FX Options and Smile Risk_. Antonio Castagna. )WILEY A John Wiley and Sons, Ltd., Publication

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "FX Options and Smile Risk_. Antonio Castagna. )WILEY A John Wiley and Sons, Ltd., Publication"

Transcription

1 FX Options and Smile Risk_ Antonio Castagna )WILEY A John Wiley and Sons, Ltd., Publication

2 Preface Notation and Acronyms IX xiii 1 The FX Market 1.1 FX rates and spot contracts 1.2 Outright and FX swap contracts 1.3 FX option contracts Exercise Expiry date and settlement date Premium Market standard practices for quoting options 1.4 Main traded FX option structures Pricing Models for FX Options 2.1 Principles of option pricing theory The Black-Scholes economy Stochastic volatility economy Change of numeraire 2.2 The black-scholes model The forward price to use in the formula BS greeks Retrieving implied volatility and strike Some relationships of the BS formula 2.3 ' The Heston Model Time-dependent parameters in the Heston model 2.4 The SABR model 2.5 The mixture approach The LMLV model The LMUV model

3 vi Contents Features of the LMLV and LMUV models and a comparison between them Extension of the LMUV model Some considerations about the choice of model 53 Dynamic Hedging and Volatility Trading Preliminary considerations A general framework Hedging with a constant implied volatility Hedging with an updating implied volatility A market model for the implied volatility Hedging Vega Hedging Delta, Vega, Vanna and Volga Vanna-Volga hedging with one implied volatility Vanna-Volga hedging with different implied volatilities The volatility smile and its phenomenology Local exposures to the volatility smile Retrieving the strikes of the main structures ATM straddle exposures Risk reversal exposures Vega-weighted butterfly exposures Scenario hedging and its relationship with Vanna-Volga hedging Scenario hedging with constant Delta options 86 The Volatility Surface General definitions Arbitrage opportunities under the three different rules Criteria for an efficient and convenient representation of the volatility surface Commonly adopted approaches to building a volatility surface Smile interpolation among strikes: the Vanna-Volga approach The Vanna-Volga approach: general setting Computing the Vanna-Volga weights and option prices Limit and no-arbitrage conditions Approximating implied volatilities Some features of the Vanna-Volga approach Hedging error for longer expiries The implied risk-neutral density and smile asymptotics Two consistency results An alternative characterization of the Vanna-Volga approach Smile interpolation among expiries: implied volatility term structure Admissible volatility surfaces Taking into account the market butterfly Building the volatility matrix in practice 120

4 vii 5 Plain Vanilla Options Pricing of plain vanilla options Delayed settlement date Cash settlement Market-making tools Inferring the implied volatility for a given strike Inferring the implied volatility for a given Delta Quoting the Vega-weighted butterfly and the risk reversal Bid/ask spreads for plain vanilla options Cutoff times and spreads Digital options Digital options pricing: the static replica approach Digital options pricing in specific model settings Delayed cash settlement date Bid/ask spreads Quotation conventions American plain vanilla options Valuation of American plain vanilla options in a BS setting Pricing of American plain vanilla options with the volatility smile Barrier Options A taxonomy of barrier options Some relationships of barrier option prices Pricing for barrier options in a BS economy The diffusion equation under single absorbing boundaries Dealing with a constant barrier Pricing formulae for barrier options One-touch (rebate) and no-touch options Double-barrier options Two absorbing states Pricing formula for double-barrier options Double-no-touch and double-touch options Probability of hitting a barrier Greek calculation Pricing barrier options in other model settings Pricing barriers with non-standard delivery Delayed settlement date Cash settlement Market approach to pricing barrier options Inclusion of the smile: the Vanna-Volga approach for barrier options The Vanna-Volga approach for barrier options: variations on the theme Slippage at the barrier level Delta-hedging near the barrier level Implicit one-touch and gearing Vega-hedge rebalancing 186

