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Managing Volatility Risk
Managing Volatility Risk Innovation of Financial Derivatives, Stochastic Models and Their Analytical Implementation Chenxu Li Submitted in partial fulfillment of the Requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2010 c 2010 Chenxu Li All Rights Reserved ABSTRACT Managing Volatility Risk Innovation of Financial Derivatives, Stochastic Models and Their Analytical Implementation Chenxu Li This dissertation investigates two timely topics in mathematical finance. In partic- ular, we study the valuation, hedging and implementation of actively traded volatil- ity derivatives including the recently introduced timer option and the CBOE (the Chicago Board Options Exchange) option on VIX (the Chicago Board Options Ex- change volatility index). In the first part of this dissertation, we investigate the pric- ing, hedging and implementation of timer options under Heston’s (1993) stochastic volatility model. The valuation problem is formulated as a first-passage-time problem through a no-arbitrage argument. By employing stochastic analysis and various ana- lytical tools, such as partial differential equation, Laplace and Fourier transforms, we derive a Black-Scholes-Merton type formula for pricing timer options. This work mo- tivates some theoretical study of Bessel processes and Feller diffusions as well as their numerical implementation. In the second part, we analyze the valuation of options on VIX under Gatheral’s double mean-reverting stochastic volatility model, which is able to consistently price options on S&P 500 (the Standard and Poor’s 500 index), VIX and realized variance (also well known as historical variance calculated by the variance of the asset’s daily return). -
Hedging Volatility Risk
Journal of Banking & Finance 30 (2006) 811–821 www.elsevier.com/locate/jbf Hedging volatility risk Menachem Brenner a,*, Ernest Y. Ou b, Jin E. Zhang c a Stern School of Business, New York University, New York, NY 10012, USA b Archeus Capital Management, New York, NY 10017, USA c School of Business and School of Economics and Finance, The University of Hong Kong, Pokfulam Road, Hong Kong Received 11 April 2005; accepted 5 July 2005 Available online 9 December 2005 Abstract Volatility risk plays an important role in the management of portfolios of derivative assets as well as portfolios of basic assets. This risk is currently managed by volatility ‘‘swaps’’ or futures. How- ever, this risk could be managed more efficiently using options on volatility that were proposed in the past but were never introduced mainly due to the lack of a cost efficient tradable underlying asset. The objective of this paper is to introduce a new volatility instrument, an option on a straddle, which can be used to hedge volatility risk. The design and valuation of such an instrument are the basic ingredients of a successful financial product. In order to value these options, we combine the approaches of compound options and stochastic volatility. Our numerical results show that the straddle option is a powerful instrument to hedge volatility risk. An additional benefit of such an innovation is that it will provide a direct estimate of the market price for volatility risk. Ó 2005 Elsevier B.V. All rights reserved. JEL classification: G12; G13 Keywords: Volatility options; Compound options; Stochastic volatility; Risk management; Volatility index * Corresponding author. -
Evidence from SME Bond Markets
Temi di discussione (Working Papers) Asymmetric information in corporate lending: evidence from SME bond markets by Alessandra Iannamorelli, Stefano Nobili, Antonio Scalia and Luana Zaccaria September 2020 September Number 1292 Temi di discussione (Working Papers) Asymmetric information in corporate lending: evidence from SME bond markets by Alessandra Iannamorelli, Stefano Nobili, Antonio Scalia and Luana Zaccaria Number 1292 - September 2020 The papers published in the Temi di discussione series describe preliminary results and are made available to the public to encourage discussion and elicit comments. The views expressed in the articles are those of the authors and do not involve the responsibility of the Bank. Editorial Board: Federico Cingano, Marianna Riggi, Monica Andini, Audinga Baltrunaite, Marco Bottone, Davide Delle Monache, Sara Formai, Francesco Franceschi, Salvatore Lo Bello, Juho Taneli Makinen, Luca Metelli, Mario Pietrunti, Marco Savegnago. Editorial Assistants: Alessandra Giammarco, Roberto Marano. ISSN 1594-7939 (print) ISSN 2281-3950 (online) Printed by the Printing and Publishing Division of the Bank of Italy ASYMMETRIC INFORMATION IN CORPORATE LENDING: EVIDENCE FROM SME BOND MARKETS by Alessandra Iannamorelli†, Stefano Nobili†, Antonio Scalia† and Luana Zaccaria‡ Abstract Using a comprehensive dataset of Italian SMEs, we find that differences between private and public information on creditworthiness affect firms’ decisions to issue debt securities. Surprisingly, our evidence supports positive (rather than adverse) selection. Holding public information constant, firms with better private fundamentals are more likely to access bond markets. Additionally, credit conditions improve for issuers following the bond placement, compared with a matched sample of non-issuers. These results are consistent with a model where banks offer more flexibility than markets during financial distress and firms may use market lending to signal credit quality to outside stakeholders. -
