Introduction Section 4000.1
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V. Black-Scholes Model: Derivation and Solution
V. Black-Scholes model: Derivation and solution Beáta Stehlíková Financial derivatives, winter term 2014/2015 Faculty of Mathematics, Physics and Informatics Comenius University, Bratislava V. Black-Scholes model: Derivation and solution – p.1/36 Content Black-Scholes model: • Suppose that stock price follows a geometric ◦ S Brownian motion dS = µSdt + σSdw + other assumptions (in a moment) We derive a partial differential equation for the price of ◦ a derivative Two ways of derivations: • due to Black and Scholes ◦ due to Merton ◦ Explicit solution for European call and put options • V. Black-Scholes model: Derivation and solution – p.2/36 Assumptions Further assumptions (besides GBP): • constant riskless interest rate ◦ r no transaction costs ◦ it is possible to buy/sell any (also fractional) number of ◦ stocks; similarly with the cash no restrictions on short selling ◦ option is of European type ◦ Firstly, let us consider the case of a non-dividend paying • stock V. Black-Scholes model: Derivation and solution – p.3/36 Derivation I. - due to Black and Scholes Notation: • S = stock price, t =time V = V (S, t)= option price Portfolio: 1 option, stocks • δ P = value of the portfolio: P = V + δS Change in the portfolio value: • dP = dV + δdS From the assumptions: From the It¯o • dS = µSdt + σSdw, ∂V ∂V 1 2 2 ∂2V ∂V lemma: dV = ∂t + µS ∂S + 2 σ S ∂S2 dt + σS ∂S dw Therefore: • ∂V ∂V 1 ∂2V dP = + µS + σ2S2 + δµS dt ∂t ∂S 2 ∂S2 ∂V + σS + δσS dw ∂S V. Black-Scholes model: Derivation and solution – p.4/36 Derivation I. -
The TIPS-Treasury Bond Puzzle
The TIPS-Treasury Bond Puzzle Matthias Fleckenstein, Francis A. Longstaff and Hanno Lustig The Journal of Finance, October 2014 Presented By: Rafael A. Porsani The TIPS-Treasury Bond Puzzle 1 / 55 Introduction The TIPS-Treasury Bond Puzzle 2 / 55 Introduction (1) Treasury bond and the Treasury Inflation-Protected Securities (TIPS) markets: two of the largest and most actively traded fixed-income markets in the world. Find that there is persistent mispricing on a massive scale across them. Treasury bonds are consistently overpriced relative to TIPS. Price of a Treasury bond can exceed that of an inflation-swapped TIPS issue exactly matching the cash flows of the Treasury bond by more than $20 per $100 notional amount. One of the largest examples of arbitrage ever documented. The TIPS-Treasury Bond Puzzle 3 / 55 Introduction (2) Use TIPS plus inflation swaps to create synthetic Treasury bond. Price differences between the synthetic Treasury bond and the nominal Treasury bond: arbitrage opportunities. Average size of the mispricing: 54.5 basis points, but can exceed 200 basis points for some pairs. I The average size of this mispricing is orders of magnitude larger than transaction costs. The TIPS-Treasury Bond Puzzle 4 / 55 Introduction (3) What drives the mispricing? Slow-moving capital may help explain why mispricing persists. Is TIPS-Treasury mispricing related to changes in capital available to hedge funds? Answer: Yes. Mispricing gets smaller as more capital gets to the hedge fund sector. The TIPS-Treasury Bond Puzzle 5 / 55 Introduction (4) Also find that: Correlation in arbitrage strategies: size of TIPS-Treasury arbitrage is correlated with arbitrage mispricing in other markets. -
How Much Do Banks Use Credit Derivatives to Reduce Risk?