5 6.13 Bid/ask spreads Monitoring frequency Other Exotic Options Introduction At-expiry barrier options Window barrier options First-then and knock-in-knock-out barrier options Auto-quanto options Forward start options Including the volatility smile in the pricing Forward implied volatility smiles Forward start barrier and bet options Dealing with notional amounts expressed in numeraire currency Variance swaps Compound, Asian and lookback options 5 8 Risk Management Tools and Analysis Introduction Implementation of the LMUV model The forward volatility surfaces Calculating the sensitivity to the movements of the volatility surface Risk monitoring tools FX spot rate-related Greeks Cash-settled options Volatility-related Greeks and sensitivities Barrier implicit one-touch, bets and digitals Interest rate-related Greeks Risk analysis of plain vanilla options ATM straddle Risk reversal Vega-weighted butterfly Risk analysis of digital options Risk analysis of exotic options Barrier options Double barrier options Bet options Correlation and FX Options Preliminary considerations Correlation in the BS setting Contracts depending on several FX spot rates Dealing with correlation and volatility smile 278? Vanna-Volga extension Linking volatility smiles 283 References 287 Index 291

Exotic Options Trading

Exotic Options Trading Exotic Options Trading Frans de Weert John Wiley & Sons, Ltd Preface Acknowledgements 1 Introduction 2 Conventional Options, Forwards and Greeks 2.1 Call and Put Options and Forwards 2.2 Pricing Calls

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

Some Practical Issues in FX and Equity Derivatives

Some Practical Issues in FX and Equity Derivatives Some Practical Issues in FX and Equity Derivatives Phenomenology of the Volatility Surface The volatility matrix is the map of the implied volatilities quoted by the market for options of different strikes

More information

Vanna-Volga Method for Foreign Exchange Implied Volatility Smile. Copyright Changwei Xiong 2011. January 2011. last update: Nov 27, 2013

Vanna-Volga Method for Foreign Exchange Implied Volatility Smile. Copyright Changwei Xiong 2011. January 2011. last update: Nov 27, 2013 Vanna-Volga Method for Foreign Exchange Implied Volatility Smile Copyright Changwei Xiong 011 January 011 last update: Nov 7, 01 TABLE OF CONTENTS TABLE OF CONTENTS...1 1. Trading Strategies of Vanilla

More information

Hedging Barriers. Liuren Wu. Zicklin School of Business, Baruch College (http://faculty.baruch.cuny.edu/lwu/)

Hedging Barriers. Liuren Wu. Zicklin School of Business, Baruch College (http://faculty.baruch.cuny.edu/lwu/) Hedging Barriers Liuren Wu Zicklin School of Business, Baruch College (http://faculty.baruch.cuny.edu/lwu/) Based on joint work with Peter Carr (Bloomberg) Modeling and Hedging Using FX Options, March

More information

Options on Foreign Exchange. 3rd Edition. Wiley Finance

Options on Foreign Exchange. 3rd Edition. Wiley Finance Brochure More information from http://www.researchandmarkets.com/reports/2242927/ Options on Foreign Exchange. 3rd Edition. Wiley Finance Description: Praise for Options on Foreign Exchange, 3rd Edition

More information

w w w.c a t l e y l a k e m a n.c o m 0 2 0 7 0 4 3 0 1 0 0

w w w.c a t l e y l a k e m a n.c o m 0 2 0 7 0 4 3 0 1 0 0 A ADR-Style: for a derivative on an underlying denominated in one currency, where the derivative is denominated in a different currency, payments are exchanged using a floating foreign-exchange rate. The

More information

Consistent pricing and hedging of an FX options book

Consistent pricing and hedging of an FX options book Consistent pricing and hedging of an FX options book L. Bisesti, A. Castagna and F. Mercurio 1 Introduction In the foreign exchange (FX) options market away-from-the-money options are quite actively traded,

More information

Pricing Barrier Options under Local Volatility

Pricing Barrier Options under Local Volatility Abstract Pricing Barrier Options under Local Volatility Artur Sepp Mail: artursepp@hotmail.com, Web: www.hot.ee/seppar 16 November 2002 We study pricing under the local volatility. Our research is mainly

More information

Consistent Pricing of FX Options

Consistent Pricing of FX Options Consistent Pricing of FX Options Antonio Castagna Fabio Mercurio Banca IMI, Milan In the current markets, options with different strikes or maturities are usually priced with different implied volatilities.

