Interest rate option pricing with volatility humps

A development of a simple model in which interest rate claims are priced in the Heath-Jarrow-Morton paradigm and so incorporate full information on the term structure. The volatility structure for forward rates is humped and includes as a special case the exponentially dampened volatility structure used in the generalized Vasicek model.Interest rates ; Options (Finance)

On Markovian representations of the term structure

The linkages between term structures separated by finite time periods can be complex. Indeed, in general, the dynamics of the term structure could depend on the entire set of information revealed since the earlier date. This path dependence, which causes difficulties in pricing interest rate claims, is usually eliminated by making specific assumptions on investment behavior or on the evolution of interest rates. In contrast, this article identifies the class of volatility structures that permits the path dependence to be captured by a single sufficient statistic. An equilibrium framework is provided where beliefs and technologies are restricted so that the resulting term structures have volatilities that belong to the restricted class. The models themselves can be characterized by a parsimonious set of parameters and can be initialized to an observed term structure without the introduction of ad-hoc time-varying parameters. Furthermore, since the dynamics of the resulting term structures are two-state Markovian, simple pricing mechanisms can be developed for interest rate claims.Interest rates

On Correlation Effects and Default Clustering in Credit Models

We establish Markovian models in the Heath, Jarrow and Morton paradigm where the credit spreads curves of multiple firms and the term structure of interest rates can be represented analytically at any point in time in terms of a finite number of state variables. The models make no restrictions on the correlation structure between interest rates and credit spreads. In addition to diffusive and jump-induced default correlations, default events can impact credit spreads of surviving firms. This feature allows a greater clustering of defaults. Numerical implementations highlight the importance of taking interest rate-credit spread correlations, credit-spread impact factors and the full credit spread curve information into account when building a unified model framework that prices any credit derivative.

The changing role of banks and the changing value of deposit guarantees

Using a model for pricing deposit guarantees that treats the bank's investments as a portfolio of default-free bonds and risky loans, the authors push back uncertainty to the level of the borrowing firm and thus are able to explore how factors like firm leverage, loan maturity, and correlation effects between the firm's assets and interest rates affect the value of deposit guarantees.Deposit insurance ; Bank loans

Inflation expectations, real rates, and risk premia: evidence from inflation swaps

This paper develops a model of the term structures of nominal and real interest rates driven by state variables representing the short-term real interest rate, expected inflation, inflation’s central tendency, and four volatility factors that follow GARCH processes. We derive analytical solutions for nominal bond yields, yields on inflation-indexed bonds that have an indexation lag, and the term structure of expected inflation. Unlike prior studies, the model’s parameters are estimated using data on inflation swap rates, as well as nominal yields and survey forecasts of inflation. The volatility state variables fully determine bonds’ time-varying risk premia and allow for stochastic volatility and correlation between bond yields, yet they have small effects on the cross section of nominal yields. Allowing for time-varying volatility is particularly important for real interest rate and expected inflation processes, but long-horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were significantly underpriced prior to 2004 and again during the 2008-2009 financial crisis.Inflation (Finance) ; Interest rates ; Asset pricing

Jump starting GARCH: pricing and hedging options with jumps in returns and volatilities

This paper considers the pricing of options when there are jumps in the pricing kernel and correlated jumps in asset returns and volatilities. Our model nests Duan’s GARCH option models, where conditional returns are constrained to being normal, as well as mixed jump processes as used in Merton. The diffusion limits of our model have been shown to include jump diffusion models, stochastic volatility models and models with both jumps and diffusive elements in both returns and volatilities. Empirical analysis on the S&P 500 index reveals that the incorporation of jumps in returns and volatilities adds significantly to the description of the time series process and improves option pricing performance. In addition, we provide the first-ever hedging effectiveness tests of GARCH option models.Options (Finance) ; Hedging (Finance)

Estimating real and nominal term structures using Treasury yields, inflation, inflation forecasts, and inflation swap rates

This paper develops and estimates an equilibrium model of the term structures of nominal and real interest rates. The term structures are driven by state variables that include the short term real interest rate, expected inflation, a factor that models the changing level to which inflation is expected to revert, as well as four volatility factors that follow GARCH processes. We derive analytical solutions for the prices of nominal bonds, inflation-indexed bonds that have an indexation lag, the term structure of expected inflation, and inflation swap rates. The model parameters are estimated using data on nominal Treasury yields, survey forecasts of inflation, and inflation swap rates. We find that allowing for GARCH effects is particularly important for real interest rate and expected inflation processes, but that long–horizon real and inflation risk premia are relatively stable. Comparing our model prices of inflation-indexed bonds to those of Treasury Inflation Protected Securities (TIPS) suggests that TIPS were underpriced prior to 2004 but subsequently were valued fairly. We find that unexpected increases in both short run and longer run inflation implied by our model have a negative impact on stock market returns.Interest rates ; Inflation (Finance) ; Asset pricing

On flexibility, capital structure, and investment decisions for the insured bank

Most models of deposit insurance assume that the volatility of a bank's assets is exogenously provided. Although this framework allows the impact of volatility on bankruptcy costs and deposit insurance subsidies to be explored, it is static and does not incorporate the fact that equityholders can respond to market events by adjusting previous investment and leverage decisions. This paper presents a dynamic model of a bank that allows for such behavior. The flexibility of being able to respond dynamically to market information has value to equityholders. The impact and value of this flexibility option are explored under a regime in which flat-rate deposit insurance is provided.Deposit insurance ; Bank capital

Regulatory taxes, investment, and financing decision for insured banks

An investigation of the effects of interest rate and credit risk on optimal capital structure and investment decisions. The authors show that with no uncertainty in interest rates, capital regulation will reduce the risk of the bank's assets, but that under interest rate uncertainty, the impact of regulation may be detrimental and raise the risk of the deposits as well as government subsidies to the bank's shareholders.Bank capital ; Deposit insurance

On credit spread slopes and predicting bank risk

The authors examine whether credit-spread curves, engendered by a mandatory subordinated-debt requirement for banks, would help predict bank risk. They extract the credit-spread curves each quarter for each bank in our sample, and analyze the information content of credit-spread slopes. They find that credit-spread slopes are significant predictors of future credit spreads. However, credit-spread slopes do not provide significant additional information on future bank-risk variables, over and above other bank-specific and market-wide information.Bank capital ; Risk