Pricing CMS-Spread Options with QuantLib
|
|
|
- Calvin Wilson
- 8 years ago
- Views:
Transcription
1 Pricing CMS-Spread Options with QuantLib Dr. André Miemiec QuantLib Workshop Düsseldorf, December 5, 2014 d-fine All rights reserved 0
2 Whatwearegoingtodo? IR-Markets& CMS Spread Options Model & QuantLib-Implementation Calibration Results A Toy Model & Conclusions d-fine All rights reserved 1
3 This are the current challenges in the Interest Rate Markets Swaptions [Hagan: (2002)] Hagan:(2014) McLoud: (2011) CMS [Hagan: (2003)] CMS-Spread [Berrahoui: (2004)] Arbitrage freeandconsistentmodellingofall threeedgesofir-marketis still a challengingopen question. d-fine All rights reserved 2
![CMS-Spread [Berrahoui: (2004)] Arbitrage freeandconsistentmodellingofall](/docs-images/40/6196154/images/page_3.jpg "threeedgesofir-marketis still a challengingopen question.")
4 CMS-Spread Options are always good for a surprise» Sample Trade (CMS 10Y-2Y), T2E 14yr, K = 0.6% Picture Removed» Two Questions: Whatis a valid rangeforthemtm? e.g. frommarket Quotes Whosepriceis therightone? Result ofa properlycalibratedmodel d-fine All rights reserved 3
5 Whereisthemarket?» Market Quotes of Single Look CMS-Spread Options (5Y): Error boundsarereasonablytight. So qualityofpricingmodelshouldbeeasilydetectable. d-fine All rights reserved 4
6 What comes next? IR-Markets& CMS Spread Options Model & QuantLib-Implementation Calibration Results A Toy Model & Conclusions d-fine All rights reserved 5
7 CMS-Spread Option Model: Forward Premium» Berrahoui sansatz: = { +, }» MarginalsF 2 (x), F 10 (x) obtainedfrom Digital CMS-Options via a modifiedconundrumpricer. = = 1 (0) ($ % )» Choise of Copulas: (asymmetric) Gaussian/Gumbel» Smile-Model: SABR d-fine All rights reserved 6
8 Marginals via CMS-Digital-Replication h = max ( ) h 11 ) & '()*+,-./ = : / 0 / & '()*+,-./ = 0 1 () () 0() + () 0() 11 3 Payer-Swaption(model free) d-fine All rights reserved 7
9 Howdo themarginalslooklike?» Example: Marginal distribution of CMS2Y in 5Y: due to SABR Herea lotof work hastobedonein ordertocureinconsistenceson thelevelofinputmarketdata. d-fine All rights reserved 8
10 Whatcomesnext? IR-Markets& CMS Spread Options Model & QuantLib-Implementation Calibration Results A Toy Model & Conclusions d-fine All rights reserved 9
11 How does the implementation perform?» Market Quotes of Single Look CMS-Spread Options: rho=0.889 QL resultsareok. Performance is critical(severalsecs per coupon). Inacceptablefora productivepricer. d-fine All rights reserved 10
12 Back on the road to improve stability and performance» Steps towards increased stability: Alter construction of marginals, i.e. retrieve it from marginals in the swap measure:? ; < = 0() 0( ) => ) McLoud has given more symmetrical versions of the original Berrahoui formula. From a numerical perspective it might be advantageous to use this symmetric version. Using a precomputedtableofmarginalsonecangetridof theperformanceissue. d-fine All rights reserved 11
13 Whatcomesnext? IR-Markets& CMS Spread Options Model & QuantLib-Implementation Calibration Results A Toy Model & Conclusions d-fine All rights reserved 12
14 Toy Model / VBA-Prototyping» Toy-Modell: lognormal marginals, no swaption smile (cf. Andersen & Piterbarg, p. 778):? ; < = 0() 0( ) => ) ATM-Density Toymodelis different fromthestandardmodel, thatquotescms-options via a normal volatility. d-fine All rights reserved 13
15 Toy Model / VBA-Prototyping» Market Quotes of Single Look CMS-Spread Options: rho= Toymodelperformsasgoodas thereal implementationandis evenfaster. Impliedparametersaresimilar. d-fine All rights reserved 14