How much do banks use credit derivatives to reduce risk? Bernadette A. Minton, René Stulz, and Rohan Williamson* June 2006 This paper examines the use of credit derivatives by US bank holding companies from 1999 to 2003 with assets in excess of one billion dollars. Using the Federal Reserve Bank of Chicago Bank Holding Company Database, we find that in 2003 only 19 large banks out of 345 use credit derivatives. Though few banks use credit derivatives, the assets of these banks represent on average two thirds of the assets of bank holding companies with assets in excess of $1 billion. To the extent that banks have positions in credit derivatives, they tend to be used more for dealer activities than for hedging activities. Nevertheless, a majority of the banks that use credit derivative are net buyers of credit protection. Banks are more likely to be net protection buyers if they engage in asset securitization, originate foreign loans, and have lower capital ratios. The likelihood of a bank being a net protection buyer is positively related to the percentage of commercial and industrial loans in a bank’s loan portfolio and negatively or not related to other types of bank loans. The use of credit derivatives by banks is limited because adverse selection and moral hazard problems make the market for credit derivatives illiquid for the typical credit exposures of banks. *Respectively, Associate Professor, The Ohio State University; Everett D. Reese Chair of Banking and Monetary Economics, The Ohio State University and NBER; and Associate Professor, Georgetown University. We are grateful to Jim O’Brien and Mark Carey for discussions. -
The Synthetic Collateralised Debt Obligation: Analysing the Super-Senior Swap Element
The Synthetic Collateralised Debt Obligation: analysing the Super-Senior Swap element Nicoletta Baldini * July 2003 Basic Facts In a typical cash flow securitization a SPV (Special Purpose Vehicle) transfers interest income and principal repayments from a portfolio of risky assets, the so called asset pool, to a prioritized set of tranches. The level of credit exposure of every single tranche depends upon its level of subordination: so, the junior tranche will be the first to bear the effect of a credit deterioration of the asset pool, and senior tranches the last. The asset pool can be made up by either any type of debt instrument, mainly bonds or bank loans, or Credit Default Swaps (CDS) in which the SPV sells protection1. When the asset pool is made up solely of CDS contracts we talk of ‘synthetic’ Collateralized Debt Obligations (CDOs); in the so called ‘semi-synthetic’ CDOs, instead, the asset pool is made up by both debt instruments and CDS contracts. The tranches backed by the asset pool can be funded or not, depending upon the fact that the final investor purchases a true debt instrument (note) or a mere synthetic credit exposure. Generally, when the asset pool is constituted by debt instruments, the SPV issues notes (usually divided in more tranches) which are sold to the final investor; in synthetic CDOs, instead, tranches are represented by basket CDSs with which the final investor sells protection to the SPV. In any case all the tranches can be interpreted as percentile basket credit derivatives and their degree of subordination determines the percentiles of the asset pool loss distribution concerning them It is not unusual to find both funded and unfunded tranches within the same securitisation: this is the case for synthetic CDOs (but the same could occur with semi-synthetic CDOs) in which notes are issued and the raised cash is invested in risk free bonds that serve as collateral. -
Understanding the Z-Spread Moorad Choudhry*
Learning Curve September 2005 Understanding the Z-Spread Moorad Choudhry* © YieldCurve.com 2005 A key measure of relative value of a corporate bond is its swap spread. This is the basis point spread over the interest-rate swap curve, and is a measure of the credit risk of the bond. In its simplest form, the swap spread can be measured as the difference between the yield-to-maturity of the bond and the interest rate given by a straight-line interpolation of the swap curve. In practice traders use the asset-swap spread and the Z- spread as the main measures of relative value. The government bond spread is also considered. We consider the two main spread measures in this paper. Asset-swap spread An asset swap is a package that combines an interest-rate swap with a cash bond, the effect of the combined package being to transform the interest-rate basis of the bond. Typically, a fixed-rate bond will be combined with an interest-rate swap in which the bond holder pays fixed coupon and received floating coupon. The floating-coupon will be a spread over Libor (see Choudhry et al 2001). This spread is the asset-swap spread and is a function of the credit risk of the bond over and above interbank credit risk.1 Asset swaps may be transacted at par or at the bond’s market price, usually par. This means that the asset swap value is made up of the difference between the bond’s market price and par, as well as the difference between the bond coupon and the swap fixed rate. -
