We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byStuart Goldsby
Modified over 2 years ago
Discussion of Structural GARCH: The Volatility-Leverage Connection by Rob Engle and Emil Siriwardane © 2013 by Andrew W. Lo All Rights Reserved Andrew W. Lo MFM Conference October 11, 2013 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAA A A A A AAA A A A
MFM © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Modigliani-Miller Proposition II: The Basic Framework Slide 2 Equity volatility increases linearly with leverage If debt is risky, the relationship is more complex Use option-pricing model (Merton, 1974)
MFM © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 3 The Basic Framework AssetsLiabilities ATAT E T = Max [ A T X, 0 ] D T = Min [ A T, X ] ATAT ATAT Company XYZ Equity is a call option on the firms assets Option-pricing model provides valuation formulas
MFM © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 4 The Basic Framework Specific case of geometric Brownian motion for A t
MFM © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 5 The Basic Framework Itôs formula yields the exact dynamics of E t = LM(A t /X,1,,r, ) is the option elasticity or gearing
MFM © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 6 The Basic Framework AtAt Call Option Elasticity
MFM © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 7 The Basic Framework Now assume a more general asset-price process
MFM Structural Interpretation From a formal perspective, not a fully structural specification –e.g., suppose asset prices followed a CEV process © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 8
MFM Structural Interpretation The benefit of BSM is specificity, not flexibility Consistency of BSM functions with GARCH? If flexibility is the goal, then: 1.Use implied volatilities, e.g., VIX 2.Use nonparametric option-pricing model (Ait-Sahalia and Lo, 1998) to estimate SPD from options, which yields LM 3.Use M&M II and multiple factors –Estimate GARCH models with D/E, CDS, etc. © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 9
MFM Structural Interpretation Complex capital structure makes this more complex –Coupon bonds are compound options (Geske, 1977) –Bond indenture provisions (Black and Cox, 1976) –Particularly problematic for financial firms Potential issue with option-pricing approach –Pricing model hinges on dynamic completeness, i.e., dynamic replication of option payoff via trading strategy –Market for corporate assets are relatively illiquid –Delta-hedging strategy may be very expensive, i.e., option- pricing formula may be a poor approximation (important for systemic risk measurement) © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 10
MFM Leverage Effect Black (1972), Christie (1982), Duffie (1995) Hasanhodzic and Lo (2013): January 2, 1973 to December 31, 2010 (241 firms) © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 11
MFM Leverage Effect © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 12 But leverage effect is the same for all-equity-financed companies!
MFM Systemic Risk Measurement During periods of financial distress, BSM option- pricing model for firms equity may be inadequate Complex capital structure is particularly relevant, e.g., AIGs credit support agreements A structural alternative is Mertons jump-diffusion model: –For lognormal Z, LM can be derived in closed-form; compare and contrast to the pure diffusion case A reduced-form alternative is regime-switching © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 13
MFM Systemic Risk Measurement Another measure of systemic risk might be the options gamma: © 2013 by Andrew W. Lo All Rights Reserved 11 October 2013 Slide 14 d1d1
Credit Risk Nicolas Beudin & Maxime Riche. Agenda 1. Overview 2. Valuation 3. Dealing with credit risk 4. Conclusion 5. Appendix 2.
Equity-to-Credit Problem Philippe Henrotte ITO 33 and HEC Paris Equity-to-Credit Arbitrage Gestion Alternative, Evry, April 2004.
Advanced Risk Management I Lecture 6 Non-linear portfolios.
Bounding Option Prices Using Semidefinite Programming S ACHIN J AYASWAL Department of Management Sciences University of Waterloo, Canada Project work for.
CHAPTER 5 CAPITAL STRUCTURE Presenters name Presenters title dd Month yyyy.
The Cost of Capital, Corporation Finance and the Theory of Investment By Franco Modigliani and Merton H. Miller David Dodge.
July 30, 2003 Bill Pauling, CFA Integrated Credit and Equity Risk Modeling Enterprise Risk Management Symposium.
Session 6: Capital Structure I C Corporate Finance Topics.
1 Derivatives & Risk Management: Part II Models, valuation and risk management.
FMG PH.D. seminar (21 October 1999) slide 1 Dynamic Hedging with Transaction Costs Outline: -Introduction -Adjusted path and Strategy -Leland model and.
1 MGT 821/ECON 873 Volatility Smiles & Extension of Mode ls.
Financial Innovation & Product Design II Dr. Helmut Elsinger « Options, Futures and Other Derivatives », John Hull, Chapter 22 BIART Sébastien The Standard.
COST OF CAPITAL AND Chapter 11. The Dividend Growth Model Approach Can be rearranged to solve for R E 1.
