Interest Rate Derivative Securities

Hedging with Interest Rate and Credit Derivatives by Banks

Usually, firms use interest rate derivatives to hedge interest rate risk. Similarly, some non-financial firms in Pakistan are also engaged in the use of interest rate derivatives to hedge their exposure to interest rate risk. Purpose: The purpose of this study is to identify determinants of interest rate derivatives used by non-financial firms in Pakistan and to identify any differences between non-financial firms using interest rate derivatives and non-interest rate derivatives. Methodology: Since interest rate derivatives are taken as dependent binary variables, binary digits 1 and 0 are assigned to firm and non-user interest rate derivatives. As a result, the Logit model is used to identify the determinants of interest rate derivative use. Besides, users and non-users of interest rate derivatives are two groups independent of each, and therefore the Mann Whitney U test is used to identify the difference between them. Results: In line with the literature, the non-parametric Mann Whitney U test resulted in significant differences between interest rate derivative users and non-users. While using the Logit model, there was a significant positive relationship between financial distress costs, asset growth, cash flow, firm size, and interest rate derivatives use. However, there was a negative relationship between profitability (ROA) and interest rate derivatives. Limitation: Since most financial firms use derivatives for trading rather than hedge purposes, the scope of the study is limited to non-financial firms that use derivatives for hedge purposes. Also, the study was launched in 2013-14, so the data collected and used for the period 2006-12 will be used. Implication: The findings suggest that large, financially distressed firms can hedge their interest rate risk and benefit from the optimal utilization of interest rate derivatives. Originality: The study was the first attempt to explore interest rate derivatives in non-financial firms in Pakistan and pave the way for further exploration of the subject matter. Besides, the original data were extracted from the annual reports of the sampled firms.

Around the time the Bretton Woods exchange rate system was breaking down in global markets, interest rates in many local markets became much less predictable, leaving businesses and investors exposed to far more interest rate risk than they were familiar with. The financial community began looking for ways to hedge and speculate this risk. To address this need to hedge interest rate risk, the futures exchanges in Chicago and London (and other financial centers) began offering interest rate contracts in addition to their historically traded commodity futures. In 1981, IBM and the World Bank entered into the first interest rate swap, soon followed by a foreign exchange swap. As the Black-Scholes model and other options pricing models became generally accepted, options on interest rates became widely traded in deep, liquid markets. Decades later, the interest rate derivatives markets, both exchange traded and over the counter (OTC), have grown into a huge global marketplace (notional amounts in billions of U.S. dollars equivalent). (See Exhibit 10.1.) These so-called plain vanilla interest rate derivatives totaled almost U.S. $355 trillion at the end of 2006, and there are many other interest rate derivatives that the Bank for International Settlements (BIS) does not report statistics on. At first glance, the BIS total appears to be roughly 10 times global gross domestic product. However, some OTC derivatives are double counted (e.g., each side of the same risk may be on the books of two banks; in practice this is difficult to net). A significant percentage of the total (exchange traded plus OTC) is a hedge against other interest rate risk but does not get netted in the statistics just cited. Most important, the numbers shown reflect notional amounts (i.e., the amounts used to as a benchmark for determining the dollar value of interest rate payments). The market value of these instruments is much smaller. Whole books have been written on each type of interest rate derivative, but the next section provides a sampling of the common types of interest rate derivatives you are likely to see on a broker-dealer fixed income trading floor.

Dynamic term structure models explain the yield curve variation well but perform poorly in pricing and hedging interest rate options. Most existing option pricing practices take the yield curve as given, thus having little to say about the fair valuation of the underlying interest rates. This paper proposes an m + n model structure that bridges the gap in the literature by successfully pricing both interest rates and interest rate options. The first m factors capture the yield curve variation, whereas the latter n factors capture the interest rate options movements that cannot be effectively identified from the yield curve. We propose a sequential estimation procedure that identifies the m yield curve factors from the LIBOR and swap rates in the first step and the n options factors from interest rate caps in the second step. The three yield curve factors explain over 99% of the variation in the yield curve but account for less than 50% of the implied volatility variation for the caps. Incorporating three additional options factors improves the explained variation in implied volatilities to over 99%.

Interest Rate Derivatives: Features, Valuation and Benefits

EMPIRICAL STUDIES ON INTEREST RATE DERIVATIVES by Xudong Sun Dr. Hongtao Yang, Examination Committee Chair Associate Professor of Mathematics University of Nevada, Las Vegas, USA Interest rate models are the building blocks of nancial market and the interest rate derivatives market is the largest derivatives market in the world. In this dissertation, we shall focus on numerical pricing of interest rate derivatives, estimating model parameters by Kalman lter, and studying various models empirically. We shall propose a frontxing nite element method to price the American put option under the quadratic term structure framework and compare it with a trinomial tree method and common nite element method. Numerical test results show the superiority of our frontxing nite element method in the aspects of computing the option and free boundary simultaneously with high accuracy. We shall also employ the Kalman lter and its variant techniques to estimate parameters of the a ne term structure models as well as quadratic term structure models. Various comparisons of di erent Kalman lter performance and both the in-sample t and out-sample t for Monte Carlo simulations as well as real treasury yield data are presented. In addition, we shall propose a general one-factor interest rate model and apply a homotopy perturbation method to valuate bond prices. One of the attractive qualities of the approximated solution of homotopy perturbation method is its fast speed of achieving the same accuracy compared to the tree method.

