A Guide to Investing in Floating-Rate Securities What You Should Know Before You Buy
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Interest Rate Options
Interest Rate Options Saurav Sen April 2001 Contents 1. Caps and Floors 2 1.1. Defintions . 2 1.2. Plain Vanilla Caps . 2 1.2.1. Caplets . 3 1.2.2. Caps . 4 1.2.3. Bootstrapping the Forward Volatility Curve . 4 1.2.4. Caplet as a Put Option on a Zero-Coupon Bond . 5 1.2.5. Hedging Caps . 6 1.3. Floors . 7 1.3.1. Pricing and Hedging . 7 1.3.2. Put-Call Parity . 7 1.3.3. At-the-money (ATM) Caps and Floors . 7 1.4. Digital Caps . 8 1.4.1. Pricing . 8 1.4.2. Hedging . 8 1.5. Other Exotic Caps and Floors . 9 1.5.1. Knock-In Caps . 9 1.5.2. LIBOR Reset Caps . 9 1.5.3. Auto Caps . 9 1.5.4. Chooser Caps . 9 1.5.5. CMS Caps and Floors . 9 2. Swap Options 10 2.1. Swaps: A Brief Review of Essentials . 10 2.2. Swaptions . 11 2.2.1. Definitions . 11 2.2.2. Payoff Structure . 11 2.2.3. Pricing . 12 2.2.4. Put-Call Parity and Moneyness for Swaptions . 13 2.2.5. Hedging . 13 2.3. Constant Maturity Swaps . 13 2.3.1. Definition . 13 2.3.2. Pricing . 14 1 2.3.3. Approximate CMS Convexity Correction . 14 2.3.4. Pricing (continued) . 15 2.3.5. CMS Summary . 15 2.4. Other Swap Options . 16 2.4.1. LIBOR in Arrears Swaps . 16 2.4.2. Bermudan Swaptions . 16 2.4.3. Hybrid Structures . 17 Appendix: The Black Model 17 A.1. -
Interest Rate and Credit Models 6
Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Interest Rate and Credit Models 6. Convexity and CMS Andrew Lesniewski Baruch College New York Spring 2019 A. Lesniewski Interest Rate and Credit Models Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Outline 1 Convexity in LIBOR 2 CMS rates and instruments 3 The uses of Girsanov’s theorem A. Lesniewski Interest Rate and Credit Models Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Convexity In financial lingo, convexity is a broadly understood and often non-specific term for nonlinear behavior of the price of an instrument as a function of evolving markets. Typically, such convexities reflect the presence of some sort of optionality embedded in the instrument. In this lecture we will focus on a number of convexities which arise in interest rates markets. Convex behavior in interest rate markets manifests itself as the necessity to include convexity corrections to various popular interest rates and they can be blessings and nightmares of market practitioners. From the perspective of financial modeling they arise as the results of valuation done under the “wrong” martingale measure. A. Lesniewski Interest Rate and Credit Models Convexity in LIBOR CMS rates and instruments The uses of Girsanov’s theorem Convexity Throughout this lecture we will be making careful notational distinction between stochastic processes, such as prices of zero coupon bonds, and their current (known) values. The latter will be indicated by the subscript 0. Thus, as in the previous lectures, (i) P0(t; T ) = P(0; t; T ) denotes the current value of the forward discount factor, (ii) P(t; T ) = P(t; t; T ) denotes the time t value of the stochastic process describing the price of the zero coupon bond maturing at T . -
Banca Popolare Dell’Alto Adige Joint-Stock Company
2016 FINANCIAL STATEMENTS 1 Banca Popolare dell’Alto Adige Joint-stock company Registered office and head office: Via del Macello, 55 – I-39100 Bolzano Share Capital as at 31 December 2016: Euro 199,439,716 fully paid up Tax code, VAT number and member of the Business Register of Bolzano no. 00129730214 The bank adheres to the inter-bank deposit protection fund and the national guarantee fund ABI 05856.0 www.bancapopolare.it – www.volksbank.it 2 3 „Wir arbeiten 2017 konzentriert daran, unseren Strategieplan weiter umzusetzen, die Kosten zu senken, die Effizienz und Rentabilität der Bank zu erhöhen und die Digitalisierung voranzutreiben. Auch als AG halten wir an unserem Geschäftsmodell einer tief verankerten Regionalbank in Südtirol und im Nordosten Italiens fest.“ Otmar Michaeler Volksbank-Präsident 4 DIE VOLKSBANK HAT EIN HERAUSFORDERNDES JAHR 2016 HINTER SICH. Wir haben vieles umgesetzt, aber unser hoch gestecktes Renditeziel konnten wir nicht erreichen. Für 2017 haben wir uns vorgenommen, unsere Projekte und Ziele mit noch mehr Ehrgeiz zu verfolgen und die Rentabilität der Bank deutlich zu erhöhen. 