Hedge Performance: Insurer Market Penetration and Basis Risk
CORE Metadata, citation and similar papers at core.ac.uk Provided by Research Papers in Economics This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: The Financing of Catastrophe Risk Volume Author/Editor: Kenneth A. Froot, editor Volume Publisher: University of Chicago Press Volume ISBN: 0-226-26623-0 Volume URL: http://www.nber.org/books/froo99-1 Publication Date: January 1999 Chapter Title: Index Hedge Performance: Insurer Market Penetration and Basis Risk Chapter Author: John Major Chapter URL: http://www.nber.org/chapters/c7956 Chapter pages in book: (p. 391 - 432) 10 Index Hedge Performance: Insurer Market Penetration and Basis Risk John A. Major Index-based financial instruments bring transparency and efficiency to both sides of risk transfer, to investor and hedger alike. Unfortunately, to the extent that an index is anonymous and commoditized, it cannot correlate perfectly with a specific portfolio. Thus, hedging with index-based financial instruments brings with it basis risk. The result is “significant practical and philosophical barriers” to the financing of propertykasualty catastrophe risks by means of catastrophe derivatives (Foppert 1993). This study explores the basis risk be- tween catastrophe futures and portfolios of insured homeowners’ building risks subject to the hurricane peril.’ A concrete example of the influence of market penetration on basis risk can be seen in figures 10.1-10.3. Figure 10.1 is a map of the Miami, Florida, vicin- John A. Major is senior vice president at Guy Carpenter and Company, Inc. He is an Associate of the Society of Actuaries. -
Risk Parity an Alternative Approach to Asset Allocation
FEATURE Risk Parity An Alternative Approach to Asset Allocation Alexander Pekker, PhD, CFA®, ASA, Meghan P. Elwell, JD, AIFA®, and Robert G. Smith III, CIMC®, AIF® ollowing the financial crisis of tors, traditional RP strategies fall short respectively, but a rather high Sharpe 2008, many members of the of required return targets and leveraged ratio, 0.86. In other words, while the investment management com- RP strategies do not provide enough portfolio is unlikely to meet the expected F munity, including Sage,intensified their potential benefits to outweigh their return target of many institutional inves- scrutiny of mean-variance optimization risks. Instead we advocate a liability- tors (say, 7 percent or higher), its effi- (MVO) and modern portfolio theory based approach that incorporates risk ciency, or “bang for the buck” (i.e., return (MPT) as the bedrock of asset alloca- budgeting, a key theme of RP, as well as per unit of risk, in excess of the risk-free tion (Elwell and Pekker 2010). Among tactical asset allocation. rate), is quite strong. various alternative approaches to asset How does this sample RP portfo- What is Risk Parity? allocation, risk parity (RP) has been in the lio compare with a sample MVO port- news lately (e.g., Nauman 2012; Summers As noted above, an RP portfolio is one folio? A sample MVO portfolio with a 2012), especially as some hedge funds, where risk, defined as standard deviation return target of 7 percent is shown in such as AQR, and large plan sponsors, of returns, is distributed evenly among table 2. Unlike the sample RP portfolio, such as the San Diego County Employees all potential asset classes;1 table 1 shows the MVO portfolio is heavily allocated Retirement Association, have advocated a sample (unleveraged) RP portfolio toward equities, and it has much higher its adoption. -
Decomposing Underwriting Spreads for GSE's and Frequent Issuer Financial Firms
Decomposing Underwriting Spreads for GSEs and Frequent Issuer Financial Firms David M. Harrison Associate Professor Rawls College of Business Administration Texas Tech University Lubbock, TX 79409 [email protected] 806.742.3190 phone 806.742.3197 fax Andrea J. Heuson Professor of Finance University of Miami P.O. Box 248094 5250 University Dr., Jenkins Bldg. Coral Gables, FL 33124 [email protected] 305.284.1866 phone 305.284.4800 fax and Michael J. Seiler Professor and Robert M. Stanton Chair of Real Estate Old Dominion University 2154 Constant Hall Norfolk, VA 23529 [email protected] 757.683.3505 phone 757.683.3258 fax Revise and Resubmit at Journal of Real Estate Finance and Economics December 2010 Decomposing Underwriting Spreads for GSEs and Frequent Issuer Financial Firms Home mortgage debt outstanding grew at a nominal rate of more than 10% per year and a real rate of more than 8% per year during the decade that began in 1997. Much