Tuesday, January 7, 2020

Measuring, Modeling, Managing and Optimizing Interest Rate and Credit Risks - Free Essay Example

Sample details Pages: 18 Words: 5444 Downloads: 2 Date added: 2017/06/26 Category Finance Essay Type Research paper Did you like this example? The credit crisis, stock market down turn, and economic slowdown have resulted in a flightto-quality that has pushed credit spreads to historic highs; interest rates have fallen steeply both in the short segment of the curve, where central banks have aggressively decreased prime rates, and in the long segment with long terms sovereign bond prices being pushed up by increased demands from pensions funds and other institutional investors, Low rates and high spread offer investors extremely interesting opportunities. but they also pose serious challenges in terms of optimal passive and active contact to interest rate and credit risks. Credit spread are expected to narrow again, although it is highly in doubt when and how this contraction will take place. Don’t waste time! Our writers will create an original "Measuring, Modeling, Managing and Optimizing Interest Rate and Credit Risks" essay for you Create order The economic stimulus junk mail being pushed through in the major economies will lead to massive issues of sovereign bonds and eventually to increases in interest rates. At the same time while the current credit crunch and economic slowdown have eased the recent inflation scare the fundamental scarcity of natural resources and political pressure on central banks to relax inflation targets mean that for the medium to Long term fears of inflation are still justifiedÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¦ In this new environment where fixedincome products have come back centre stage there is a clear and pressing need for investors and assets managers to better understand the refined techniques that can be used to optimize investment in fixedincome products and manage the associated risks. In this chapter is planned to equip participant with the state of the art techniques to arange interest rate and credit risks to seize current opportunities in the fixed income market, and to hedge the ris ks associated with an instable credit and interest rate setting This chapter provides participants with advanced techniques to: Measure the impact of changes in interest rates and credit spreads on fixed income portfolios Model changes in interest rates and credit spreads Get around away the impact of such changes from both asset management and asset liability management standpoint,. Optimize the exposure of bonds portfolios to these changes in the context of fixed income portfolio construction Apply active strategies to benefit from expected changes in the interest rate and credit environments Interest Rate Risk Modeling I will first review empirical facts regarding the multidimensional nature of interest rate risks and present the main economic theories of the term structure of interest rates. He will then introduce competing methodologies for yield curve estimation. Finally, he will present stochastic models of term structure dynamics which make it possibl e to generate estimates for the distribution of asset and liability returns as a function of interest rate uncertainty, Measuring Interest Rate Risks:- ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Terms arrangement of interest rates empirical properties and classic theories ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Dynamics of the term structure stylized facts and theories ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Estimating the term structure direct versus indirect methods, Modeling Interest Rate Risks ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Single and multi factor models of interest rates and bond returns ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Factor models for inflation rate uncertainty and liability returns ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Model calibration empirical issues, Fixed-Income Strategies in the New Environment In fixed income strategies I will first introduce a variety of directional and relative value market timing strategies, and present arbitrage and quasi-arbitrage opportunities related to bonds, futures, and inflation-linked bonds. He will then discuss standard structured products and strategy linked notes offering exposure to proprietary benchmarks and algorithmic trading strategies. He will conclude with a review of recent market trends and an examination of current trade opportunities in a relative value framework, Semi Hedged Market Timing Strategies ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Carry and roll down strategies ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Butterfly strategies construction approaches {50/50, principal component Analysis and minimum variance} and optimization, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Conditional curve trades how to optimize the return or risk profile ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Cross market trades ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Volatility t rades gamma and Vega products Arbitrages and Quasi Arbitrage Opportunities ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Bonds versus strip arbitrage ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Cash carry arbitrage ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Asset swaps and inflation linked versus nominal bonds