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

Derivatives: Principles and Practice

Derivatives: Principles and Practice Derivatives: Principles and Practice Rangarajan K. Sundaram Stern School of Business New York University New York, NY 10012 Sanjiv R. Das Leavey School of Business Santa Clara University Santa Clara, CA

More information

OPTIONS, FUTURES, & OTHER DERIVATI

OPTIONS, FUTURES, & OTHER DERIVATI Fifth Edition OPTIONS, FUTURES, & OTHER DERIVATI John C. Hull Maple Financial Group Professor of Derivatives and Risk Manage, Director, Bonham Center for Finance Joseph L. Rotinan School of Management

More information

Validation of New Pricing Model for Exotic Options Pioneering Again

Validation of New Pricing Model for Exotic Options Pioneering Again Final Year Report Sept 2010 Validation of New Pricing Model for Exotic Options Pioneering Again Trainee: Dima HAMZE Tutor: Nadia ISRAEL Responsible: Alain CHATEAUNEUF Acknowledgements I would like to take

More information

Foreign Exchange Symmetries

Foreign Exchange Symmetries Foreign Exchange Symmetries Uwe Wystup MathFinance AG Waldems, Germany www.mathfinance.com 8 September 2008 Contents 1 Foreign Exchange Symmetries 2 1.1 Motivation.................................... 2

More information

SUPER COMPUTER CONSULTING INC.

SUPER COMPUTER CONSULTING INC. SUPER COMPUTER CONSULTING INC. 1070 Westfield Way, Mundelein, IL 60060 USA Phone: (847) 837-0200 Fax: (847) 837-0228 e-mail: info@supercc.com http://www.supercc.com EXOTIC OPTIONS Including Second Generation

More information

IL GOES OCAL A TWO-FACTOR LOCAL VOLATILITY MODEL FOR OIL AND OTHER COMMODITIES 15 // MAY // 2014

IL GOES OCAL A TWO-FACTOR LOCAL VOLATILITY MODEL FOR OIL AND OTHER COMMODITIES 15 // MAY // 2014 IL GOES OCAL A TWO-FACTOR LOCAL VOLATILITY MODEL FOR OIL AND OTHER COMMODITIES 15 MAY 2014 2 Marie-Lan Nguyen / Wikimedia Commons Introduction 3 Most commodities trade as futures/forwards Cash+carry arbitrage

More information

Basic Black-Scholes: Option Pricing and Trading

Basic Black-Scholes: Option Pricing and Trading Basic Black-Scholes: Option Pricing and Trading BSc (HONS 1 st Timothy Falcon Crack Class), PGDipCom, MCom, PhD (MIT), IMC Contents Preface Tables Figures ix xi xiii 1 Introduction to Options 1 1.1 Hedging,

More information

WHAT S NEW IN THOMSON REUTERS EIKON FOR JANUARY 2011 FX & MONEY MARKETS

WHAT S NEW IN THOMSON REUTERS EIKON FOR JANUARY 2011 FX & MONEY MARKETS THOMSON REUTERS EIKON WHAT S NEW IN THOMSON REUTERS EIKON FOR JANUARY 2011 FX & MONEY MARKETS Thomson Reuters Training It is essential to keep up to date with new functionality and features for Thomson

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 the SABR model

Properties of the SABR model U.U.D.M. Project Report 2011:11 Properties of the SABR model Nan Zhang Examensarbete i matematik, 30 hp Handledare och examinator: Johan Tysk Juni 2011 Department of Mathematics Uppsala University ABSTRACT

More information

arxiv:0904.1074v3 [q-fin.pr] 3 May 2010

arxiv:0904.1074v3 [q-fin.pr] 3 May 2010 Vanna-Volga methods applied to FX derivatives: from theory to market practice Frédéric Bossens, Grégory Rayée, Nikos S. Skantzos and Griselda Deelstra arxiv:0904.1074v3 [q-fin.pr] 3 May 2010 Termeulenstraat

More information

Write clearly; the grade will also take into account the quality of the presentation and the clarity of the explanations

Write clearly; the grade will also take into account the quality of the presentation and the clarity of the explanations Name: Student-ID number: Write clearly; the grade will also take into account the quality of the presentation and the clarity of the explanations Question Points Score 1 29 2 17 3 19 4 2 5 2 6 1 Total:

More information

Or part of or all the risk is dynamically hedged trading regularly, with a. frequency that needs to be appropriate for the trade.