Economic Quarterly
Forecasting the Effects of Reduced Defense Spending Peter Irel’and and Chtitopher Omk ’ I. INTRODUCTION $1 cut in defense spending acts to decrease the total demand for goods and services in each period by $1. The end of the Cold War provides the United Of course, so long as the government has access to States with an opportunity to cut its defense the same production technologies that are available spending significantly. Indeed, the Bush Administra- to the private sector, this prediction of the tion’s 1992-1997 Future Years Defense Program neoclassical model does not change if instead the (presented in 1991 and therefore referred to as the government produces the defense services itself.’ “1991 plan”) calls for a 20 percent reduction in real defense spending by 1997. Although expenditures A permanent $1 cut in defense spending also related to Operation Desert Storm have delayed the reduces the government’s need for tax revenue; it implementation of the 199 1 plan, policymakers con- implies that taxes can be cut by $1 in each period. tinue to call for defense cutbacks. In fact, since Bush’s Households, therefore, are wealthier following the plan was drafted prior to the collapse of the Soviet cut in defense spending; their permanent income in- Union, it seems likely that the Clinton Administra- creases by $b1. According to the permanent income tion will propose cuts in defense spending that are hypothesis, this $1 increase in permanent income even deeper than those specified by the 1991 plan. induces households to increase their consumption by This paper draws on both theoretical and empirical $1 in every period, provided that their labor supply economic models to forecast the effects that these does not change. -
Computation of Binomial Option Pricing Model with Parallel
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by KHALSA PUBLICATIONS I S S N 2 2 7 8 - 5 6 1 2 Volume 11 Number 5 International Journal of Management and Information T e c h n o l o g y Computation Of Binomial Option Pricing Model With Parallel Processing On A Linux Cluster Harya Widiputra Faculty of Information Technology, Perbanas Institute Jakarta, Indonesia [email protected] ABSTRACT Binary Option Pricing Model (BOPM) is one approach that can be utilized to calculate the value of either call or put option. BOPM generally works by building a binomial tree diagram, also known as lattice diagram to explore all possible option values that occur based on the intrinsic price of the underlying asset in a range of specific time period. Due to its basic characteristics BOPM is renowned for its longer lead times in calculating option values while also acknowledged as a technique that can provide an assessment of the most fair option value. Therefore, this study aims to shorten the BOPM completion time of calculating the value of an option by building a computer cluster and presently implement the BOPM algorithm into a form that can be run in parallel processing. As an outcome, a Linux-based computer cluster has been built and conversion of BOPM algorithm so that it can be executed in parallel has been performed and also implemented using Python in this research. Conclusively, results of conducted experiments confirm that the implementation of BOPM algorithm in a form that can be executed in parallel and its application on a computer cluster was able to limit the growth of the completion time whilst at the same time maintain quality of calculated option values. -
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. -
Corporate Bonds and Debentures
Corporate Bonds and Debentures FCS Vinita Nair Vinod Kothari Company Kolkata: New Delhi: Mumbai: 1006-1009, Krishna A-467, First Floor, 403-406, Shreyas Chambers 224 AJC Bose Road Defence Colony, 175, D N Road, Fort Kolkata – 700 017 New Delhi-110024 Mumbai Phone: 033 2281 3742/7715 Phone: 011 41315340 Phone: 022 2261 4021/ 6237 0959 Email: [email protected] Email: [email protected] Email: [email protected] Website: www.vinodkothari.com 1 Copyright & Disclaimer . This presentation is only for academic purposes; this is not intended to be a professional advice or opinion. Anyone relying on this does so at one’s own discretion. Please do consult your professional consultant for any matter covered by this presentation. The contents of the presentation are intended solely for the use of the client to whom the same is marked by us. No circulation, publication, or unauthorised use of the presentation in any form is allowed, except with our prior written permission. No part of this presentation is intended to be solicitation of professional assignment. 2 About Us Vinod Kothari and Company, company secretaries, is a firm with over 30 years of vintage Based out of Kolkata, New Delhi & Mumbai We are a team of qualified company secretaries, chartered accountants, lawyers and managers. Our Organization’s Credo: Focus on capabilities; opportunities follow 3 Law & Practice relating to Corporate Bonds & Debentures 4 The book can be ordered by clicking here Outline . Introduction to Debentures . State of Indian Bond Market . Comparison of debentures with other forms of borrowings/securities . Types of Debentures . Modes of Issuance & Regulatory Framework . -