OPTIONS PRICING AND HEDGING WITH GARCH.THE PRICING KERNEL.HULL AND WHITE.THE PLUG-IN ESTIMATOR AND GARCH GAMMA.ENGLE-MUSTAFA – IMPLIED GARCH.DUAN AND EXTENSIONS.ENGLE.
Chapter 15 Fundamentals of Corporate Finance Fifth Edition Slides by Matthew Will McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc.
Structural Models. 2 Source: Moody’s-KMV What do we learn from these plots? The volatility of a firm’s assets is a major determinant of its.
Copyright © 2002 by Harcourt Inc.All rights reserved. CHAPTER 17 Capital Structure Decisions: Extensions MM and Miller models Hamadas equation Financial.
1 SAMSI Credit Risk Working Group Presentation Model for Unified Valuation of Credit and Equity Derivatives Apoorv Mathur (Ongoing work) Joint Work with.
INVESTMENTS | BODIE, KANE, MARCUS Copyright © 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written.
McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Option Valuation CHAPTER 15.
Option Valuation The Black-Scholes-Merton Option Pricing Model.
Credit Risk in Derivative Pricing Frédéric Abergel Chair of Quantitative Finance École Centrale de Paris.
Chapter 17 Principles of Corporate Finance Tenth Edition Does Debt Policy Matter? Slides by Matthew Will McGraw-Hill/Irwin Copyright © 2011 by the McGraw-Hill.
Chapter 23 Credit Risk Options, Futures, and Other Derivatives, 8th Edition, Copyright © John C. Hull
Options An Introduction to Derivative Securities.
50 years of Finance André Farber Université Libre de Bruxelles Inaugurale rede, Francqui Leerstoel VUB 2 December 2004.
Option Valuation CHAPTER OPTION VALUATION: INTRODUCTION.
1 Chapter 16 Capital Structure Decisions: Part II.
MODIGLIANI – MILLER THEOREM ANASTASIIA TISETSKA. AGENDA: MODIGLIANI–MILLER I – LEVERAGE, ARBITRAGE AND FIRM VALUE MODIGLIANI–MILLER II – LEVERAGE,
© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Option Valuation Chapter Twenty- Four.
Advanced Finance Risky debt (2) Professor André Farber Solvay Business School Université Libre de Bruxelles.
CHAPTER 5 CREDIT RISK 1. Chapter Focus Distinguishing credit risk from market risk Credit policy and credit risk Credit risk assessment framework Inputs.
11.1 Options, Futures, and Other Derivatives, 4th Edition © 1999 by John C. Hull The Black-Scholes Model Chapter 11.
INVESTMENTS | BODIE, KANE, MARCUS Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 18 Option Valuation.
RISK MANAGEMENT: AN INTRODUCTION TO FINANCIAL ENGINEERING Chapter 24.
Estimating Credit Exposure and Economic Capital Using Monte Carlo Simulation Ronald Lagnado Vice President, MKIRisk IPAM Conference on Financial Mathematics.
Chapter 2- Capital Structure Determination. After studying this chapter, you should be able to: Define “capital structure.” Explain the net operating.
Revision 1. Corporate finance: – Equity underwriting – Debt underwriting & bond pricing – M&A advisory Asset management – Derivative products (swaps,
Session 2: Options I C Corporate Finance Topics Summer 2006.
Risk Management & Real Options Interlude The Link to Financial Options and Black-Scholes Stefan Scholtes Judge Institute of Management University of Cambridge.
McGraw-Hill/Irwin Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. Option Valuation 16.
16- 1 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Fundamentals of Corporate Finance Sixth Edition Richard.
Does Debt Policy Matter? Principles of Corporate Finance Brealey and Myers Sixth Edition Slides by Matthew Will Chapter 17 © The McGraw-Hill Companies,
© 2012 McGraw-Hill Ryerson LimitedChapter The value of a firm from two angles AssetsLiabilities and Stockholder’s Equity Value of cash flows from.
Applied Finance Lectures 1. What is finance? 2. The diffusion of the discounted cash flow method 3. Markowitz and the birth of modern portfolio theory.
JUMP DIFFUSION MODELS Karina Mignone Option Pricing under Jump Diffusion.
Credit Risk: Modeling, Valuation and Hedging ~ 整理 : 田宇正.
16- 1 McGraw Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All rights reserved Fundamentals of Corporate Finance Chapter 16 McGraw Hill/Irwin.
Financing and Valuation Principles of Corporate Finance Seventh Edition Richard A. Brealey Stewart C. Myers Slides by Matthew Will Chapter 19 McGraw Hill/Irwin.
Credit Risk Models Question: What is an appropriate modeling approach to value defaultable debt (bonds and loans)?
© 2017 SlidePlayer.com Inc. All rights reserved.