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Interest rate modeling and the pricing of related derivatives remain subjects of increasing importance in financial mathematics and risk management. This book provides an accessible introduction to these topics by a step-by-step presentation of concepts with a focus on explicit calculations. Each chapter is accompanied with exercises and their complete solutions, making the book suitable for advanced undergraduate and graduate level students.

Key Features:A complete introduction accessible to advanced undergraduatesAlso covers recent aspects of interest rate modelingIncludes many graphs illustrating the multidimensional aspects of interest rate modelsEach chapter is accompanied with exercises and their complete solutions.

Can increased uncertainty about the future cause a contraction in output and its components? An identified uncertainty shock in the data causes significant declines in output, consumption, investment, and hours worked. Standard general-equilibrium models with flexible prices cannot reproduce this comovement. However, uncertainty shocks can easily generate comovement with countercyclical markups through sticky prices. Monetary policy plays a key role in offsetting the negative impact of uncertainty shocks during normal times. Higher uncertainty has even more negative effects if monetary policy can no longer perform its usual stabilizing function because of the zero lower bound. We calibrate our uncertainty shock process using fluctuations in implied stock market volatility, and show that the model with nominal price rigidity is consistent with empirical evidence from a structural vector autoregression. We argue that increased uncertainty about the future likely played a role in worsening the Great Recession. The economic mechanism we identify applies to a large set of shocks that change expectations of the future without changing current fundamentals.

We show that the compensation for rare events accounts for a large fraction of the average equity and variance risk premia. Exploiting the special structure of the jump tails and the pricing thereof, we identify and estimate a new Investor Fears index. The index reveals large time-varying compensation for fears of disasters. Our empirical investigations involve new extreme value theory approximations and high-frequency intraday data for estimating the expected jump tails under the statistical probability measure, and short maturity out-of-the-money options and new model-free implied variation measures for estimating the corresponding risk-neutral expectations.

In a model with heterogeneous-risk-aversion agents facing margin constraints, we show how securities' required returns increase in both their betas and their margin requirements. Negative shocks to fundamentals make margin constraints bind, lowering risk-free rates and raising Sharpe ratios of risky securities, especially for high-margin securities. Such a funding-liquidity crisis gives rise to \"bases,\" that is, price gaps between securities with identical cash-flows but different margins. In the time series, bases depend on the shadow cost of capital, which can be captured through the interest-rate spread between collateralized and uncollateralized loans and, in the cross-section, they depend on relative margins. We test the model empirically using the credit default swap—bond bases and other deviations from the Law of One Price, and use it to evaluate central banks' lending facilities.

A growing literature documents important gains in asset return volatility forecasting via use of realized variation measures constructed from high-frequency returns. We progress by using newly developed bipower variation measures and corresponding nonparametric tests for jumps. Our empirical analyses of exchange rates, equity index returns, and bond yields suggest that the volatility jump component is both highly important and distinctly less persistent than the continuous component, and that separating the rough jump moves from the smooth continuous moves results in significant out-of-sample volatility forecast improvements. Moreover, many of the significant jumps are associated with specific macroeconomic news announcements.

We use a novel pricing model to imply time series of diffusive volatility and jump intensity from S&P 500 index options. These two measures capture the ex ante risk assessed by investors. Using a simple general equilibrium model, we translate the implied measures of ex ante risk into an ex ante risk premium. The average premium that compensates the investor for the ex ante risks is 70% higher than the premium for realized volatility. The equity premium implied from option prices is shown to significantly predict subsequent stock market returns.

This book shows how current and recent market prices convey information about the probability distributions that govern future prices. Moving beyond purely theoretical models, Stephen Taylor applies methods supported by empirical research of equity and foreign exchange markets to show how daily and more frequent asset prices, and the prices of option contracts, can be used to construct and assess predictions about future prices, their volatility, and their probability distributions. Stephen Taylor provides a comprehensive introduction to the dynamic behavior of asset prices, relying on finance theory and statistical evidence. He uses stochastic processes to define mathematical models for price dynamics, but with less mathematics than in alternative texts. The key topics covered include random walk tests, trading rules, ARCH models, stochastic volatility models, high-frequency datasets, and the information that option prices imply about volatility and distributions. Asset Price Dynamics, Volatility, and Predictionis ideal for students of economics, finance, and mathematics who are studying financial econometrics, and will enable researchers to identify and apply appropriate models and methods. It will likewise be a valuable resource for quantitative analysts, fund managers, risk managers, and investors who seek realistic expectations about future asset prices and the risks to which they are exposed.

We study the effects of monetary policy on economic activity separately identifying the effects of a conventional change in the fed funds rate from the policy of forward guidance. We use a structural VAR identified using external instruments from futures market data. The response of output to a fed funds rate shock is found to be consistent with typical monetary VAR analyses. However, the effect of a forward guidance shock that increases long-term interest rates has an expansionary effect on output. This counterintuitive response is shown to be tied to the asymmetric information between the Federal Reserve and the public.