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.     

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.     

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.     

Interest rate swaps

This instructional case is intended to introduce graduate and undergraduate financial accounting and finance students to derivatives using interest rate swaps. The major learning objective is to understand derivative accounting methods, using interest rate swaps, as proposed by the Financial Accounting Standards Board's recent Exposure Draft. A secondary learning objective is to understand key features of a management control system for derivatives' activities. Both matched and unmatched interest rate swap examples are used in this case. The matched swap is based on an actual swap done by a bank for one of its customers. The case is written from the perspective of an audit partner writing a report summarizing interest rate swap accounting and related management controls for a client who wanted to recognize all gains and losses related to its interest rate swaps immediately in current earnings.     

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.     

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.     

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.     

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。     

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.     

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.     

Determinants of interest rate swap spreads

This study argues that an interest rate swap, as a non-redundant security, creates surplus which will be shared by swap counterparties to compensate their risks in swaps. This action in turns affects swap spreads. Analyzing the time series impacts of the changes of risks of swap counterparties on swap spreads, we conclude that both lower and higher rating bond spreads have positive impacts on swap spreads. We also derive a risk–spread relation to test if swap counterparties are firms with differential credit ratings. Since the risk allocation between swap counterparties varies over business cycles, hence this factor needs to be controlled. We conclude that (1) similar results hold if the business cycle factor is controlled and (2) swap spreads contain procyclical element and are less cyclical than lower credit rating bond spreads.     

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.     

Debt-for-Equity Swaps under a Rational Expectations Equilibrium

This paper analyzes LDC debt-for-equity swaps under a rational expectations equilibrium. Under full information, the swap can never be strictly preferred by the LDC, the MNC, and the bank. Under the postulated informational asymmetry assumptions the same results obtain, leading to the “lemons” market in reverse. Under rational expectations, the swap can only occur if the loan is correctly valued relative to all private information in the economy. Given that some swaps do occur, future models must reflect the unique features of 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。     

Volatility as an Asset Class: European Evidence

Abstract

Volatility movements are known to be negatively correlated with stock index returns. Hence, investing in volatility appears to be attractive for investors seeking risk diversification. The most common instruments for investing in pure volatility are variance swaps, which now enjoy an active over-the-counter (OTC) market. This paper investigates the risk-return tradeoff of variance swaps on the Deutscher Aktienindex and Euro STOXX 50 index over the time period from 1995 to 2004. We synthetically derive variance swap rates from the smile in option prices. Using quotes from two large investment banks over two months, we validate that the synthetic values are close to OTC market prices. We find that variance swap returns exhibit an option-like profile compared to returns of the underlying index. Given this pattern, it is crucial to account for the non-normality of returns in measuring the performance of variance swap investments. As in the US, the average returns of selling variance swaps are found to be strongly positive and too large to be compatible with standard equilibrium models. The magnitude of the estimated risk premium is related to variance uncertainty and past index returns. This indicates that the variance swap rate does not seem to incorporate all past information relevant for forecasting future realized variance.     

Pricing Property Index Linked Swaps with Counterparty Default Risk

This paper extends Bjork and Clapham (Journal of Housing Economics 11:418–432, 2002) model for pricing real estate index total return swaps. Our extension considers counterparty default risk within a first passage contingent claims model. We price total return swaps on property indices with different levels of default risk. We develop this model under same assumptions as Bjork and Clapham (Journal of Housing Economics 11:418–432, 2002) and find that total return swap price is no longer zero. Total return swap payer must charge a spread over the market interest rate that compensates him for the exposure to this additional risk. Based on commercial property indices in the UK, we observe that computed spreads are much lower than a sample of quotes obtained from one of the traders in the market.     

Variance risk in commodity markets

We analyze the variance risk of commodity markets. We construct synthetic variance swaps and find significantly negative realized variance swap payoffs in most markets. We find evidence of commonalities among the realized payoffs of commodity variance swaps. We also document comovements between the realized payoffs of commodity, equity and bond variance swaps. Similar results hold for expected variance swap payoffs. Furthermore, we show that both realized and expected commodity variance swap payoffs are distinct from the realized and expected commodity futures returns, indicating that variance risk is unspanned by commodity futures.     

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.     

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.