Or part of or all the risk is dynamically hedged trading regularly, with a. frequency that needs to be appropriate for the trade. Option position (risk) management Correct risk management of option position is the core of the derivatives business industry. Option books bear huge amount of risk with substantial leverage in the position.

More information

DIGITAL FOREX OPTIONS

DIGITAL FOREX OPTIONS DIGITAL FOREX OPTIONS OPENGAMMA QUANTITATIVE RESEARCH Abstract. Some pricing methods for forex digital options are described. The price in the Garhman-Kohlhagen model is first described, more for completeness

More information

ENGINEERING AND HEDGING OF CORRIDOR PRODUCTS - with focus on FX linked instruments -

ENGINEERING AND HEDGING OF CORRIDOR PRODUCTS - with focus on FX linked instruments - AARHUS SCHOOL OF BUSINESS AARHUS UNIVERSITY MASTER THESIS ENGINEERING AND HEDGING OF CORRIDOR PRODUCTS - with focus on FX linked instruments - AUTHORS: DANIELA ZABRE GEORGE RARES RADU SIMIAN SUPERVISOR:

More information

F3 Excel Edition Release Notes

F3 Excel Edition Release Notes F3 Excel Edition Release Notes F3 Excel Edition Release Notes Software Version: 4.3 Release Date: July 2014 Document Revision Number: A Disclaimer FINCAD makes no warranty either express or implied, including,

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

You can find the Report on the SaxoTrader under the Account tab. On the SaxoWebTrader, it is located under the Account tab, on the Reports menu.

You can find the Report on the SaxoTrader under the Account tab. On the SaxoWebTrader, it is located under the Account tab, on the Reports menu. The FX Options Report What is the FX Options Report? The FX Options Report gives you a detailed analysis of your FX and FX Options positions across multiple currency pairs, enabling you to manage your

More information

VALUATION IN DERIVATIVES MARKETS

VALUATION IN DERIVATIVES MARKETS VALUATION IN DERIVATIVES MARKETS September 2005 Rawle Parris ABN AMRO Property Derivatives What is a Derivative? A contract that specifies the rights and obligations between two parties to receive or deliver

More information

The Complete Guide to Option Strategies

The Complete Guide to Option Strategies The Complete Guide to Option Strategies Advanced and Basic Strategies on Stocks, ETFs, Indexes, and Stock Indexes MICHAEL D. MULLANEY WILEY John Wiley & Sons, Inc. Contents Preface Acknowledgments xv xx

More information

Introduction to Options. Derivatives

Introduction to Options. Derivatives Introduction to Options Econ 422: Investment, Capital & Finance University of Washington Summer 2010 August 18, 2010 Derivatives A derivative is a security whose payoff or value depends on (is derived

More information

Hedging Exotic Options

Hedging Exotic Options Kai Detlefsen Wolfgang Härdle Center for Applied Statistics and Economics Humboldt-Universität zu Berlin Germany introduction 1-1 Models The Black Scholes model has some shortcomings: - volatility is not

More information

Risk Management and Governance Hedging with Derivatives. Prof. Hugues Pirotte

Risk Management and Governance Hedging with Derivatives. Prof. Hugues Pirotte Risk Management and Governance Hedging with Derivatives Prof. Hugues Pirotte Several slides based on Risk Management and Financial Institutions, e, Chapter 6, Copyright John C. Hull 009 Why Manage Risks?

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

Learn. Commodity Options Trading & Risk Management ORM2. Commodity Derivatives Strategy

Learn. Commodity Options Trading & Risk Management ORM2. Commodity Derivatives Strategy Learn Commodity Options Trading & Risk Management ORM2 2 days of intensive and comprehensive options/risk management training with practical analysis of option trading strategies and risk management with

More information

FX Derivatives Terminology. Education Module: 5. Dated July 2002. FX Derivatives Terminology

FX Derivatives Terminology. Education Module: 5. Dated July 2002. FX Derivatives Terminology Education Module: 5 Dated July 2002 Foreign Exchange Options Option Markets and Terminology A American Options American Options are options that are exercisable for early value at any time during the term

