The pricing of interest rate swaps

Interest rate swaps have become an important tool for financial institutions because they provide a convenient way to reduce interest rate risk. Swaps allow financial institutions to obtain short-term deposits in the local deposit market and then transform these into longer-term liabilities. The growth of swaps has been explosive, with the swap market growing from nothing in 1981 to an estimated $889 billion in 1987. In addition to their role in managing interest rate risk, swaps have become important to financial managers for other reasons, and as a result the swap market is monitored by financial managers as are money and capital markets. Because of its growing importance, an empirical perspective on how swaps are priced is needed. This article develops a simple market model and then estimates the model using data provided by three major swap market participants.     

An empirical analysis of bank interest rate swaps

Considering the characteristics of banks that do and do not report interest rate swaps, the long-term interest rate exposure of a bank and the likelihood and extent of swap market participation are found to be positively related. Key to the finding is the inclusion of variables related to the provision of swap market intermediary services, which significantly explain both the likelihood of swap market participation and the notional value of outstanding swaps. The results suggest that the likelihood and extent of swap market participation by low-capitalized banks is less than for other banks.     

Risk management of real estate: The case of real estate swaps

Real estate swaps are a recent financial innovation based upon the principle of comparative advantage. A real estate swap is a useful tool for real estate risk management and for participating in real estate investment without the high costs associated with real estate. Potential economic benefits and costs associated with real estate swaps are considered and real estate swaps are compared to alternative tools for real estate risk management. The expected utility and effectiveness of risk management with a swap in a multiperiod framework are analyzed. The analysis finds that the subject property's return and its risk characteristics (as reflected in its correlation with interest rate and property index returns) delimit the risk management potential of a given swap position. Optimal swap positions are shown for various regions and property types based on historical return series, from the period between 1983 and 1992, and the parameters of the dynamic model developed.     

An Economic Analysis of Interest Rate Swaps

Interest rate swaps, a financial innovation in recent years, are based upon the principle of comparative advantage. An interest rate swap is a useful tool for active liability management and for hedging against interest rate risk. The purpose of this paper is to provide a simple economic analysis of interest rate swaps. Alternative uses of and the appropriate valuation procedure for interest rate swaps are described.     

Modeling volatility and changes in the swap spread

We investigate the determinants of changes in U.S. interest rate swap spreads using a model that explicitly allows for volatility interactions between swaps of different terms to maturity. Changes in the swap spread are found to be positively related to interest rate volatility, to changes in the default risk premium in the corporate bond market, and to changes in the liquidity premium for government securities. Swap spread changes are negatively related to changes in the level of interest rates and changes in the slope of the term structure. We also find that there is a strong and significant volatility interaction among spreads for swaps of different maturities and that the process for the conditional variance of the spread is highly persistent across all maturities.     

The effect of the new risk-based capital requirements on the market for swaps

The new risk-based capital requirements for banks cover swap agreements as well as the normal on-balancesheet items. The capital calculation is based on a fixed small percentage plus the current market value of the swap, if it is positive. Using option valuation methodology, anticipated capital requirements over the life of a swap are calculated. These requirements are compared to cushions that banks might want to hold against the risks of above average loss rates. For interest rate swaps, the cost of the capital requirements is small, amounting to about 1 bp/year on a swap; in a matched pair, this would amount to 2 bp in the bid-offer spread. On currency swaps, the cost of the capital requirements appears to be much more substantial, closer to 4 bp per year on a swap. In a matched pair, the excess of the capital requirements over desired cushion could amount to 7 bp in the bid offer spread.     

Swaps: Plain and Fanciful

The outstanding face amount of plain vanilla interest rate swaps exceeds two trillion dollars. While pricing and hedging of such swaps appear to be quite simple, many existing theories are based on the incorrect characterization of a swap as a simple exchange of a fixed for a floating rate note. This characterization is not consistent with standarized swap contracts and the treatment of swaps in bankruptcy. This paper provides an alternative perspective on swaps.     