2016 wird als das Jahr der Umwandlung in eine Aktien- Beziehungen und wollen auch in Zukunft Kredite für Familien und gesellschaft in die Geschichte der Volksbank eingehen. kleine sowie mittlere Unternehmen im Einzugsgebiet vergeben. Diese vom Gesetzgeber aufgelegte Herausforderung haben Unser vorrangiges Ziel ist es, beste Lösungen für unsere die Mitglieder im Rahmen der Mitgliederversammlung im gegenwärtig fast 60.000 Mitglieder und über 260.000 Kunden November mit einer überwältigenden Mehrheit von 97,5 Prozent zu finden. angenommen. Gleichzeitig haben wir die Weichen gestellt, um All dies wird uns in die Lage versetzen, in Zukunft wieder auch als AG eine erfolgreiche und tief verankerte Regionalbank Dividenden auszuschütten. -
Fedwire Securities Service
Federal Reserve Banks Fedwire Securities Service Issuer Guide V1.1 Last Updated - August 2021 Fedwire is a registered service mark of the Federal Reserve Banks 1 African Development Bank 6 Avenue Joseph Anoma, Plateau http://www.afdb.org/ 01 BP 1387 [email protected] Abidjan 01 (225) 20.20.44.44 Côte d‘Ivoire The African Development Bank (AFDB) is a multilateral development bank established in 1963 to encourage sustainable economic growth and reduce poverty in Africa. Regional members include any African country that has the status of an independent state. Non- regional countries that are participants in, or contributing to, the African Development Fund, a separate legal entity administered by the African Development Bank to provide loan financing to regional member countries, may be admitted as non-regional member countries. The United States became a non-regional member of the African Development Bank in 1983 pursuant to the African Development Bank Act. Class Product Interest Minimum Multiple Record Date Payment Date Corresponding Code Description Payment Clearing Memo AFDB Bond Semi-annually $1,000 $1,000 Varies Varies 250 AFNT Note Semi-annually $100,000 $1,000 TBD TBD 250 2 Asian Development Bank 815 Connecticut Street, NW http://www.adb.org/ Washington, DC 20006 (202) 728-1500 The Asian Development Bank (ADB) is a multilateral development bank established in 1966 to promote economic growth, environmentally sustainable growth, and regional integration to reduce poverty in Asia and the Pacific region. The Asian Development Bank is owned by its 67 members, including regional and non-regional members. The United States became a member in 1966. -
Derivative Instruments and Hedging Activities
www.pwc.com 2015 Derivative instruments and hedging activities www.pwc.com Derivative instruments and hedging activities 2013 Second edition, July 2015 Copyright © 2013-2015 PricewaterhouseCoopers LLP, a Delaware limited liability partnership. All rights reserved. PwC refers to the United States member firm, and may sometimes refer to the PwC network. Each member firm is a separate legal entity. Please see www.pwc.com/structure for further details. This publication has been prepared for general information on matters of interest only, and does not constitute professional advice on facts and circumstances specific to any person or entity. You should not act upon the information contained in this publication without obtaining specific professional advice. No representation or warranty (express or implied) is given as to the accuracy or completeness of the information contained in this publication. The information contained in this material was not intended or written to be used, and cannot be used, for purposes of avoiding penalties or sanctions imposed by any government or other regulatory body. PricewaterhouseCoopers LLP, its members, employees and agents shall not be responsible for any loss sustained by any person or entity who relies on this publication. The content of this publication is based on information available as of March 31, 2013. Accordingly, certain aspects of this publication may be superseded as new guidance or interpretations emerge. Financial statement preparers and other users of this publication are therefore cautioned to stay abreast of and carefully evaluate subsequent authoritative and interpretative guidance that is issued. This publication has been updated to reflect new and updated authoritative and interpretative guidance since the 2012 edition. -