More information

Option Calculators User Manual

Option Calculators User Manual Option Calculators User Manual Option Calculators provide means for implied volatility calculation, option contracts pricing and calculation of option price sensitivities (greeks). Currently, through our

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

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

Handbook FXFlat FX Options

Handbook FXFlat FX Options Handbook FXFlat FX Options FXFlat Trading FX Options When you open an FX options account at FXFlat, you can trade options on currency pairs 24- hours a day, 5.5 days per week. The FX options features in

More information

DIFFERENT PATHS: SCENARIOS FOR n-asset AND PATH-DEPENDENT OPTIONS II

DIFFERENT PATHS: SCENARIOS FOR n-asset AND PATH-DEPENDENT OPTIONS II DIFFERENT PATHS: SCENARIOS FOR n-asset AND PATH-DEPENDENT OPTIONS II David Murphy Market and Liquidity Risk, Banque Paribas This article expresses the personal views of the author and does not necessarily

More information

The real P&L in Black-Scholes and Dupire Delta hedging

The real P&L in Black-Scholes and Dupire Delta hedging International Journal of Theoretical and Applied Finance c World Scientific Publishing Company The real P&L in Black-Scholes and Dupire Delta hedging MARTIN FORDE University of Bristol, Department of Mathematics,

More information

MANAGING OPTIONS RISK FOR EXOTIC OPTIONS

MANAGING OPTIONS RISK FOR EXOTIC OPTIONS MANAGING OPTIONS RISK FOR EXOTIC OPTIONS An exotic derivative is one for which no liquid market exists. As a general rule, the only liquid options are European-exercise calls and puts, including interest

More information

The Implied Volatility Surfaces

The Implied Volatility Surfaces The Implied Volatility Surfaces August 13, 2007 1 Introduction The volatility surface, or matrix (we will use without any distinction the two terms), is the map of the implied volatilities quoted by the

More information

Cash-settled swaptions How wrong are we?

Cash-settled swaptions How wrong are we? Cash-settled swaptions How wrong are we? Marc Henrard Quantitative Research - OpenGamma 7th Fixed Income Conference, Berlin, 7 October 2011 ... Based on: Cash-settled swaptions: How wrong are we? Available

More information

Study on the Volatility Smile of EUR/USD Currency Options and Trading Strategies

Study on the Volatility Smile of EUR/USD Currency Options and Trading Strategies Prof. Joseph Fung, FDS Study on the Volatility Smile of EUR/USD Currency Options and Trading Strategies BY CHEN Duyi 11050098 Finance Concentration LI Ronggang 11050527 Finance Concentration An Honors

More information

Exam P - Total 23/23 - 1 -

Exam P - Total 23/23 - 1 - Exam P Learning Objectives Schools will meet 80% of the learning objectives on this examination if they can show they meet 18.4 of 23 learning objectives outlined in this table. Schools may NOT count a

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

STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400&3400 STAT2400&3400 STAT2400&3400 STAT2400&3400 STAT3400 STAT3400

STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400&3400 STAT2400&3400 STAT2400&3400 STAT2400&3400 STAT3400 STAT3400 Exam P Learning Objectives All 23 learning objectives are covered. General Probability STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 STAT2400 1. Set functions including set notation and basic elements

More information

SWAPTION PRICING OPENGAMMA QUANTITATIVE RESEARCH

SWAPTION PRICING OPENGAMMA QUANTITATIVE RESEARCH SWAPTION PRICING OPENGAMMA QUANTITATIVE RESEARCH Abstract. Implementation details for the pricing of European swaptions in different frameworks are presented.. Introduction This note describes the pricing

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

Contents. List of Figures. List of Tables. Acknowledgments PART I INTRODUCTION 1

Contents. List of Figures. List of Tables. Acknowledgments PART I INTRODUCTION 1 List of Figures List of Tables Acknowledgments Preface xv xix xxi xxiii PART I INTRODUCTION 1 1 The Evolution of Financial Analysis 3 1.1 Bookkeeping 3 1.2 Modern finance 8 1.3 Departments, silos and analysis