arbitrage, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Rich cheap analysis of bonds Structured Products and Strategy Linked Notes ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Standard structured products range accrual multi callable snow ball, spread options., ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Structured products with strategies as underlying general properties method of construction, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Examples of strategies Trade Opportunities in the New Situation ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Recent market trends, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Relative value approach in volatility matrix government or swap spreads And credit curves, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Trad e opportunities, Interest Rate Risk Management and Portfolio Construction In interest rate risk management and portfolio construction I will first present an in-depth overview of the modern techniques for managing interest rate risk either through dynamic adjustments of the factor exposure or through investment in interest rate derivatives, He will then introduce advanced techniques for estimating risk and return parameters for bond portfolio construction. Finally he will discuss the application of dynamic risk controlled strategies to fixedincome investment and show how to implement optimal substitution of treasury securities with corporate bonds to benefit from the upside potential of credit sensitive asset while hedging some of their risks,,, Interest Rate Risk prevarication from the Assets Management and ALM Perspectives ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Dynamic interest rate risk hedging duration and beyond,, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Static interests rate risk hedging futures swaps swaptions caps floors, asset swaps,, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Hedging bond portfolios asset management and ALM perspectives,, Dynamic Replacement of Credit and Interest Rate Risks:- ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Starting static to dynamic risk managemen123665 ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Energetic core satellites strategies in a fixed income environment, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Optimal substitution of independent bonds for corporate bonds, Credit Investing The market products In Credits investing I will first review the size and structure of the credit market setting out the main players, the products and the sources of credit risk. He will then detail the mechanics of the main credit products, from fixed- and floating rate bonds to credit default swaps and CDS indices, He will conclude with a discussion of products that allow investors to express a view on the macro credit environment and its volatility, and with a review of credit-based structured products,, The Credit Markets ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ An over view of the credit markets size structure players and asset types 45698 ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Rating agencies role rating methodologies, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ The role of credit derivatives now looking forward, Cash based Credit Instruments ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Fixed and floating rate bonds credit risk spread measures and interest rate risk ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ The asset swaps mechanics uses and risks The Credit Default Swaps ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Complete analysis of the CDS contracts, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ The CDS cash basis definition and behavior ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ The standard valuation model for a CDS contract ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Forward CDS digital CDS loan CDS and options on CDS, The CDS index ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Detailed mechanics of the standard CDS index contract, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Price quotation convention and CDS index valuation, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Defining and explaining the CDS index skew /.,/,/ Advanced Index Products ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Credit index options expressing a view on macro credit volatility ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Index tranches expressing a leveraged view on systemic credit risk, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Credit based C.P.P.I and C.P.D.Os, Credit Risk Model The session will focus on models used in the credit markets to assess corporate credit risk and to price and risk manages products and portfolios. I will search and introduce the Merton model and show how its extensions can assist in the evaluation of corporate risk, He will then discuss a popular pricing model used to detect arbitrage opportunities amongst credit products. He will follow with a discussion of the modeling of the risk of credit portfolios, the pros and cons of standard models will be reviewed; the pitfalls of using VaR as a credit risk measure will be exposed and an alternative proposed. He will conclude on risk return optimization for credit p ortfolios, Models Used in Credit Investing ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Structural models and their applications to debt equity arbitrage risk management and rating estimation ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Reduced form intensity models and their application to the pricing of credit risky pay offs, Portfolio Credit Risk Managements ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ identify the risks in a credit portfolio interest rate risk spread instability and correlation recovery rate uncertainty and default co rrelation ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ The Gaussian copula model for portfolio credit theory and implementation, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ The Credit Metrics and KMV portfolio models, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Beyond copula models fully dynamic approaches, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Risk measures for portfolio credit the problems with VaR, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Risk return optimizations for portfolio credit using cohere nt risk measures, CREDIT Trading Strategies The session will join the product and modelling knowledge gained to discuss a number of credit trading strategies. The Dominic O-Kane will first look at standard credit curve trades which can be implemented using cash or CDS. He will explain the characteristics of the CDS cash basis and the technicalities of trading this basis, He will then go over the analysis and risk of debt equity trading strategies and conclude with an analysis of index based strategies that make it possible to trade particular versus systemic credit, Bond Strategies ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Standard curve trades level slopes and twist with default risk, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Relative value in the capital structure senior versus subordinated claims, CDS Curve Strategies ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Interpreting the shape of the CDS curl, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Building a tool for trade analysis, ÃÆ' ¢Ãƒ ¢Ã ¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Trading CDS forwards, Trading the CDS Cash Basis ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Drivers of the CDS cash basis, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ How to identifing investigate implement riskmanage CDS basis trades, Debt Equity Arbitrage Using CDS ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Trade analysis using a structural models, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Event driven tradings ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Hedge ratios guess scenario based risk analysis, CDS Index Strategies ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Hedging a bonds portfolios, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Beta strategies using CDS indices to take a systemic credit risk, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Trading the CDS index skew, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ Trading the index roll, ÃÆ' ¢Ãƒ ¢Ã¢â‚¬Å¡Ã‚ ¬Ãƒâ€šÃ‚ ¢ CDS index curve trades using forwards, Chapter Introduction to European Fixed Income Securities and Markets Introduction In this chap ter we discus on Eurpon ;;;;fixed income marktes ans securties,, A bonds is a debt capital market tool issued by a borrower, who is then required to repay to the lender investors the amount borrowed plus interest over a specified period of time; Bonds are also known as fixed income instrument, or fixed interest instruments in the real markets. Usually bonds are measured to be those debt securities with terms to maturity of over one year. Debt issued with a maturity of less than one year is considered to be money market debt. There are many different types of bonds that can be issued. The most common bond is the conventional Bond. This is a bond paying periodic interest payments at a fixed rate over a fixed period to maturity or redemption, with the return of principal {the par or nominal value of the bond} on the maturity date. All other bonds will be variations of this basic structure. A bond is therefore a financial contract from the person or body that has issued the bond, that is, the borrowed funds. Unlike shares or equity capital, bonds carry no ownership privileges. The bond remains an interest bearing obligation of the issuer until it is repaid, which is usually on its maturity date. The some types of bonds in the European market reflect the different types of issuers and their respective requirements. Some bonds are safer investments than others. The advantage of bonds to an investor is that they represent a fixed source of current income with an assurance of repayment of the loan on maturity, Bonds issued by developed country governments are deemed to be guaranteed investments in that the final repayment is virtually certain. For a corporate bond in the event of default of the issuing entity, bondholders rank above shareholders for compensation payments, There is lower risk associated with bonds compared to shares as an investment, and therefore almost invariably a lower return in the long term. In this chapter we will provide a basic exp lanation of the various types of fixed income instruments encountered in the European markets as well as the definitions of some key terms and concepts that will assist the reader throughout the remainder of the book. Important groups of investors in these markets are briefly discussed in the last section of the chapter DESCRIPTION OF THE BASIC FEATURES A bond, like any security can be thought of as a package of cash flows,, A