16 Conclusions» QL-Implementation: A working implementation for CMS-Spread Options is nearly directly achievable by reusing several codepiecesalreadycontainedin QuantLib. The main task is the generation of the marginal distributions. Empirical evidence indicates that a direct construction of the marginals using the well established conundrum method is not fast enough for productivepurposes. The prerecording of the marginal distribution before entering the integration is likely to solve this deficiency but was not implemented yet. Some suggestions to improve the stability of the pricer were made. CalibrationtoMarket Quotesworks fine.» Toy-Model: In additionthestudyofa toymodelseemstoindicate, thata calibratedmodelcanbeobtainedby plugging ATM marginals from the swap measure more or less directly into the copula method. Again, calibrationtomarket Quotesworks fine. Parameters haveslightlychanged. d-fine All rights reserved 15
17 References (1) P. S. Hagan, D. Kumar, A.S. Lesniewski, andd.e. Woodward, Managing SmileRisk, Wilmott Magazine, September (2) P.S. Hagan, D. Kumar, A.S. Lesniewski, andd.e. Woodward, Arbitrage-Free SABR, Wilmott Magazine, (3) P.S. Hagan, Convexity Conundrums: Pricing CMS Swaps, Caps, and Floors, Wilmott Magazine, September (4) S. Benaim, M. Dodgson, and D. Kainth, An arbitrage-free method for smile extrapolation, Royal Bank of Scotland, Technical report, (5) P. McLoud, The CMS Spread Triangle, RISK, 1:126, (6) M. Berrahoui, Pricing CMS Spread Options and Digital CMS Spread Options with Smile, Wilmott Magazine, (7) A.K.H. Geisselmeyer, Consistent Pricing of CMS and CMS Spread Options with SABR-like Distributions and Power-t Copulas,UniCredit& Universities, Working Paper Series, No. 29, May2012 (8) L. Andersen, V.Piterbarg, Interest Rate Modelling, Vol. 3 d-fine All rights reserved 16
18 Ihre Ansprechpartner bei d-fine Dr. André Miemiec Manager Tel Mobile d-fine GmbH Frankfurt München London Wien Zürich Zentrale Dr. Mark W. Beinker Partner Tel Mobile d-fine GmbH Opernplatz 2 D Frankfurt/Main T F: d-fine All rights reserved 17
19
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
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
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
Consistent Pricing of CMS and CMS Spread Options with SABR-like Distributions and Power-t Copulas
Consistent Pricing of CMS and CMS Spread Options with SABR-like Distributions and Power-t Copulas Andreas K.H. Geisselmeyer March, 2012 Abstract Today, European-style CMS spread options are often priced
INTEREST RATES AND FX MODELS
INTEREST RATES AND FX MODELS 4. Convexity and CMS Andrew Lesniewski Courant Institute of Mathematical Sciences New York University New York February 20, 2013 2 Interest Rates & FX Models Contents 1 Introduction
SWAP AND CAP/FLOORS WITH FIXING IN ARREARS OR PAYMENT DELAY
SWAP AND CAP/FLOORS WITH FIXING IN ARREARS OR PAYMENT DELAY OPENGAMMA QUANTITATIVE RESEARCH Abstract. Pricing methods for swaps and caps/floors with fixing in arrears or payment delays are proposed. The
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
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
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
PricingofAccreting Swaptions using QuantLib. Dr. André Miemiec, 13./14. Nov. 2013
PricingofAccreting Swaptions using QuantLib Dr. André Miemiec, 13./14. Nov. 2013 Agenda 1. Introduction 2. Model Description 3. Implementation in QuantLib 4. Pricing Quality Introduction Origin of the
The interest volatility surface
The interest volatility surface David Kohlberg Kandidatuppsats i matematisk statistik Bachelor Thesis in Mathematical Statistics Kandidatuppsats 2011:7 Matematisk statistik Juni 2011 www.math.su.se Matematisk
the term structure of interest rates