互换利差特征与影响因素——基于人民币利率互换市场的研究

互换利差（Swap spread）是利率互换研究中最重要的问题之一。在国内相关研究仍属空白的情况下,本文首次对人民币利率互换市场的互换利差的变动特征和影响因素进行了统计和计量分析。结果表明,我国互换利差的影响因素较多,包括融资成本、流动性、违约风险因素、利率预期、曲线期限特征因素等。不同基准的利率互换利差影响因素不同,且短期和中长期互换利差影响因素也不相同。另外还发现,不同基准的互换之间、互换与现券之间的定价经常存在扭曲现象,实务中存在较大的套利机会。     

Interest Rate Swaps and Corporate Financing Choices

This paper describes the firm's decision to borrow short-term versus long-term and shows how the introduction of interest rate swaps affects this choice. The model shows that in the absence of a swap market, interest rate uncertainty can lead firms to substitute long-term for short-term financing. However, when swaps exist, there is a tendency for firms that expect their credit quality to improve to borrow short-term and use swaps to hedge interest rate risk. The model suggests that, while the demand for fixed for floating swaps is enhanced, the demand for floating for fixed swaps is reduced by the presence of asymmetric information.     

Pre‐Issuance Hedging of Fixed‐Rate Debt

This article analyzes several corporate hedging strategies to manage interest rate risk on fixed‐rate debt prior to issuance. The authors start by considering these strategies using a highly stylized model: a binomial forward interest rate tree that, while simple in design, illustrates derivative pricing methodologies that are used in practice. Under a given rate volatility assumption, they demonstrate expected outcomes when entering a forward bond contract, a forward‐starting pay‐fixed interest swap, and a purchased option on that swap, as well as the “default” alternative of doing nothing. In principle, the decision of whether or not to hedge, as well as how to do so, depends on management's view of future interest rate volatility and degree of comfort with possible outcomes. The authors then assess the pros and cons of hedging strategies, with considerable emphasis on practical considerations. For example, while their theoretical model would allow an issuer to “lock” a specific debt issuance, in practice one can hedge only “benchmark” interest rate risk. The authors describe the use of both Treasury locks and forward‐starting swaps to address unexpected benchmark yield changes, and discuss how factors such as the time to issuance affect an issuer's choice of instrument. For instance, Treasury locks are typically used when the time to issuance is relatively short, while interest rate swaps are more common for longer times to issuance. The article also discusses circumstances in which a “do nothing” strategy may be preferable to other alternatives, as well as the disadvantages of issuing in advance. Finally, the authors describe the impact of financial accounting on different hedge strategies.     

The analytic pricing of asymmetric defaultable swaps

Swaps where both parties are exposed to credit risk still lack convincing pricing mechanisms. This article presents a reduced-form model where the event of default is related to structural characteristics of each party. The cash flows submitted to credit risk are identified before the swap is priced. Analytical pricing formulas for interest rate and currency swaps are computed using a Gaussian model for risky bonds. Currency swaps exhibit additional correlation risk. The benefits from netting depend on the balance between exposures and market conditions in valuation. We show that sources of credit risk asymmetries are also likely to impact on credit spreads.     

Swap Rates and Credit Quality

This article presents a model for valuing claims subject to default by both contracting parties, such as swaps and forwards. With counterparties of different default risk, the promised cash flows of a swap are discounted by a switching discount rate that, at any given state and time, is equal to the discount rate of the counterparty for whom the swap is currently out of the money (that is, a liability). The impact of credit-risk asymmetry and of netting is presented through both theory and numerical examples, which include interest rate and currency swaps.     