bonds cash flows come in two forms coupon interest payments and the maturity value or par value. In European markets many bonds deliver annual cash flows, As an illustration, consider a 6% coupon bond issued by the Spanish government that matures on 31 January 2008,The coupon rate is the rate of interest that is multiplied by the maturity value to determine the size of the bonds coupon payments, Note that this bond delivers annual coupon payment, Suppose one owns this bond in June 2003. what cash flows can the bondholder expect between now and the mat urity date assuming the maturity value is ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬A 100 On each 31 January for the years 2004 through 2008 the bondholder will receive annual coupon payments of ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬A 6. Moreover on the maturity date the bondholder receives the maturity value of ÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬A 100 which is the bonds terminal cash flow, Type of Issuer A primary distinguishing feature of a bond is its issuer. The nature of the issuer will affect the way the bond is viewed in the market. There are four issuers of bonds: sovereign governments and their agencies, local government authorities, supranational bodies such as the World Bank, and corporations. Within the corporate bond market there is a wide range of issuers, each with differing abilities to satisfy their contractual obligations to investors. The largest bond markets are those of sovereign borrowers, the government bond markets. Term to Maturity The term to maturity of a bond is the number of years after which the issuer will repay the requirement, During the term the issuer will also make periodic interest payments on the debt. The maturity of a bond refers to the date that the debt will cease to exist, at which time the issuer will redeem the bond by paying the principal. The practice in the market is often to refer simply to a bonds term or maturity The provisions under which a bond is issued may allow either the issuer or investor to alter a bonds term to maturity after a set notice period, and such bonds need to be analyses in a different way. The term to maturity is an important consideration in the makeup of a bond. It indicates the time period over which the bondholder can expect to receive the coupon payments and the number of years before the principal will be paid in full, The bonds give up also depends on the term to maturity. Finally the price of a bond will change over its life as yields in the market change and as it approaches maturity. As we will discover later the volatility of a bonds price is dependent on its maturity, assuming other factors constant the longer a bonds maturity the greater the price volatility resulting from a change in market yields. Coupon Types As noted the coupon rate is the interest rate the issuer agrees to pay each year. The coupon rate is used to determine the annual coupon payment which can be delivered to the bondholder once per year or in two or more equal installments, As noted for bonds issued in European bond markets and the Eurobond markets coupon payments are made annually, Conversely in the UK US, and Japan, the usual practice is for the issuer to pay the coupon in two semiannual installments. An important exception is structured products which often deliver cash flows more frequently certain bonds do not make any coupon payments at all and these issues are known as zerocoupon bond,. A zerocoupon bond has only one cash flow which is the maturity value. Zerocoupon bonds are i ssued by corporations and governments. Security Description screen of a zerocoupon bond issued by the French bank BNP Paribus that matures March 11, 2005. Since the maturity value is AÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬1000 the price will be at a discount to AÃÆ' ¢Ãƒ ¢Ã¢â€š ¬Ã… ¡Ãƒâ€šÃ‚ ¬ 1000, The difference between the price paid for the bond and the maturity value is the interest realized by the bondholder. One important type of zerocoupon bond is called strips. In essence strips are government zerocoupon bonds. However, strips are issued by governments directly but are created by dealer firms Conventional coupon bonds can be stripped or broken apart into a series of individual cash flows which would then trade separately as zerocoupon bonds. This is a common practice in European government bond markets.Since zerocoupon bonds can created from coupon payments or the maturity value, a distinction is made between the two. Currency Denomination The cash flows of a fixed income security can be denominated in any currency. For bonds issued by countries within the European Union the issuer typically makes both coupon payments and maturity value payments in Euros. However there is nothing that prohibits the issuer from making payments in other currencies. The bonds indenture can specify that the issuer may make payments in some other specified currency, There are some issues whose coupon payments are in one currency and whose maturity value is in another currency. An issue with this feature is called a dual currency issue . NONCONVENTIONAL BONDS The definition of bonds given earlier in this chapter referred to conventional or plain vanilla bonds. There are many variations on vanilla bonds and we can introduce a few of them here. Securitized Bonds There is a large market in bonds whose interest and principal payments are backed by an underlying cash flow from another assets,. By