of the increase was funded by investors who purchased mortgage-backed securities through a market supported by Fannie Mae and Freddie Mac – two Government Sponsored Enterprises (GSEs) charged with improving intermediation in the residential mortgage market. Furthermore, both housing and non-housing GSEs and large domestic financial institutions took sizeable investment positions in mortgage-backed securities, funding this increased investment by borrowing in the bond market using callable and non-callable debt agreements. Recent developments make clear that many of these investments carried significant credit risk. This paper investigates the determinants of underwriting fees charged to active GSE and financial industry borrowers on debt issuances, how such fees change over time, and how they vary with the characteristics of the debt, the underwriting mechanism, and the issuer. -
The Cross-Section of Volatility and Expected Returns
THE JOURNAL OF FINANCE • VOL. LXI, NO. 1 • FEBRUARY 2006 The Cross-Section of Volatility and Expected Returns ANDREW ANG, ROBERT J. HODRICK, YUHANG XING, and XIAOYAN ZHANG∗ ABSTRACT We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While con- siderable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Camp- bell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of fu- ture market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. -
The Behavior of Residential Mortgage Yields Since 1951. Jack M. Guttentag
This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: Essays on Interest Rates, Volume 1 Volume Author/Editor: Jack M. Guttentag and Phillip Cagan, eds. Volume Publisher: NBER Volume ISBN: 0-87014-201-1 Volume URL: http://www.nber.org/books/gutt69-1 Publication Date: 1969 Chapter Title: The Behavior of Residential Mortgage Yields Since 1951 Chapter Author: Jack M. Guttentag Chapter URL: http://www.nber.org/chapters/c1208 Chapter pages in book: (p. 29 - 76) 2 TheBehavior of Residential Mortgage Yields Since 1951 Jack M. Guttentag This chapter reports some selected findings drawn from a study of the behavior of residential mortgage interest rates in the period since 1951. The findings reported here are based in part on new monthly and quarterly time series on residential mortgage rates and terms drawn from the internal records of some large life insurance com- panies.' These new data have a combination of important attributes heretofore not available in any single series. First, the date of record is the date when loans were committed or authorized by lenders, rather than the date on which funds were dis- bursed. Hence the long and erratic lag characteristic of a series recorded on a disbursement basis is largely eliminated. Second, the data cover all three types of residential mortgages (FHA, VA, and conventional); separate series are also available on mortgages acquired through correspondents as opposed to those originated directly by life insurance companies. Third, the data include loan-value ratios and maturities, as well as fees and charges collected and paid by the lender over and above the contract rate. -
Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities
The Bond Market Association Uniform Practices/Standard Formulas Chapter SF Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities Table of Contents A. Computational Accuracy SF-3 B. Prepayments SF-4 1. Cash Flows SF-4 2. Mortgage Prepayment Models SF-5 3. Average Prepayment Rates for Mortgage Pools SF-11 4. ABS Prepayment Rates for Asset Pools SF-13 C. Defaults SF-16 1. Mortgage Cash Flows with Defaults: Description of Basic Concepts SF-16 2. Specifying Mortgage Default Assumptions: Standards and Definitions SF-17 3. Standard Formulas for Computing Mortgage Cash Flows with Defaults SF-18 4. The Standard Default Assumption (SDA) SF-20 5. Use of the SDA for Products Other Than 30-Year Conventional Mortgages SF-22 6. Numerical Examples of SDA SF-22 D. Assumptions for Generic Pools SF-39 1. Mortgage Maturity SF-39 2. Mortgage Age SF-40 3. Mortgage Coupon SF-43 E. Day Counts SF-44 1. Calendar Basis SF-44 2. Delay Days SF-44 02/01/99 SF-1 All rights reserved. Reproduction in any form is strictly forbidden. © 1999 The Bond Market Association. The Bond Market Association Uniform Practices/Standard Formulas F. Settlement-Based Calculations SF-45 1. General Rules SF-45 2. CMO Bonds with Unknown Settlement Factors SF-46 3. Freddie Mac Multiclass PCs (REMICs) SF-47 G. Yield and Yield-Related Measures SF-48 1. General Rules SF-48 2. Calculations for Floating-Rate MBS SF-52 3. Putable Project Loans SF-55 H. Accrual Instruments SF-56 1. Average Life of Accrual Instruments SF-56 2. -
Greenbook Part 2