Exposure Draft A framework Yield for Curve Extrapolation estimating and long term nominal and interest extrapolating rate target settingv Yield Curve Extrapolation and long term nominal interest rate target
Options On Credit Default Index Swaps
Options On Credit Default Index Swaps Yunkang Liu and Peter Jäckel 20th May 2005 Abstract The value of an option on a credit default index swap consists of two parts. The first one is the protection value
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
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
Options On Credit Default Index Swaps *
Options On Credit Default Index Swaps * Yunkang Liu and Peter Jäckel Credit, Hybrid, Commodity and Inflation Derivative Analytics Structured Derivatives ABN AMRO 250 Bishopsgate London EC2M 4AA Abstract:
Option Pricing. Chapter 12 - Local volatility models - Stefan Ankirchner. University of Bonn. last update: 13th January 2014
Option Pricing Chapter 12 - Local volatility models - Stefan Ankirchner University of Bonn last update: 13th January 2014 Stefan Ankirchner Option Pricing 1 Agenda The volatility surface Local volatility
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
Credit volatility : Options and beyond
Credit volatility : Options and beyond Jerome.Brun@sgcib.com joint work with F. Rhazal, L. Luciani, T. Bounhar Société Générale Corporate and Investment Banking 25 June 2008, Credit Risk Workshop EVRY
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
Valuing High Yield Bonds: a Business Modeling Approach. Thomas S. Y. Ho. President. Thomas Ho Company, Ltd. 55 Liberty Street, 4B
Valuing High Yield Bonds: a Business Modeling Approach by Thomas S. Y. Ho President Thomas Ho Company, Ltd 55 Liberty Street, 4B New York, NY 10005-1003 USA Tel: 1-212-571-0121 tom.ho@thomasho.com and
Interest Rate Volatility
Interest Rate Volatility I. Volatility in fixed income markets Andrew Lesniewski Baruch College and Posnania Inc First Baruch Volatility Workshop New York June 16-18, 2015 Outline Linear interest rate
#1 USD Inflation Swaps. #1 USD inflation Options
Deutsche Deutsche Bank Bank Corporate Corporate && Investment Investment Bank Bank #1 USD Inflation Swaps #1 USD inflation Options Strictly Private and Confidential CPI The Consumer Price Index Consumer
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,
lambda (options leverage)
lambda (options leverage) INTRODUCTION The lambda (option leverage) is defined as the percentage change in an option price divided by the percentage change in an underlying price. Also called effective
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
American Monte Carlo for Bermudan CVA. Roland Lichters
American Monte Carlo for Bermudan CVA Roland Lichters IKB QuantLib Workshop, 4 December 2014 Outline Background Problem Way Out Example and Results Appendix 2014 Quaternion Risk Management Ltd. 2 Outline
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
Markovian projection for volatility calibration
cutting edge. calibration Markovian projection for volatility calibration Vladimir Piterbarg looks at the Markovian projection method, a way of obtaining closed-form approximations of European-style option
Option-implied probability distributions for future inflation
224 Quarterly Bulletin 212 Q Option-implied probability distributions for future inflation By Tom Smith of the Bank s Macro Financial Analysis Division. (1) Beliefs about future inflation play a major
How To Understand The Latest Features Of F3 Excel Edition 4.3.3
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,
Training Agenda. Structuring and Pricing Derivatives using Numerix CrossAsset XL, CrossAsset SDKs & CAIL (C++/Java/C#)