securitizing the asset a borrower can provide an element of cash flow backing to investors. For instance a mortgage bank can use the cash inflows it receives on its mortgage book as asset backing for an issue of bonds. Such an issue would be known as a mortgage backed security because residential mortgages rarely run to their full term, but are usually paid off earlier by homeowners the notes that are backed by mortgages are also prepaid ahead of their legal final maturity, This feature means that MBS securities are not bullet bonds like vanilla securities, but are instead known as Amortizing bonds . Bonds with Embedded Options Some bonds include a provision in their offer particulars that gives either the bondholder or the issuer an option to enforce early redemption of the bond. The most common type of option fixed in a bond is a call feature A call provision grants the issuer the right to redeem all or part of the debt before the specified maturity date. An issuing company may wish to include such a feature as it allows it to replace an old bond issue with a lower coupon rate issue if interest rates in the market have declined. As a call feature allows the issuer to change the maturity date of a bond it is considered harmful to the bondholders interests therefore the market price of the bond at any time will reflect this, A call option is included in all asset backed securities based on mortgages for obvious reasons. PRICING A CONVENTIONAL BOND The principles of pricing in the bond market are exactly the same as those in other financial markets which states that the price of any financial instrument is equal to the net present value today of all the future cash flows from the instrument In this Chapter bond pricing will be explained. this chapter we will just present the basic elements of bond pricing, ACCRUED INTEREST, CLEAN PRICE, AND DIRTY PRICE All bonds coupon paying bonds accrue interest on a daily basis and this is then paid out on the coupon date, In determination of the fair price for a bond that is not purchased on a coupon date accrued interest must be incorporated into the price. Accrued interest is the amount of interest earned by the bonds seller since the last coupon payment date. The calculation of accrued interest will differ across bonds due to day count conventions that will be discussed shortly. In all major bond markets the convention is to quote price as a clean price. This is the price of the bond as given by the present value of its cash flows but excluding coupon interest that has accrued on the bond since the last dividend payment. As all bonds accrue interest on a daily basis, even if a bond is held for only one day interest will have been earned by the bondholder. However we have referred already to a bonds all in price which is the price that is actually paid for the bond in the market. This is also known as the dirty price which is the clean price of a bond plus accrued interest. In other words the accrued interest must be added to the quote price to get the total consideration for the bond Accrual Day Count Conventions The accrued interest calculation for a bond is dependent on the day count basis specified for the bond in question. We have already seen that when bonds are traded in the market the actual consideration that changes hands is made up of the clean price of the bond together with the accrued that has accumulated on the bond since the last coupon payment these two components make up the dirty price of the bond. When calculating the accrued interest, the market will use the appropriate day count convention for that bond, A particular market will apply one of five different methods to calculate accrued interest. RISKS ASSOCIATED WITH INVESTING IN FIXED INCOME SECURITIES Risk can thought of as the possibility of unpleasant surprise. Fixed income securities expose the investors to one or more of the following types of risk (1) Interest rate risk, (2) Credit risk, (3) Call and prepayment risk, (4) Exchange rate risk, (5) Liquidity risk, (6) Inflation or purchasing power risk, Interest Rate Risk A fundamental property is that an upward change in a bonds price results in a downward move in the yield and vice versa. This result makes sense because the bonds price is the present value of the expected future cash flows. As the required yield decreases the present value of the bonds cash flows will increase, This inverse relationship embodies the major risk faced by investors in fixed income securities interest rate risk. Interest rate risk is the possibility that the value of a bond or bond portfolio will decline due to an adverse movement in interest rates, Call and Prepayment Risk As noted a bond may contain an embedded option which permits the issuer to call or retire all or part of the issue before the maturity date. The bondholder, in effect is the writer of the call option. From the bondholders perspective there are three disadvantages of the embedded call option. First relative to bond that is option free the call option introduces uncertainty into the cash flow pattern. Second since the issuer is more likely to call the bond when interest rates have fallen, if the bond is called, then the bondholder must reinvest the proceeds received at the lower interest rates. Third a callable bonds upside potential is reduced because the bond price will not rise above the price at which the issuer can call the bond. Collectively these three disadvantages are referred to as call risk. MBS and ABS that