More information

General Forex Glossary

General Forex Glossary General Forex Glossary A ADR American Depository Receipt Arbitrage The simultaneous buying and selling of a security at two different prices in two different markets, with the aim of creating profits without

More information

SYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0-008)

SYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0-008) SYLLABUS The ACI Dealing Certificate (Prometric Code: 3I0-008) Examination delivered in ENGLISH and GERMAN The ACI Dealing Certificate is a foundation programme that allows candidates to acquire a working

More information

International Swaps and Derivatives Association, Inc. Disclosure Annex for Foreign Exchange Transactions

International Swaps and Derivatives Association, Inc. Disclosure Annex for Foreign Exchange Transactions International Swaps and Derivatives Association, Inc. Disclosure Annex for Foreign Exchange Transactions This Annex supplements and should be read in conjunction with the General Disclosure Statement.

More information

No-arbitrage conditions for cash-settled swaptions

No-arbitrage conditions for cash-settled swaptions No-arbitrage conditions for cash-settled swaptions Fabio Mercurio Financial Engineering Banca IMI, Milan Abstract In this note, we derive no-arbitrage conditions that must be satisfied by the pricing function

More information

An Introduction to Exotic Options

An Introduction to Exotic Options An Introduction to Exotic Options Jeff Casey Jeff Casey is entering his final semester of undergraduate studies at Ball State University. He is majoring in Financial Mathematics and has been a math tutor

More information

Double Barrier Cash or Nothing Options: a short note

Double Barrier Cash or Nothing Options: a short note Double Barrier Cash or Nothing Options: a short note Antonie Kotzé and Angelo Joseph May 2009 Financial Chaos Theory, Johannesburg, South Africa Mail: consultant@quantonline.co.za Abstract In this note

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

Likewise, the payoff of the better-of-two note may be decomposed as follows: Price of gold (US$/oz) 375 400 425 450 475 500 525 550 575 600 Oil price

Likewise, the payoff of the better-of-two note may be decomposed as follows: Price of gold (US$/oz) 375 400 425 450 475 500 525 550 575 600 Oil price Exchange Options Consider the Double Index Bull (DIB) note, which is suited to investors who believe that two indices will rally over a given term. The note typically pays no coupons and has a redemption

More information

Stephane Crepey. Financial Modeling. A Backward Stochastic Differential Equations Perspective. 4y Springer

Stephane Crepey. Financial Modeling. A Backward Stochastic Differential Equations Perspective. 4y Springer Stephane Crepey Financial Modeling A Backward Stochastic Differential Equations Perspective 4y Springer Part I An Introductory Course in Stochastic Processes 1 Some Classes of Discrete-Time Stochastic

More information

Introduction to Equity Derivatives. February 2008 - The Derivatives Consulting Group Ltd www.dcgconsultants.com

Introduction to Equity Derivatives. February 2008 - The Derivatives Consulting Group Ltd www.dcgconsultants.com Introduction to Equity Derivatives Course Agenda Part 1: Introduction to Equities The Basics Types of Stock Dividends Corporate Actions Underlyings Market Institutions Part 2: Introduction to Derivatives

More information

Options: Definitions, Payoffs, & Replications

Options: Definitions, Payoffs, & Replications Options: Definitions, s, & Replications Liuren Wu Zicklin School of Business, Baruch College Options Markets Liuren Wu (Baruch) s Options Markets 1 / 34 Definitions and terminologies An option gives the

More information

Computational Finance Options

Computational Finance Options 1 Options 1 1 Options Computational Finance Options An option gives the holder of the option the right, but not the obligation to do something. Conversely, if you sell an option, you may be obliged to

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

S 1 S 2. Options and Other Derivatives

S 1 S 2. Options and Other Derivatives Options and Other Derivatives The One-Period Model The previous chapter introduced the following two methods: Replicate the option payoffs with known securities, and calculate the price of the replicating

More information

Module I Financial derivatives an introduction Forward market and products

Module I Financial derivatives an introduction Forward market and products Module I 1. Financial derivatives an introduction 1.1 Derivative markets 1.1.1 Past and present 1.1.2 Difference between exchange traded and OTC derivatives 1.2 Derivative instruments 1.2.1 Concept and