Training Agenda Structuring and Pricing Derivatives using Numerix CrossAsset XL, CrossAsset SDKs & CAIL (C++/Java/C#) Numerix Training: CrossAsset XL and SDKs (C++/Java/C#): Orientation Implementation
Bootstrapping the interest-rate term structure
Bootstrapping the interest-rate term structure Marco Marchioro www.marchioro.org October 20 th, 2012 Bootstrapping the interest-rate term structure 1 Summary (1/2) Market quotes of deposit rates, IR futures,
FX Options and Smile Risk_. Antonio Castagna. )WILEY A John Wiley and Sons, Ltd., Publication
FX Options and Smile Risk_ Antonio Castagna )WILEY A John Wiley and Sons, Ltd., Publication Preface Notation and Acronyms IX xiii 1 The FX Market 1.1 FX rates and spot contracts 1.2 Outright and FX swap
ING Insurance Economic Capital Framework
ING Insurance Economic Capital Framework Thomas C. Wilson Chief Insurance Risk Officer Kent University, September 5, 2007 www.ing.com Objectives of this session ING has been using economic capital internally
Bank of America AAA 10.00% T-Bill +.30% Hypothetical Resources BBB 11.90% T-Bill +.80% Basis point difference 190 50
Swap Agreements INTEREST RATE SWAP AGREEMENTS An interest rate swap is an agreement to exchange interest rate payments on a notional principal amount over a specific period of time. Generally a swap exchanges
Model Independent Greeks
Model Independent Greeks Mathematical Finance Winter School Lunteren January 2014 Jesper Andreasen Danske Markets, Copenhagen kwant.daddy@danskebank.com Outline Motivation: Wots me Δelδa? The short maturity
Fixed Income Arbitrage
Risk & Return Fixed Income Arbitrage: Nickels in Front of a Steamroller by Jefferson Duarte Francis A. Longstaff Fan Yu Fixed Income Arbitrage Broad set of market-neutral strategies intended to exploit
FORWARDS AND EUROPEAN OPTIONS ON CDO TRANCHES. John Hull and Alan White. First Draft: December, 2006 This Draft: March 2007
FORWARDS AND EUROPEAN OPTIONS ON CDO TRANCHES John Hull and Alan White First Draft: December, 006 This Draft: March 007 Joseph L. Rotman School of Management University of Toronto 105 St George Street
JENS HENRIK EGGERT CHRISTENSEN RESEARCH ADVISOR, FINANCIAL RESEARCH FEDERAL RESERVE BANK OF SAN FRANCISCO 101 MARKET STREET, SAN FRANCISCO, CA 94105
JENS HENRIK EGGERT CHRISTENSEN RESEARCH ADVISOR, FINANCIAL RESEARCH FEDERAL RESERVE BANK OF SAN FRANCISCO 101 MARKET STREET, SAN FRANCISCO, CA 94105 JENS.CHRISTENSEN@SF.FRB.ORG 415.974.3115 US VISA STATUS:
Learning Curve An introduction to the use of the Bloomberg system in swaps analysis Received: 1st July, 2002
Learning Curve An introduction to the use of the Bloomberg system in swaps analysis Received: 1st July, 2002 Aaron Nematnejad works in the fixed income analytics team at Bloomberg L.P. in London. He graduated
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
Advanced Fixed Income Analytics Lecture 1
Advanced Fixed Income Analytics Lecture 1 Backus & Zin/April 1, 1999 Vasicek: The Fixed Income Benchmark 1. Prospectus 2. Models and their uses 3. Spot rates and their properties 4. Fundamental theorem
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
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
Dynamic Factor Copula Model
Dynamic Factor Copula Model Ken Jackson Alex Kreinin Wanhe Zhang July 6, 2009 Abstract The Gaussian factor copula model is the market standard model for multi-name credit derivatives. Its main drawback
EQUITY DERIVATIVES AND STRUCTURED EQUITY PRODUCTS
NEW YORK 17 & 18 September 2007 LONDON 26 & 27 September 2007 EQUITY AND STRUCTURED EQUITY PRODUCTS ADVANCED TECHNIQUES FOR PRICING, HEDGING AND TRADING Course highlights: Compare and evaluate the leading
Rate curves for forward Euribor estimation and CSA-discounting