Opposition, CFTC V. Banc De Binary
Case 2:13-cv-00992-MMD-VCF Document 37 Filed 08/08/13 Page 1 of 30 Kathleen Banar, Chief Trial Attorney (IL Bar No. 6200597) David Slovick, Senior Trial Attorney (IL Bar No. 6257290) Margaret Aisenbrey, Trial Attorney (Mo Bar No. 59560) U.S. Commodity Futures Trading Commission 1155 21 St. NW Washington, DC 20581 [email protected], [email protected], [email protected] (202) 418-5335 (202) 418-5987 (facsimile) Blaine T. Welsh (NV Bar No. 4790) Assistant United States Attorney United States Attorney’s Office 333 Las Vegas Boulevard, Suite 5000 Las Vegas, Nevada 89101 [email protected] (702) 388-6336 (702) 388-6787 (facsimile) UNITED STATES DISTRICT COURT DISTRICT OF NEVADA ) U.S. COMMODITY FUTURES TRADING ) COMMISSION, ) ) Case No. 2:13-cv-00992-MMD-VCF Plaintiff, ) ) PLAINTIFF’S OPPOSITION TO v. ) DEFENDANT’S MOTION TO ) DISMISS COUNTS ONE, THREE ) AND FOUR OF THE COMPLAINT BANC DE BINARY LTD. (A/K/A E.T. ) BINARY OPTIONS LTD.), ) ) Defendant. ) ) 1 Case 2:13-cv-00992-MMD-VCF Document 37 Filed 08/08/13 Page 2 of 30 The United States Commodity Futures Trading Commission (“CFTC” or “Commission”) opposes Banc de Binary’s Motion to Dismiss Counts I, III and IV of the Complaint (“Defendant’s Motion”),1 and states as follows: I. SUMMARY Since at least May 2012 Banc de Binary Ltd. (A/K/A E.T. Binary Options) (“Banc de Binary” or “Defendant”) has been violating the CFTC’s long-standing ban on trading options contracts with persons located in the United States off of a contract market designated by the CFTC for that purpose (i.e., “off-exchange”). -
Macroeconomic and Foreign Exchange Policies of Major Trading Partners of the United States
REPORT TO CONGRESS Macroeconomic and Foreign Exchange Policies of Major Trading Partners of the United States U.S. DEPARTMENT OF THE TREASURY OFFICE OF INTERNATIONAL AFFAIRS December 2020 Contents EXECUTIVE SUMMARY ......................................................................................................................... 1 SECTION 1: GLOBAL ECONOMIC AND EXTERNAL DEVELOPMENTS ................................... 12 U.S. ECONOMIC TRENDS .................................................................................................................................... 12 ECONOMIC DEVELOPMENTS IN SELECTED MAJOR TRADING PARTNERS ...................................................... 24 ENHANCED ANALYSIS UNDER THE 2015 ACT ................................................................................................ 48 SECTION 2: INTENSIFIED EVALUATION OF MAJOR TRADING PARTNERS ....................... 63 KEY CRITERIA ..................................................................................................................................................... 63 SUMMARY OF FINDINGS ..................................................................................................................................... 67 GLOSSARY OF KEY TERMS IN THE REPORT ............................................................................... 69 This Report reviews developments in international economic and exchange rate policies and is submitted pursuant to the Omnibus Trade and Competitiveness Act of 1988, 22 U.S.C. § 5305, and Section -
Not for Reproduction Not for Reproduction
Structured Products Europe Awards 2011 to 10% for GuardInvest against 39% for a direct Euro Stoxx 50 investment. “The problem is so many people took volatility as a hedging vehicle over There was also €67.21 million invested in the Theam Harewood Euro time that the price of volatility has gone up, and everybody has suffered Long Dividends Funds by professional investors. Spying the relationship losses of 20%, 30%, 40% on the cost of carry,” says Pacini. “When volatility between dividends and inflation – that finds companies traditionally spiked, people sold quickly, preventing volatility from going up on a paying them in line with inflation – and given that dividends are mark-to-market basis.” House of the year negatively correlated with bonds, the bank’s fund recorded an The bank’s expertise in implied volatility combined with its skills in annualised return of 18.98% by August 31, 2011, against the 1.92% on structured products has allowed it to mix its core long forward variance offer from a more volatile investment in the Euro Stoxx 50. position with a short forward volatility position. The resulting product is BNP Paribas The fund systematically invests in dividend swaps of differing net long volatility and convexity, which protects investors from tail maturities on the European benchmark; the swaps are renewed on their events. The use of variance is a hedge against downside risks and respective maturities. There is an override that reduces exposure to the optimises investment and tail-risk protection. > BNP Paribas was prepared for the worst and liabilities, while providing an attractive yield.