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

Basel Committee on Banking Supervision

Basel Committee on Banking Supervision Basel Committee on Banking Supervision Basel III: The standardised approach for measuring counterparty credit risk exposures: Frequently asked questions August 2015 This publication is available on the

More information

On the Valuation of Power-Reverse Duals and Equity-Rates Hybrids

On the Valuation of Power-Reverse Duals and Equity-Rates Hybrids On the Valuation of Power-Reverse Duals and Equity-Rates Hybrids Oliver Caps oliver.caps@dkib.com RMT Model Validation Rates Dresdner Bank Examples of Hybrid Products Pricing of Hybrid Products using a

More information

Third Edition. Philippe Jorion GARP. WILEY John Wiley & Sons, Inc.

Third Edition. Philippe Jorion GARP. WILEY John Wiley & Sons, Inc. 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Third Edition Philippe Jorion GARP WILEY John Wiley & Sons, Inc.

More information

FX Key products Exotic Options Menu

FX Key products Exotic Options Menu FX Key products Exotic Options Menu Welcome to Exotic Options Over the last couple of years options have become an important tool for investors and hedgers in the foreign exchange market. With the growing

More information

Lecture 4: The Black-Scholes model

Lecture 4: The Black-Scholes model OPTIONS and FUTURES Lecture 4: The Black-Scholes model Philip H. Dybvig Washington University in Saint Louis Black-Scholes option pricing model Lognormal price process Call price Put price Using Black-Scholes

More information

PRICING DISCRETELY SAMPLED PATH-DEPENDENT EXOTIC OPTIONS USING REPLICATION METHODS

PRICING DISCRETELY SAMPLED PATH-DEPENDENT EXOTIC OPTIONS USING REPLICATION METHODS PRICING DISCRETELY SAMPLED PATH-DEPENDENT EXOTIC OPTIONS USING REPLICATION METHODS M. S. JOSHI Abstract. A semi-static replication method is introduced for pricing discretely sampled path-dependent options.

More information

Case Study: Double No Touch and Other FX Option Strategies for Low Volatility Markets

Case Study: Double No Touch and Other FX Option Strategies for Low Volatility Markets Case Study: Double No Touch and Other FX Option Strategies for Low Volatility Markets This case study covers various foreign exchange (FX) option strategies that take advantage of low volatility market

More information

INTEREST RATES AND FX MODELS

INTEREST RATES AND FX MODELS INTEREST RATES AND FX MODELS 8. Portfolio greeks Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York March 27, 2013 2 Interest Rates & FX Models Contents 1 Introduction

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

Advanced Equity Derivatives by Oliver Brockhaus

Advanced Equity Derivatives by Oliver Brockhaus Advanced Equity Derivatives by Oliver Brockhaus London: 19th & 20th November 2012 This workshop provides TWO booking options Register to ANY ONE day of the workshop Register to BOTH days of the workshop

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

TEX MULTIDEALER TRADING SYSTEM

TEX MULTIDEALER TRADING SYSTEM User Guide 360T SEF TEX MULTIDEALER TRADING SYSTEM USER GUIDE 360T SWAP EXECUTION FACILITY FOR THE MARKET MAKER 360 TREASURY SYSTEMS AG, 2015-1 - 1 INTRODUCTION In July 2010, the Dodd-Frank Wall Street

More information

On Market-Making and Delta-Hedging

On Market-Making and Delta-Hedging On Market-Making and Delta-Hedging 1 Market Makers 2 Market-Making and Bond-Pricing On Market-Making and Delta-Hedging 1 Market Makers 2 Market-Making and Bond-Pricing What to market makers do? Provide

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

THE TIME-DISCRETE METHOD OF LINES FOR OPTIONS AND BONDS

THE TIME-DISCRETE METHOD OF LINES FOR OPTIONS AND BONDS THE TIME-DISCRETE METHOD OF LINES FOR OPTIONS AND BONDS APDEApproach % " 24 BSV ViSfVs^i + pbi

More information

THE MAIN RISKS OF AN FX OPTIONS PORTFOLIO

THE MAIN RISKS OF AN FX OPTIONS PORTFOLIO THE MAIN RISKS OF AN FX OPTIONS PORTFOLIO Abstract. In this document we study the risks of an FX options portfolio; we will focus on which, we think, are the main sources of risk. Besides, we analyze also