are securitized by loans where the borrower has the option to prepay are exposed to similar risks. This is called prepayment risk, Exchange Rate Risk If a European investor buys a bond whose cash flows are denominated in a currency other than euros they are exposed to an additional risk. Namely the euro denominated cash flows are dependent on the exchange rate at the time the payments are received. For example suppose a European investor purchases a US corporate bond whose payments are denominated in US dollars. If the dollar depreciates relative to the euro, then fewer euros will be received. This risk is called exchange rate risk. Thus, if an investor buys a bond in a currency other than her own, she is, in essence, making two investments an investment in the bond and an investment in the currency. Liquidity Risk Liquidity involves the ease with which investors can buy or sell securities quickly at close to their perceived true values. Liquidity risk is the risk that the investor will have to buy or sell at security at a price above or below its true value. One widely used indicator of liquidity is the size of the spread between the bid price and the ask price other things equal the wider the bid ask spread the greater the liquidity risk. For investors who buy bonds with the intent of holding them until maturity liquidity risk is of secondary importance, Inflation or Purchasing Power Risk Inflation or purchasing power risk reflects the possibility of the erosion of the purchasing power of bonds cash flows due to inflation. Bonds whose coupon payments are fixed with long maturities are especially vulnerable to this type of risk. Floaters and inflation indexed bonds have relatively low exposures to inflation risk. INVESTORS There is a large variety of players in the bond markets each trading some or all of the different instruments available to suit their own purposes. We can group the main types of investors according to the time horizon of their investment activity, Short-Term Institutional Investors Short term institutional investors include banks and building societies, money market fund managers, central banks and the treasury desks of some types of corporate. Such bodies are driven by short-term investment views, often subject to close guidelines, and will be driven by the total return available on their investments. Banks will have an additional requirement to maintain liquidity often in fulfillment of regulatory authority rules, by holding a proportion of their assets in the form of easily tradable short-term instruments, Long-Term Institutional Investors Typically long term institutional investors include pension funds and life assurance companies. Their investment horizon is long-term, reflecting the nature of their liabilities. Often they will seek to match these liabilities by holding long-dated bonds. Mixed Horizon Institutional Investors Mixed horizon institutional investors are possibly the largest category of investors and will include general insurance companies and most corporate bodies. Like banks and financial sector companies, they are also very active in the primary market, issuing bonds to finance their operations. Market Professionals Market professionals include the banks and specialist financial mediators mentioned above, firms that one would not automatically classify as investors although they will also have an investment objective. Their time horizon will range from one day to the very long term. They include the proprietary trading desks of investment banks as well as bonds market makers in securities houses and banks who are providing a service to their customers. Proprietary traders will actively position themselves in the market in order to gain trading profit, for example, in response to their view on where they think interest rate levels are headed. These participants will trade direct with other market professionals and investors, or via brokers. Market makers or traders are wholesalers in the bond markets; they make two-way prices in selected bonds. Firms will not necessarily be active market makers in all types of bonds; smaller firms often specialize in certain sectors. Chapter 7 Quantitative study of Computational Finance 7.3Quantitative and Computational Finance:- Quantitative Finance as a branch of modern finance is one of the best growing areas within the corporate world, Together with the superiority and difficulty of modern financial products this exciting control continues to act as the motivating factor for new numerical models and the subsequent development of associated computational schemes, Alternative names for this subject area are Mathematical Finance, Financial Mathematics or Financial Engineering, This is a course in the applied aspects of mathematical finance in particular derivative pricing ,The necessary understanding of products and markets required will be covered during the course. The overall theme of the course is to develop the Partial Differential Equation approach to the pricing of options, As well as a 2 hour examination during the summer term students will undertake a short computing project where they will use statistical and computational techniques to perform derivative pricing, Simulation Methods in Fina nce Brief introduction to Stochastic Differential Equations drift diffusion Its Lemma, The statistics of random number generation in Excel, Simulating asset price SDEs in Excel, Financial Products and Markets Introduction to the financial markets and the