Prefatory Note The attached document represents the most complete and accurate version available based on original copies culled from the files of the FOMC Secretariat at the Board of Governors of the Federal Reserve System. This electronic document was created through a comprehensive digitization process which included identifying the best- preserved paper copies, scanning those copies,1 and then making the scanned versions text-searchable.2 Though a stringent quality assurance process was employed, some imperfections may remain. Please note that this document may contain occasional gaps in the text. These gaps are the result of a redaction process that removed information obtained on a confidential basis. All redacted passages are exempt from disclosure under applicable provisions of the Freedom of Information Act. 1 In some cases, original copies needed to be photocopied before being scanned into electronic format. All scanned images were deskewed (to remove the effects of printer- and scanner-introduced tilting) and lightly cleaned (to remove dark spots caused by staple holes, hole punches, and other blemishes caused after initial printing). 2 A two-step process was used. An advanced optimal character recognition computer program (OCR) first created electronic text from the document image. Where the OCR results were inconclusive, staff checked and corrected the text as necessary. Please note that the numbers and text in charts and tables were not reliably recognized by the OCR process and were not checked or corrected by staff. Confidential (FR) Class III FOMC June 30, 1993 RECENT DEVELOPMENTS Prepared for the Federal Open Market Committee By the staff of the Board of Governors of the Federal Reserve System CONTENTS II DOMESTIC NONFINANCIAL DEVELOPMENTS Employment and unemployment................................. -
ABSTRACT LUCY, ZACHARY MARC. Analysis of Fixed Volume Swaps For
ABSTRACT LUCY, ZACHARY MARC. Analysis of Fixed Volume Swaps for Hedging Financial Risk at Large-Scale Wind Projects (Under the direction of Dr. Jordan Kern). Large scale wind power projects are increasingly selling power directly into wholesale electricity markets without the benefits of stable (fixed price) off-take agreements. As a result, many wind power producers are incentivized to use financial hedging contracts to mitigate exposure to price risk. One particular hedging contract - the “fixed volume price swap” - has gained prevalence, but it poses several liabilities for wind power producers that reduce its effectiveness. In this paper, we explore problems associated with fixed volume swaps and examine two different interventions to improve contract performance for wind power producers. Using a hypothetical wind power project in the Southwest Power Pool (SPP) market as a case study, we first look at how “shape risk” (an imbalance between actual wind power production and hourly production targets specified by contract terms) negatively impacts contract performance and whether this could be remedied through improved contract design. Using a multi-objective optimization algorithm, we find examples of alternative contract parameters (hourly wind power production targets) that are more effective at increasing revenues during low performing months and do so at a lower cost than conventional fixed volume swaps. Then we examine how “basis risk” (a discrepancy in market prices between the “node” where the wind project injects power into the grid, and the regional hub price) can negatively impact contract performance. We statistically manipulate basis risk as a proxy for the effects of increased transmission and its effect on contract performance. -
CAIA Member Contribution Long Term Investors, Tail Risk Hedging, And
CAIA Member Contribution Long Term Investors, Tail Risk Hedging, and the Role of Global Macro in Institutional Andrew Rozanov, CAIA Portfolios Managing Director, Head of Permal Sovereign Advisory 24 Alternative Investment Analyst Review Long Term Investors 1. Introduction This paper focuses on two related topics: the tension between the fundamental premise of long-term investing and the post-crisis pressure to mitigate tail risks; and new approaches to asset allocation and the potential role of global macro strategies in institutional portfolios. To really understand why these issues are increasingly coming to the fore, it is important to recall the sheer magnitude of losses suffered by sovereign wealth funds and other long-term investors at the peak of the recent financial crisis and to appreciate how shocked they were to see large double-digit percentage drops, not only in their own portfolios, but also in portfolios of institutions that many of them were looking to as potential role models, namely the likes of Yale and Harvard university endowments. Losses for many broadly diversified, multi-asset class portfolios ranged anywhere from 20% to 30% in the course of just a few months. In one of the better publicized cases, Norway’s sovereign fund lost more than 23%, or in dollar equivalent more than $96 billion, an amount that at the time constituted their entire accumulated investment returns since inception in 1996. Some of the longer standing sovereign wealth funds in Asia and the Middle East, which had long invested in a wide range of alternative asset classes such as private equity, real estate and hedge funds, are rumoured to have done even worse in that infamous year.