Glossary of Bond Terms
Glossary of Bond Terms Accreted value- The current value of your zero-coupon municipal bond, taking into account interest that has been accumulating and automatically reinvested in the bond. Accrual bond- Often the last tranche in a CMO, the accrual bond or Z-tranche receives no cash payments for an extended period of time until the previous tranches are retired. While the other tranches are outstanding, the Z-tranche receives credit for periodic interest payments that increase its face value but are not paid out. When the other tranches are retired, the Z-tranche begins to receive cash payments that include both principal and continuing interest. Accrued interest- (1) The dollar amount of interest accrued on an issue, based on the stated interest rate on that issue, from its date to the date of delivery to the original purchaser. This is usually paid by the original purchaser to the issuer as part of the purchase price of the issue; (2) Interest deemed to be earned on a security but not yet paid to the investor. Active tranche- A CMO tranche that is currently paying principal payments to investors. Adjustable-rate mortgage (ARM)- A mortgage loan on which interest rates are adjusted at regular intervals according to predetermined criteria. An ARM's interest rate is tied to an objective, published interest rate index. Amortization- Liquidation of a debt through installment payments. Arbitrage- In the municipal market, the difference in interest earned on funds borrowed at a lower tax-exempt rate and interest on funds that are invested at a higher-yielding taxable rate. -
Pricing Models for Bermudan-Style Interest Rate Derivatives and Options
Erim - 05 omslag Pietersz 9/23/05 1:41 PM Pagina 1 Design: B&T Ontwerp en advies www.b-en-t.nl Print: Haveka www.haveka.nl Pricing models for Bermudan-style interest rate 71 RAOUL PIETERSZ derivatives Bermudan-style interest rate derivatives are an important class of RAOUL PIETERSZ options. Many banking and insurance products, such as mortgages, cancellable bonds, and life insurance products, contain Bermudan interest rate options associated with early redemption or cancella- tion of the contract. The abundance of these options makes evident Pricing models for that their proper valuation and risk measurement are important to banks and insurance companies. Risk measurement allows for off- Bermudan-style setting market risk by hedging with underlying liquidly traded assets rate derivatives Pricing models for Bermudan-style interest and options. Pricing models must be arbitrage-free, and consistent with (calibrated to) prices of actively traded underlying options. interest rate derivatives Model dynamics need be consistent with the observed dynamics of the term structure of interest rates, e.g., correlation between inte- rest rates. Moreover, valuation algorithms need be efficient: Finan- cial decisions based on derivatives pricing calculations often need to be made in seconds, rather than hours or days. In recent years, a successful class of models has appeared in the literature known as market models. This thesis extends the theory of market models, in the following ways: (i) it introduces a new, efficient, and more accurate approximate pricing technique, (ii) it presents two new and fast algorithms for correlation-calibration, (iii) it develops new models that enable efficient calibration for a whole new range of deriva- tives, such as fixed-maturity Bermudan swaptions, and (iv) it presents novel empirical comparisons of the performance of existing calibra- tion techniques and models, in terms of reduction of risk. -
Exotic Interest-Rate Options