利率互换交易策略分析

2007年,利率互换交易无论是交易量还是交易结构上都获得了长足的发展,2007年12月基于Shibor的交易量首次超过长期以来一直居于首位的FR007。该文对2007年末到2008年初这段时间内互换曲线的形变、互换利差变化以及互换交易策略等方面进行了较为详尽的分析和总结,对利率互换的研究和交易有一定的借鉴意义。     

The Default Risk of Swaps

We characterize the exchange of financial claims from risky swaps. These transfers are among three groups: shareholders, debtholders, and the swap counterparty. From this analysis we derive equilibrium swap rates and relate them to debt market spreads. We then show that equilibrium swaps in perfect markets transfer wealth from shareholders to debtholders. In a simplified case, we obtain closed-form solutions for the value of the default risk in the swap. For interest-rate swaps, we obtain numerical solutions for the equilibrium swap rate, including default risk. We compare these with equilibrium debt market default risk spreads.     

Analysis of Credit Risks in Asset-Backed Securitization Transactions in Singapore

Asset-backed securitization (ABS) is a relatively new financial instrument in Singapore's capital market, which has been accepted by developers (originators) as an alternative source of financing. Credit assessment and rating requirements have not been imposed on the ABS bond issues. Default-risk evaluation has also been understated, if not omitted, in the process of structuring ABS deals. This is the first study that applies a theoretical default-risky swaps valuation model to evaluate credit risks in ABS bonds in Singapore. The Monte-Carlo simulation results, based on the Century Square shopping mall ABS case, show significant effects of the changes in rental volatility and default-free interest rate volatility on the default-risk premium of swap. More specifically, an increase in the rental volatility reduces the default-risky swap values significantly. However, an increase in the instantaneous default-free interest rate volatility increases the default-risk premium of swaps, and this effect is only observed in the high default-free interest rate volatility regime (above 20 percent). The results suggest that the rental dynamics of the securitized real estate are critical in determining the default risks of ABS deals. The fixed-rate (coupon yield) and floating-rate (rental cash flows) should therefore be adequately determined to reflect the default risks, which may be caused by the rental dynamics of the securitized real estate.     

A synthetic factor approach to the estimation of value-at-risk of a portfolio of interest rate swaps

In this paper we decompose the interest rate swap yield curves of 10 major currencies into their common factors and find that the first two factors, interpreted as parallel shift and rotation, explain between 97.1% and 98.6% of the variation in the interest rate swap rates across all 10 currencies. The main contribution of the paper however is that we then model these two factors as simplified synthetic factors so that they may be used to develop an innovative approach to the computation of Value-at-Risk (VaR) for a portfolio of interest rate swaps.     

Can the choice of interpolation method explain the difference between swap prices and futures prices?

The standard model linking the swap rate to the rates in a contemporaneous strip of futures interest rate contracts typically produces biased estimates of the swap rate. Institutional differences usually require some form of interpolation to be employed and may in principle explain this empirical result. Using Australian data, we find evidence consistent with this explanation and show that model performance is greatly improved if an alternative interpolation method is used. In doing so, we also provide the first published Australian evidence on the accuracy of the futures‐based approach to pricing interest rate swaps.     

Pricing default swaps: Empirical evidence

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.     

当前经济形势与互换利率走势判断

2010年上半年,利率互换市场交投活跃。随着市场对经济增长和政策运用预期的不断修正,互换利率继1月创出新高后一路振荡下行。预计下半年,在基本面、政策面、资金面和利率自身波动节奏的相互作用下,市场参与者的预期将反复进行修正,互换利率将呈现宽幅震荡。     

Exploring the components of credit risk in credit default swaps

In this paper, we test the influence of various fundamental variables on the pricing of credit default swaps. The theoretical determinants that are important for pricing credit default swaps include the risk-free rate, industry sector, credit rating, and liquidity factors. We suggest a linear regression model containing these different variables, especially focusing on liquidity factors. Unlike bond spreads which have been shown to be inversely related to liquidity (i.e., the greater the liquidity, the lower the spread), there is no a priori reason that the credit default swap spread should exhibit the same relationship. This is due to the economic characteristics of a credit default swap compared to a bond. Our empirical result shows that all the fundamental variables investigated have a significant effect on the credit default swap spread. Moreover, our findings suggest that credit default swaps that trade with greater liquidity have a wider credit default swap spread.