Rate curves for forward Euribor estimation and CSA-discounting Ferdinando M. Ametrano Banca IMI - Financial Engineering ferdinando.ametrano@bancaimi.com Goals To provide key elements for rate curve estimation
Pricing complex options using a simple Monte Carlo Simulation
A subsidiary of Sumitomo Mitsui Banking Corporation Pricing complex options using a simple Monte Carlo Simulation Peter Fink Among the different numerical procedures for valuing options, the Monte Carlo
EQUITY LINKED NOTES: An Introduction to Principal Guaranteed Structures Abukar M Ali October 2002
EQUITY LINKED NOTES: An Introduction to Principal Guaranteed Structures Abukar M Ali October 2002 Introduction In this article we provide a succinct description of a commonly used investment instrument
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
Equity forward contract
Equity forward contract INRODUCION An equity forward contract is an agreement between two counterparties to buy a specific number of an agreed equity stock, stock index or basket at a given price (called
Perspectives September
Perspectives September 2013 Quantitative Research Option Modeling for Leveraged Finance Part I Bjorn Flesaker Managing Director and Head of Quantitative Research Prudential Fixed Income Juan Suris Vice
Interest Rate Swaps. Key Concepts and Buzzwords. Readings Tuckman, Chapter 18. Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps
Interest Rate Swaps Key Concepts and Buzzwords Swaps Swap Spreads Credit Risk of Swaps Uses of Swaps Readings Tuckman, Chapter 18. Counterparty, Notional amount, Plain vanilla swap, Swap rate Interest
Fixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
Hedging Pension Liabilities
Hedging Pension Liabilities when there are incomplete markets and regulatory uncertainty Sampension, 2012 Outline Introduction 1 Introduction 2 3 4 Outline Introduction 1 Introduction 2 3 4 Sampension
Monte Carlo Methods and Models in Finance and Insurance
Chapman & Hall/CRC FINANCIAL MATHEMATICS SERIES Monte Carlo Methods and Models in Finance and Insurance Ralf Korn Elke Korn Gerald Kroisandt f r oc) CRC Press \ V^ J Taylor & Francis Croup ^^"^ Boca Raton
How To Write A Credit Risk Book
CRM validation Jérôme BRUN, Head of model validation (market risk) June 2011 Introduction and agenda 1 3 amendments on the trading book to be implemented in 2011 Incremental Risk Charge (IRC) & Comprehensive
Intensive developments in interest rate modeling have
Interest Rate Model Selection A conscientious choice for mortgage investors. Alexander Levin Intensive developments in interest rate modeling have delivered a bold but confusing model selection choice
CHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support
CHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS 1. a. The closing price for the spot index was 1329.78. The dollar value of stocks is thus $250 1329.78 = $332,445. The closing futures price for the March contract was 1364.00,
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
Floating-Rate Securities
Floating-Rate Securities A floating-rate security, or floater, is a debt security whose coupon rate is reset at designated dates and is based on the value of a designated reference rate. - Handbook of
Autumn Investor Seminar. Workshops. Managing Variable Annuity Risk
Autumn Investor Seminar Workshops Managing Variable Annuity Risk Jean-Christophe Menioux Kevin Byrne Denis Duverne Group CRO CIO AXA Equitable Chief Financial Officer Paris November 25, 2008 Cautionary
Master of Mathematical Finance: Course Descriptions
Master of Mathematical Finance: Course Descriptions CS 522 Data Mining Computer Science This course provides continued exploration of data mining algorithms. More sophisticated algorithms such as support