products which are traded in them Equities indices foreign exchange fixed income world and commoditys, Options contracts and strategys for speculation and hedging Black-Schools framework Comparison reduction and basic solution for the heat equation, Black Schools PDE simple European calls and puts put call parity,The PDE for pricing commodity and currency options,Discontinuous payoffs Binary and Digital options,The Greeks theta delta gamma Vega and rho and their role in hedging, Computational Finance Solving the pricing PDE numerically using Explicit Implicit and Crank Nicholson Finite Difference Schemes. Stability criteria, Monte Carlo Technique for derivative pricing, Fixed-Income Products Preface to the properties and features of fixed income products yield time period and convexity,Stochastic interest rate models stochastic different equation for the spot interest rate bond pricing PDE popular models for the spot rate solutions of the bond pricing equation 7.4Fixed Income:- The fixed income market demands a vast selection of investment options with a variety of credit quality maturities and yields to meet investors objectives, to accomplish this, fixed income groups frequently create and modify mathematical models to calculate bond pricing perform yield analysis calculate cash flows and develop hedging strategies, Fixed income research groups use the thousands of prewritten math and graphics functions in Math Works products to access bond data perform statistical analysis calculate spreads determine bonds and derivative pricing perform sensitivity analyses and run Monte Carlo simulations, Advanced graphics and rendering capabilities in MATLAB make reviewing cash flows visualizing decision trees plotting spot and forward curves and creating deployable interactive 2-D and 3-D models easy, 7.5 Equity:- Smart security investing requires in depth research and analysis, measuring all the influencing factors is an essential part of risk management, As a result research groups continually create and modify mathematical models to calculate stock value review forecasts and develop innovative risk strategies, Equity research groups use the thousands of math and graphics functions in Math Works products to access stock data perform statistical analysis determine derivatives pricing perform sensitivity analyses and run Monte Carlo simulations, The graphics capabilities in MATLAB offer a variety of ways to review time series data visualize portfolio risks and returns and create forecasting graphs 7.6 Investment Management and Trading:- To meet the investment needs of individuals institutions and governments investment firms needed to deliver a wide range of investment opportunities with risk adjusted performance and consistent returns over time, To accomplish this financial professionals need to develop and use mathematical models to optimize portfolios and develop trading strategies and systems that can respond to market conditions, Investment management and trading research groups use the thousands of math and graphics functions in Math Works products to easily access securities data perform statistical analysis determine pricing conduct sensitivity and principal component analyses and implement buy and sell criteria, The graphics capabilities in MATLAB offer a selection of ways to easily review time series data visualize portfolio risks and returns and create forecasting graphs, With Math Works deployment tools, you can easily compile and integrate your MATLAB algorithms into your system, 7.7Mathematical and statistical approaches:- According to Fund of Funds analyst Fred Gem There are two types of quantitative analysis and therefore two types of quants, One type works primarily with mathematical models and the other primarily with statistical models, While there is no logical reason why one person can not do both kinds of work this does not seem to happen perhaps because these types demand different skill sets and, much more important different psychologies, A typical problem for a numerically oriented quantitative analyst would be to develop a model for pricing and managing a complex derivative product, A typical problem for statistically oriented quantitative analyst would be to develop a model for deciding which stocks are relatively expensive and which stocks are relatively cheap, the model might include a companies book value to price ratio its trailing earnings to price ratio and other accounting factors, An investment manager might implement this analysis by buying the underpriced stocks selling the overpriced stocks or both, One of the principal mathematical tools of quantitative finance is stochastic calculus, According to a July 2008 Aite Group report today quants often use alpha generation platforms to help them develop financial models, These software solutions enable quants to centralize and modernize the alpha generation process, 7.8Areas of Computational Finance application:- Areas where computational finance techniques are employed include: Investment banking , Forecasting, Risk Management software , Corporate strategic planning , Securities trading and financial risk management , Derivatives trading and risk management, Investment management, Pension scheme, Insurance policy, Mortgage agreement, Lottery design, Islamic banking , Currency peg , Gold and commodity valuation , Collateralized debt obligation , Credit default swap, Bargaining, Market mechanism design,

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