Exotic interest-rate options Marco Marchioro www.marchioro.org November 10th, 2012 Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 1 Lecture Summary • Exotic caps, floors, and swaptions • Swaps with exotic floating-rate legs • No-arbitrage methods (commodity example) • Numeraires and pricing formulas • stochastic differential equations (SDEs) • Partial differential equations (PDEs) • Feynman-Kac formula • Numerical methods: analytical approximations Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 2 Common exotic interest-rate options There are all sorts of exotic interest-rate options. The least exotic, i.e. commonly traded, types are • Caps and floors with a digital payoff • Caps and floors with barriers • Bermuda and American Swaptions Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 3 Caps and floors with a digital payoff A vanilla Cap has caplets with payoff Payoff CapletV = NT (6m; 9m) max [(3m-Libor − K); 0] (1) A digital Cap has caplets with payoff 8 > NT (6m; 9m) R for 3m-Libor ≥ K Payoff < CapletD = (2) :> 0 for 3m-Libor < K Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 4 Advanced Derivatives, Interest Rate Models 2010{2012 c Marco Marchioro Exotic interest-rate options 5 Caps and floors with barriers A barrier Cap has caplets with payoff Payoff CapletV = NT (6m; 9m) max [(3m-Libor − K); 0] (3) • Knock-in: paid if 3m-Libor touches a barrier rknock-in • Knock-out: paid if 3m-Libor does not reach rknock-out Discrete barriers are checked at certain given barrier dates Continuous barriers are checked on each daily Libor fixing Digital payoffs are also available. -
Floating Rate Note Examplary Underlying: Underlying Rate
Floating Rate Note Examplary Underlying: Underlying rate In general, Floating Rate Notes (FRN) offer you floating coupon payments based on an underlying interest rate and a redemption at 100% of the nominal value on the redemption date (subject to the credit risk of the issuer). The floating coupon is subject to a minimum coupon (floor). The payout profile is for illustrative purposes only and is based on the assumption that no exceptional cancellation will occur, in accordance with the issuer’s product documentation. Main features of a sample product Currency Term Return USD 3 years Underlying rate, minimum 2.90% p.a. Participation Capital no additional participation Floor at 100% (subject to issuer risk) You may consider an investment in this product, if You look for a way to enhance yield on your cash positions You are familiar with both structured products and fixed income markets You are comfortable being exposed to floating coupon payments based on an underlying interest rate You intend to be invested in this product until its redemption date You wish to be invested in the investment currency of the product. If your reference currency is not equal to the investment currency of the product, the return may increase or decrease in reference currency terms as a result of exchange rate fluctuations Summary of main product- Summary of main product- specific benefits specific risks Quarterly adjustment of the coupon Decreasing underlying rate resulting in lower Floor offering a minimum coupon payment coupon payments (but not below the floor) Full capital protection on the redemption date If the currency of the product is different from your reference currency, the return may increase or decrease as a result of currency fluctuations You are fully exposed to the default risk of the issuer. -
Convexity Adjustment for Constant Maturity Swaps and Libor-In-Arrears Basis Swaps12
TMG Financial Products Inc. 475 Steamboat Road Greenwich, CT 06830 Thomas S. Coleman 15 November 1995 VP, Risk Management, 203-861-8993 revised 30 August 1996 CONVEXITY ADJUSTMENT FOR CONSTANT MATURITY SWAPS AND LIBOR-IN-ARREARS BASIS SWAPS12 INTRODUCTION The Constant Maturity Swap or Treasury (CMS or CMT) market is large and active. The difficulty of evaluating the implicit convexity cost, however, makes the markets more opaque than would otherwise be the case. This note lays out a practical method for calculating the value of the convexity adjustment for the linear CMS/CMT and LIBOR-in-arrears payments. Both CMT/CMS and LIBOR-in-arrears swaps share the characteristic that the payment on one side of the swap is linear with respect to its index while the offsetting hedge is convex. The linearity of the payment (relative to the convex hedges) imposes a cost that leads to the "convexity adjustment" made to the linear payment. The basis of the approach used here is to 1. Find for each reset date the equivalent martingale measure (forward measure using a zero bond as numeraire) which makes the PV of a traded swap equal to its market value. In practical terms, this reduces to finding the "adjusted mean" of the rate distribution as of the reset date. For log-normally distributed rates, there are approximations which make this fast. 2. The same forward measure is then used to calculate the PV of the CMS/CMT swap or the LIBOR-in-arrears payment (which is not actively traded). This PV incorporates the convexity cost of the linear payment relative to its (traded) convex hedge. -