There are many examples of interest rate derivatives that are actively traded in over-the counter markets and in organized exchanges. Caps, floors, Treasury bond options, Treasury bond futures options, Eurodollar futures options, and swaptions are just some examples of this important class of derivatives in financial markets. They are classified as “interest rate derivatives” because their stochastic movements are directly related to the interest rate movements in a way that is analogous to the stock option price that moves in step with the underlying stock price.

In this paper, we examine the impact of interest rate risk factors on the interest rate derivatives (IRD) usage by commercial banks in India. We focus our analysis during the period 2008-2010. We have taken this period to highlight that during and after global financial crisis, what were the main factors that influence the interest rate derivatives usage by Indian commercial banks. We have used simulation analysis and regression analysis to identify the interest rate risk factors. Using Tobit fixed effect analysis, we are able to provide empirical evidence that interest rate risk drives the derivatives usages by Indian commercial banks. Our results indicate that asset size, the impact of interest rate shock on equity capital are positively related to use of derivatives for hedging as well as trading and interest rate sensitivity factor is negatively related to the use of derivatives for hedging and trading. New generation private banks have relatively large exposure to derivatives for trading purpose.

A cyclical square-root model for the term structure of interest rates

This chapter is devoted to stochastic interest rate models. Since the 1970s stochastic interest rate models have played a central role in Finance, not only in research but also in practical applications. These models were immediately implemented by practitioners to accurately price financial securities, like interest rate derivatives. Their pricing, however, was mathematically far more demanding than equity pricing, due to the fact that the whole term structure of interest rates and its development over time was required.

Sweeping changes in financial regulation have occurred throughout much of the world following the global credit crisis that began in 2007. Shifts in the regulatory paradigm governing derivatives have been especially dramatic and have already altered the landscape for interest rate derivatives and participants in interest rate derivatives activity. This chapter reviews the products that comprise the global interest rate derivatives market, recent market activity across different products, currencies, and market structures (i.e., exchange-traded interest rate derivatives, non-cleared swaps, and cleared swaps), and the new regulations governing interest rate derivatives in the United States and Europe. The chapter also documents the bifurcation in liquidity for certain non-dollar swaps (especially EUR-denominated swaps) that has arisen as a result of regulatory uncertainties involving the disparate international implementation of recent regulatory changes. A detailed Appendix presents a self-contained overview of the new regulatory framework itself.

In the more classical models for equities and interest rates evolution, constant volatility is usually assumed. However, in practice the volatilities are not constant in financial markets and different models allowing a varying local or stochastic volatility also appear in the literature. Particularly, here we consider the SABR model that has been first introduced in a paper by Hagan and coworkers, where an asymptotic closed-form formula for the implied volatility of European plain-vanilla options with short maturities is proposed. More recently, different works (Mercurio and Morini, Modeling Interest Rates: Advances in Derivatives Pricing, Risk Books 2009; Hagan and Lesniewski, LIBOR market model with SABR style stochastic volatility. Working Paper. http://lesniewski.us/papers/working/SABRLMM.pdf, 2008; Rebonato, A time-homogeneous SABR-consistent extension of the LMM. Risk, 2008) have extended the use of SABR model in the context of LIBOR market models for the evolution of forward rates (SABR-LMM). One drawback of these models in practice comes from the increase of computational cost, mainly due to the growth of model parameters to be calibrated. Additionally, sometimes either it is not always possible to compute an analytical approximation for the implied volatility or its expression results to be very complex, so that numerical methods (for example, Monte Carlo in the calibration process) have to be used. In this work we mainly review some recently proposed global optimization techniques based on Simulated Annealing (SA) algorithms and its implementation on Graphics Processing Units (GPUs) in order to highly speed up the calibration and pricing of different kinds of options and interest rate derivatives. Finally, we present some examples corresponding to real market data.KeywordsSABR volatility modelsSABR/LIBOR market modelsParallel simulated annealingGPUs

Evidence reported by Geczy, Minton and Schrand (1997) showed that foreign exchange risk had a significant influence on the use of currency derivatives but that interest cover and financial leverage did not. In this study, we suggest that the reason why foreign exchange risk was significant but interest cover and financial leverage were not significant in the evidence was because currency derivatives were used to measure the dependent variable. We verify the validity of this suggestion by testing the influence of interest cover and financial leverage on the use of interest rate derivatives. Our sample comprises 140 firms in the UK, 48 of which use interest rate derivatives. Evidence observed shows that interest cover and financial leverage have a significant influence on the use of interest rate derivatives and that foreign exchange risk does not. We also compare the previous evidence referred to above with our results to determine whether there is a difference between the factors that motivate firms to use currency derivatives or interest rate derivatives. The result of the comparison indicates that dependence on overseas product and capital markets, tax, institutional shareholding and economies of scale are the factors that motivate firms to use currency derivatives. The result also indicates that high interest cover (i.e. interest/profit before interest and tax)or total debt ratio, economies of scale and directors’ shareholding are the factors that motivate firms to use interest rate derivatives.

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.

Interest Rate Derivatives and Firm Value: Evidence from Mandatory Versus Voluntary Hedging