The Irony In The Derivatives Discounting
The Irony In The Derivatives Discounting Marc Henrard Head of Quantitative Research, Banking Department, Bank for International Settlements, CH-4002 Basel (Switzerland), e-mail: Marc.Henrard@bis.org Abstract
The Pricing for Interest Sensitive Products of Life Insurance Firms
Modern Economy, 2011, 2, 194-202 doi:10.4236/me.2011.23025 Published Online July 2011 (http://www.scirp.org/journal/me) The Pricing for Interest Sensitive Products of Life Insurance Firms Abstract James
Invesco Great Wall Fund Management Co. Shenzhen: June 14, 2008
: A Stern School of Business New York University Invesco Great Wall Fund Management Co. Shenzhen: June 14, 2008 Outline 1 2 3 4 5 6 se notes review the principles underlying option pricing and some of
A Day in the Life of a Trader
Siena, April 2014 Introduction 1 Examples of Market Payoffs 2 3 4 Sticky Smile e Floating Smile 5 Examples of Market Payoffs Understanding risk profiles of a payoff is conditio sine qua non for a mathematical
Massachusetts State Treasurer s Office (STO) Guidelines for Current and Advance Refundings
Massachusetts State Treasurer s Office (STO) Guidelines for Current and Advance Refundings The STO intends to evaluate refunding opportunities for Massachusetts bonds based on a refunding efficiency approach.
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.
OpenGamma Quantitative Research Multi-curves Framework with Stochastic Spread: A Coherent Approach to STIR Futures and Their Options
OpenGamma Quantitative Research Multi-curves Framework with Stochastic Spread: A Coherent Approach to STIR Futures and Their Options Marc Henrard marc@opengamma.com OpenGamma Quantitative Research n. 11
Interest rate Derivatives
Interest rate Derivatives There is a wide variety of interest rate options available. The most widely offered are interest rate caps and floors. Increasingly we also see swaptions offered. This note will
Valuation of Equity Derivatives
Valuation of Equity Derivatives Dr Mark Beinker TRONGnet school Bielefeld, 1./. June 011 1 What s a derivative? More complex financial products are derived from simpler products What s not a derivative?
GN47: Stochastic Modelling of Economic Risks in Life Insurance
GN47: Stochastic Modelling of Economic Risks in Life Insurance Classification Recommended Practice MEMBERS ARE REMINDED THAT THEY MUST ALWAYS COMPLY WITH THE PROFESSIONAL CONDUCT STANDARDS (PCS) AND THAT
Caps and Floors. John Crosby
Caps and Floors John Crosby Glasgow University My website is: http://www.john-crosby.co.uk If you spot any typos or errors, please email me. My email address is on my website Lecture given 19th February
Lisa Borland. A multi-timescale statistical feedback model of volatility: Stylized facts and implications for option pricing
Evnine-Vaughan Associates, Inc. A multi-timescale statistical feedback model of volatility: Stylized facts and implications for option pricing Lisa Borland October, 2005 Acknowledgements: Jeremy Evnine
How To Understand The Financial Market For Insurers In Swissitzerland
Actuarial and Insurance Solutions Financial Market Analysis at endyear 2014 15 th January 2015 Audit. Tax. Consulting. Corporate Finance. Contents Executive Summary 1 1 Interest Rates 2 2 Equity Markets
THE FVA-DVA PUZZLE: RISK MANAGEMENT AND COLLATERAL TRADING STRATEGIES
THE FVA-DVA PUZZLE: RISK MANAGEMENT AND COLLATERAL TRADING STRATEGIES CLAUDIO ALBANESE AND STEFANO IABICHINO Abstract. In the aftermath of the crisis, valuations of fixed income derivatives have significantly
Modelling Corporate Bonds