The Efficient Pricing of CMS and CMS Spread Derivatives
Delft University of Technology Faculty of Electrical Engineering, Mathematics and Computer Science Delft Institute of Applied Mathematics The efficient pricing of CMS and CMS spread derivatives A thesis submitted to the Delft Institute of Applied Mathematics in partial fulfillment of the requirements for the degree MASTER OF SCIENCE in APPLIED MATHEMATICS by Sebastiaan Louis Cornelis Borst Delft, the Netherlands September 2014 Copyright c 2014 by Sebastiaan Borst. All rights reserved. MSc THESIS APPLIED MATHEMATICS \The efficient pricing of CMS and CMS spread derivatives" Sebastiaan Louis Cornelis Borst Delft University of Technology Daily supervisor Responsible professor Dr. N. Borovykh Prof. dr. ir. C.W. Oosterlee Other thesis committee members Dr. P. Cirillo September 2014 Delft, the Netherlands Abstract Two popular products on the interest rate market are Constant Maturity Swap (CMS) deriva- tives and CMS spread derivatives. This thesis focusses on the efficient pricing of CMS and CMS spread derivatives, in particular the pricing of CMS and CMS spread options. The notional values for these products are usually quite large, so even small errors when pricing these products can lead to substantial losses. Therefore, the pricing of these products has to be accurate. It is possible to use sophisticated models (e.g. Libor Market Model) to price these products, however the downside is that these models generally have high computational costs; they are not very efficient. To efficiently price CMS options the Terminal Swap Rate (TSR) approach can be used. From this approach TSR models are obtained, we will consider four different TSR models. Two of these TSR models are established in the literature, the other two TSR models are developed in this thesis. -
TREASURY FLOATING RATE NOTE TERM SHEET I. ISSUER United States Treasury II. DATED DATE Last Calendar Day of a Month. III. ISSUE
TREASURY FLOATING RATE NOTE TERM SHEET I. ISSUER United States Treasury II. DATED DATE Last calendar day of a month. III. ISSUE DATE Original issue offerings will be issued on the last calendar day of a month, or the first business day thereafter. Reopening offerings will be issued on the last Friday of a month, or the first business day thereafter. IV. MATURITY DATE Last calendar day of the month two years after the Dated Date. V. MATURITY PAYMENT Principal will be paid on the Maturity Date, or the first business day thereafter. VI. INTEREST DATES Quarterly from the Dated Date, to and including the Maturity Date, on the last calendar day of a month. VII. INTEREST PAYMENTS Interest will be paid on each Interest Date, or the first business day thereafter. VIII. INTEREST: A. ACCRUAL PERIOD From and including, the Dated Date or last Interest Payment date to, but excluding the next Interest Payment date or Maturity Date. B. INTEREST ACCRUAL In general, the interest accrual for a particular calendar day in an Accrual Period shall be the Index Rate computed from the most recent auction of 13-week Treasury bills that took place on a day before the accrual day, plus the Spread, divided by 360, subject to a minimum of zero. However, a 13-week Treasury bill auction whose rate becomes effective in the two business day Lock-Out Period prior to an FRN Issue Date or FRN Interest Date shall be ignored for purposes of calculating the interest accrual on that FRN for that day. Instead, the rate in effect for the Lock-Out Period will be from the most recent 13-week Treasury bill auction result that occurred prior to the start of the Lock-Out Period.