage principle. Using this idea, we obtain

More information

INSTITUTE OF ECONOMIC STUDIES

INSTITUTE OF ECONOMIC STUDIES INSIUE OF ECONOMIC SUDIES Faculty of social sciences of Charles University Option Contracts Lecturer s Notes No. Course: Financial Market Instruments I eacher: Oldřich Dědek VII. BASIC FEAURES OF OPION

More information

Option pricing in detail

Option pricing in detail Course #: Title Module 2 Option pricing in detail Topic 1: Influences on option prices - recap... 3 Which stock to buy?... 3 Intrinsic value and time value... 3 Influences on option premiums... 4 Option

More information

Bull Call Spread. BACK TO BASICS: Spread Yourself Around: Example. By David Bickings, Optionetics.com

Bull Call Spread. BACK TO BASICS: Spread Yourself Around: Example. By David Bickings, Optionetics.com Bull Call Spread BACK TO BASICS: Spread Yourself Around: Example By David Bickings, Optionetics.com Options are a fantastic investment to make money on the rise and fall of an asset. This is no surprise

More information

11 Option. Payoffs and Option Strategies. Answers to Questions and Problems

11 Option. Payoffs and Option Strategies. Answers to Questions and Problems 11 Option Payoffs and Option Strategies Answers to Questions and Problems 1. Consider a call option with an exercise price of $80 and a cost of $5. Graph the profits and losses at expiration for various

More information

Ratio Spreads. Jim Bittman. Mechanics, Motivation & Managing. Senior Instructor The Options Institute at CBOE

Ratio Spreads. Jim Bittman. Mechanics, Motivation & Managing. Senior Instructor The Options Institute at CBOE Ratio Spreads Mechanics, Motivation & Managing Jim Bittman Senior Instructor The Options Institute at CBOE Disclaimer In order to simplify the computations, commissions have not been included in the examples

More information

Use the option quote information shown below to answer the following questions. The underlying stock is currently selling for $83.

Use the option quote information shown below to answer the following questions. The underlying stock is currently selling for $83. Problems on the Basics of Options used in Finance 2. Understanding Option Quotes Use the option quote information shown below to answer the following questions. The underlying stock is currently selling

More information

Simplified Option Selection Method

Simplified Option Selection Method Simplified Option Selection Method Geoffrey VanderPal Webster University Thailand Options traders and investors utilize methods to price and select call and put options. The models and tools range from

More information

Covered Calls. Benefits & Tradeoffs

Covered Calls. Benefits & Tradeoffs 748627.1.1 1 Covered Calls Enhance ETFs with Options Strategies January 26, 2016 Joe Burgoyne, OIC Benefits & Tradeoffs Joe Burgoyne Director, Options Industry Council www.optionseducation.org 2 The Options

More information

Summary of Interview Questions. 1. Does it matter if a company uses forwards, futures or other derivatives when hedging FX risk?

Summary of Interview Questions. 1. Does it matter if a company uses forwards, futures or other derivatives when hedging FX risk? Summary of Interview Questions 1. Does it matter if a company uses forwards, futures or other derivatives when hedging FX risk? 2. Give me an example of how a company can use derivative instruments to

More information