Modelling Corporate Bonds Current Issues In Life Assurance London 28 April 2004 / Edinburgh 20 May 2004 Andrew Smith email AndrewDSmith8@deloitte.co.uk Presentation Outline Why model corporate bonds? Corporate
Lecture 2 Bond pricing. Hedging the interest rate risk
Lecture 2 Bond pricing. Hedging the interest rate risk IMQF, Spring Semester 2011/2012 Module: Derivatives and Fixed Income Securities Course: Fixed Income Securities Lecturer: Miloš Bo ović Lecture outline
The Single Name Corporate CDS Market. Alan White
The Single Name Corporate CDS Market Alan White CDS Structure Single Name DJ Index Products CDS Notional x [ ] bp p.a. Buyer Credit Risk of ABC Seller 125 Equally Weighted Names Buyer Delivery 10MM Principal
CHAPTER 7 SUGGESTED ANSWERS TO CHAPTER 7 QUESTIONS
INSTRUCTOR S MANUAL: MULTINATIONAL FINANCIAL MANAGEMENT, 9 TH ED. CHAPTER 7 SUGGESTED ANSWERS TO CHAPTER 7 QUESTIONS 1. Answer the following questions based on data in Exhibit 7.5. a. How many Swiss francs
arxiv:1407.5528v1 [q-fin.pr] 21 Jul 2014
![arxiv:1407.5528v1 [q-fin.pr] 21 Jul 2014](/thumbs/27/11975749.jpg "arxiv:1407.5528v1 [q-fin.pr] 21 Jul 2014")
ARBITRAGE-FREE PREDICTION OF THE IMPLIED VOLATILITY SMILE PETROS DELLAPORTAS AND ALEKSANDAR MIJATOVIĆ arxiv:1407.5528v1 [q-fin.pr] 21 Jul 2014 Abstract. This paper gives an arbitrage-free prediction for
Market Microstructure: An Interactive Exercise
Market Microstructure: An Interactive Exercise Jeff Donaldson, University of Tampa Donald Flagg, University of Tampa ABSTRACT Although a lecture on microstructure serves to initiate the inspiration of
Finite Differences Schemes for Pricing of European and American Options
Finite Differences Schemes for Pricing of European and American Options Margarida Mirador Fernandes IST Technical University of Lisbon Lisbon, Portugal November 009 Abstract Starting with the Black-Scholes
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
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
INTRODUCTION TO TRADING AND INVESTING IN FIXED INCOME SIMULATION TRAINING@THE DEALING ROOM
INTRODUCTION TO TRADING AND INVESTING IN FIXED INCOME SIMULATION TRAINING@THE DEALING ROOM Leading Excellence in Banking & Finance OUR PARTNERS CapitalWave provides truly dynamic educational simulation
CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS
1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries
IMPLICIT OPTIONS IN LIFE INSURANCE CONTRACTS The case of lump sum options in deferred annuity contracts Tobias S. Dillmann Institut fur Finanz- und Aktuarwissenschaften c/o Abteilung Unternehmensplanung
PRICING OF SWAPS AND SWAPTIONS
MSC. FINANCE MASTER THESIS DEP. OF ECONOMICS AND BUSINESS AARHUS MARCH 2013 PRICING OF SWAPS AND SWAPTIONS MSC. FINANCE STUDENT: MIKKEL KRONBORG OLESEN STUDENT NR.: 283755 SUPERVISOR: PETER LØCHTE JØRGENSEN
January to December 2015 Face-to-face classroom courses in London for the A.C.I. exams:
A.C.I. EXAM COURSES January to December 2015 Face-to-face classroom courses in London for the A.C.I. exams: A.C.I. Diploma A.C.I. Dealing Certificate A.C.I. Operations Certificate (All courses are also
1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
A comparison between different volatility models. Daniel Amsköld
A comparison between different volatility models Daniel Amsköld 211 6 14 I II Abstract The main purpose of this master thesis is to evaluate and compare different volatility models. The evaluation is based
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
OIS Discounting: Changing the Way Interest Rate Swaps are Valued By: Bryan Kern, February 2012
OIS Discounting: Changing the Way Interest Rate Swaps are Valued By: Bryan Kern, February 2012 What is OIS? T Figure 1 plots the Federal Funds curve against a curve that is much more familiar to many participants