U.U.D.M. Project Report 2009:4 Structured products: Pricing, hedging and applications for life insurance companies Mohamed Osman Abdelghafour Examensarbete i matematik, 30 hp Handledare och examinator: Johan Tysk Mars 2009 Department of Mathematics Uppsala University Acknowledgement I would like to express my appreciation to Professor Johan Tysk my supervisor, not only for his exceptional help on this project, but also for the courses (Financial Mathematics and Financial Derivatives) that he taught which granted me the understanding options theory and the necessary mathematical background to come write this thesis. I would also like to thank him because he is the one who introduced me to the Financial Mathematics Master at the initial stage of my studies. Also thanks to the rest of the professors in the Financial Mathematics and Financial Economics Programme who provided instruction, encouragement and guidance, I would like to say Thank you to you all. They did not only teach me how to learn, they also taught me how to teach, and their excellence has always inspired me. Finally, I would like to thank my Father, Ramadan for his financial support and encouragement, my mother, and my wife Nellie who for their patience and continuous support, when I was studying and writing this thesis. 1 Introduction Chapter 1 Financial derivatives 1.1 What is the structured product? 1.1.1 Equity-linked structured products 1.1.2 Capital-Guaranteed Products 1.2 Financial Derivative topics 1.21 Futures and Forward contracts pricing and hedging 1.2.2 The fundamental exposure types 1.2.3 European type Options 1.2.4 American type options 1.2.5 Bermudian Options 1.2.6 Asian option types 1.2.7 Cliquet options Chapter 2 interest rate structured products 2.1 Floating Rate Notes (FRNs, Floaters) 2.2 Options on bonds 2.3 Interest Rate Caps and Floors 2.4 Interest rate swap (IRS) 2.5 European payer (receiver) swaption 2.6 Callable/Putable Zero Coupon Bonds 2.7 Chapter 3 Structured Swaps 3.1 Variance swaps 2 Chapter 1 Introduction In recent years many investment products have emerged in the financial markets and one of the most important products are so-called structured products. Structured products involve a large range of investment products that combine many types of investments into one product through the process of financial engineering. Retail and institutional investors nowadays need to understand how to use such products to manage risks and enhance their returns on their investment. As structured products investment require some derivatives instruments knowledge. The author will present some derivative introduction and topics that will be used in the main context of structured products . Structured investment products are tailored, or packaged, to meet certain financial objectives of investors. Typically, these products provide investors with capital protection, income generation and/or the opportunity to generate capital growth. So the author will present the use of such products and their payoff and analyse the use of different strategies. In fact, those products can be considered ready-made investment strategy available for investors so the investor will save time and effort to establish such complex investment strategies. In the pricing models and hedging, the author will tackle mainly the basic models of underlying equities and interest rate derivatives and he will give some pricing examples. Structured products tend to involve periodical interest payments and redemption (which might not be protected). A part of the interest payment is used to buy the derivatives part. What sets them apart from bonds is that both interest payments and redemption amounts depend in a rather complicated fashion on the movements of for example basket of assets, basket of indices exchange rates or future interest rates. Since structured products are made up of simpler components, I usually break them down into their integral parts when I need to value them or assess their risk profile and any hedging strategies. 3 This approach should facilitate the analysis and pricing of the individual components. For many product groups, no uniform naming conventions have evolved yet, and even where such conventions exist, some issuers will still use alternative names. I use the market names for products which are common; at the same time, I try to be as accurate as possible. Commonly used alternative names are also indicated in each product’s description. 1.1 What are structured products? Definition: Structured products are investment instruments that combine at least one derivative contract with underlying assets such as equity and fixed-income securities. The value of the derivative may depend on one or several underlying assets. Furthermore, unlike a portfolio with the same constituents the structured product is usually wrapped in a legally compliant, ready-to-invest format and in this sense it is a packaged portfolio. Structured investments have been part of diversified portfolios in Europe and Asia for many years, while the basic concept for these products originated in the United States in the 1980s. Structured investments 'compete' with a range of alternative investment vehicles, such as individual securities, mutual funds, ETFs (exchange traded fund) and closed-end funds. The recent growth of these instruments is due to innovative features, better pricing and improved liquidity. The idea behind a structured investment is simple: to create an investment product that combines some of the best features of equity and fixed income namely upside potential with downside protection. This is accomplished by creating a "basket" of investments that can include bonds, CDs, equities, commodities, currencies, real estate investment trusts, and derivative products. 4 This mix of investments in the basket determines its potential upside, as well as downside protection. The usual components of a structured product are a zero-coupon bond component and an option component. The payout from the option can be in the form of a fixed or variable coupon, or can be paid out during the lifetime of the product or at maturity. The zero-coupon bond component serves as buffer for yield-enhancement strategies which profit from actively accepting risk. Therefore, the investor cannot suffer a loss higher than the note, but may lose significant part of it. The zero-coupon bond component is a floor for the capital-protected products. Other products, in particular various dynamic investment strategies, adjust the proportion of the zero-coupon bond over time depending on a predetermined rule. 1.1.1 Equity-linked structured products The classification refers to the implicit option components of the product. In a first step, I distinguish between products with plain vanilla and those with exotic options components. While in a second step, exotic products can be uniquely identified and named, a similar differentiation within the group of plain-vanilla products is not possible. Their payment profiles can be replicated by one or more plain-vanilla options, whereby the option types (call or put) and position (long or short) is product-specific. Therefore, I assign terms to some products that best characterize their payment profiles. A classic structured product has the basic characteristics of a bond. As a special- feature, the issuer has the right to redeem it at maturity either by repayment of its- nominal value or delivery of a previously fixed number of specified shares. Most structured products can be divided into two basic types: with and without coupon payments generally referred to as reverse convertibles and discount certificates. 5 In order to value structured products, I decompose them by means of duplication, i.e., the reconstruction of product payment profiles through several single components. Thereby, I ignore transactions costs and market frictions, e.g., tax influences. 1.1.2 Capital-Guaranteed Products Capital-guaranteed products have three distinguishing characteristics: • Redemption at a minimum guaranteed percentage of the face value (redemption- at face value (100%) is frequently guaranteed). • No or low nominal interest rates. • Participation in the performance of underlying assets The products are typically constructed in such a way that the issue price is as close as possible to the bond’s face value (with adjustment by means of the nominal interest rate). It is also common that no payments (including coupons) are made until the product’s maturity date. The investor’s participation in the performance of the underlying asset can take an extremely wide variety of forms. In the simplest variant, the redemption amount is determined as the product of the face value- and the percentage change in the underlying asset’s price during the term of the product. If this value is lower than the guaranteed redemption amount; the instrument is redeemed at the guaranteed amount. This can also be expressed as the following formula: R=N(1+max(0,ST-S0)) 6 S0 = N + N . max(0,ST-S0)) S0 where R: redemption amount N: face value S0 : original price of underlying asset ST : Price of underlying asset at maturity. Therefore, these products have a number of European call options on the underlying asset embedded in them. The number of options is equal to the face value divided by the initial price (cf. the last term in the formula). The instrument can thus, be interpreted as a portfolio of zero coupon bonds (redemption amount and coupons) and European call options. The possible range of capital-guaranteed products