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

TABLE OF CONTENTS. A. Put-Call Parity 1 B. Comparing Options with Respect to Style, Maturity, and Strike 13

TABLE OF CONTENTS. A. Put-Call Parity 1 B. Comparing Options with Respect to Style, Maturity, and Strike 13 TABLE OF CONTENTS 1. McDonald 9: "Parity and Other Option Relationships" A. Put-Call Parity 1 B. Comparing Options with Respect to Style, Maturity, and Strike 13 2. McDonald 10: "Binomial Option Pricing:

More information

Setting the scene. by Stephen McCabe, Commonwealth Bank of Australia

Setting the scene. by Stephen McCabe, Commonwealth Bank of Australia Establishing risk and reward within FX hedging strategies by Stephen McCabe, Commonwealth Bank of Australia Almost all Australian corporate entities have exposure to Foreign Exchange (FX) markets. Typically

More information

Managers Directive AIFs. Issued :

Managers Directive AIFs. Issued : Information page Alternative Investment Fund Managers Directive AIFMs managing leveraged AIFs Issued : 7t May 2013 Table of Contents 1. Introduction... 3 2. General provisions applicable to AIFs using

More information

The market for exotic options

The market for exotic options The market for exotic options Development of exotic products increased flexibility for risk transfer and hedging highly structured expression of expectation of asset price movements facilitation of trading

More information

MANAGEMENT OF ASIAN AND CLIQUET OPTION EXPOSURES FOR INSURANCE COMPANIES: SPVA APPLICATIONS (II) >>>>>>>>>>>>>

MANAGEMENT OF ASIAN AND CLIQUET OPTION EXPOSURES FOR INSURANCE COMPANIES: SPVA APPLICATIONS (II) >>>>>>>>>>>>> MANAGEMENT OF ASIAN AND CLIQUET OPTION EXPOSURES FOR INSURANCE COMPANIES: SPVA APPLICATIONS (II) >>>>>>>>>>>>> PRODUCT INNOVATION CONTEXT The insurance industry witnessed a significant retrenchment in

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

Using the SABR Model

Using the SABR Model Definitions Ameriprise Workshop 2012 Overview Definitions The Black-76 model has been the standard model for European options on currency, interest rates, and stock indices with it s main drawback being

More information

Analytically Tractable Stochastic Stock Price Models

Analytically Tractable Stochastic Stock Price Models Archil Gulisashvili Analytically Tractable Stochastic Stock Price Models 4Q Springer Contents 1 Volatility Processes 1 1.1 Brownian Motion 1 1.2 s Geometric Brownian Motion 6 1.3 Long-Time Behavior of

More information

Contents. Bibliografische Informationen http://d-nb.info/996662502. digitalisiert durch

Contents. Bibliografische Informationen http://d-nb.info/996662502. digitalisiert durch Part I Methodology 1 Introduction 3 1.1 Basic Concepts. 3 1.2 Preliminary Examples 4 1.2.1 Vanilla Interest-Rate Swap 4 1.2.2 Cancellable Swap.. 5 1.2.3 Managing Credit Risk Collateral, Credit Default

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

FX Barriers with Smile Dynamics

FX Barriers with Smile Dynamics FX Barriers with Smile Dynamics Glyn Baker, Reimer Beneder and Alex Zilber December 16, 2004 Abstract Our mandate in this work has been to isolate the features of smile consistent models that are most

More information

OpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem

OpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem OpenGamma Quantitative Research Adjoint Algorithmic Differentiation: Calibration and Implicit Function Theorem Marc Henrard marc@opengamma.com OpenGamma Quantitative Research n. 1 November 2011 Abstract

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

or enters into a Futures contract (either on the IPE or the NYMEX) with delivery date September and pay every day up to maturity the margin

or enters into a Futures contract (either on the IPE or the NYMEX) with delivery date September and pay every day up to maturity the margin Cash-Futures arbitrage processes Cash futures arbitrage consisting in taking position between the cash and the futures markets to make an arbitrage. An arbitrage is a trade that gives in the future some

More information