To simultaneously account for the properties of interest-rate term structure and foreign exchange rates within one arbitrage-free framework, we propose a class of multi-currency quadratic models (MCQM) with an (m + n) factor structure in the pricing kernel of each economy. The m factors model the term structure of interest rates. The n factors capture the portion of the exchange rate movement that is independent of the term structure. Our modeling framework represents the first in the literature that not only explicitly allows independent currency movement, but also guarantees internal consistency across all economies without imposing any artificial constraints on the exchange rate dynamics. We estimate a series of multi-currency quadratic models using U.S. and Japanese LIBOR and swap rates and the exchange rate between the two economies. Estimation shows that independent currency factors are essential in releasing the tension between the currency movement and the term structure of interest rates.

We consider the design and estimation of quadratic term structure models. We start with a list of stylized facts on interest rates and interest rate derivatives, classified into three layers: (1) general statistical properties, (2) forecasting relations, and (3) conditional dynamics. We then investigate the implications of each layer of property on model design and strive to establish a mapping between evidence and model structures. We calibrate a two-factor model that approximates these three layers of properties well, and show that a flexible specification for the market price of risk is important in capturing the stylized evidence in forecasting relations while factor interactions are indispensable in generating the hump-shaped dynamics of bond yields.

This paper provides a comprehensive analysis of the short-term interest-rate dynamics based on three different data sets and two flexible parametric specifications. The significance of nonlinearity in the short-rate drift declines with increasing maturity for the interest-rate series used in the study. Using a flexible diffusion specification and incorporating GARCH volatility and non-normal innovation reduce the need for a nonlinear drift specification. Finally, the nonlinear drift specification performs better than the linear drift specification only when the short-term interest-rate levels reach historical highs.

Equity index volatility variation and its interaction with the index return can come from three distinct channels. First, index volatility increases with the market’s aggregate financial leverage. Second, positive shocks to systematic risk increase the cost of capital and reduce the valuation of future cash flows, generating a negative correlation between the index return and its volatility, regardless of financial leverage. Finally, large negative market disruptions show self-exciting behaviors. This article proposes a model that incorporates all three channels and examines their relative contribution to index option pricing and stock option pricing for different types of companies.

We identify and characterize a class of term structure models where bond yields are quadratic functions of the state vector.We label this class the quadratic class and aim to lay a solid theoretical foundation for its future empirical application.We consider asset pricing in general and derivative pricing in particular under the quadratic class.We provide two general transform methods in pricing a wide variety of fixed income derivatives in closed or semi-closed form.We further illustrate how the quadratic model and the transform methods can be applied to more general settings.

This paper examines the interaction between default risk and interest-rate risk in determining the term structure of credit default swap spreads at different industry sectors and credit-rating classes. The paper starts with a parsimonious three-factor interest-rate dynamic term structure and projects the credit spread at each industry sector and rating class to these interest-rate factors while also allowing the projection residual dynamics to depend on the level of the interest-rate factors. Estimation shows that credit risk exhibits intricate dynamic interactions with the interest-rate factors.

We develop a new option pricing framework that tightly integrates with how institutional investors manage options positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no-arbitrage constraints on its current shape. Within this framework, we show that just like option implied volatilities, realized and expected volatilities can also be constructed specific to, and different across, option contracts. Applying the new theory to the S&P 500 index time series and options data, we extract volatility risk and risk premium from the volatility surfaces, and find that the extracted risk premium significantly predicts future stock returns.

The classic Black-Scholes option pricing model assumes that returns follow Brownian motion, but return processes differ from this benchmark in at least three important ways. First, asset prices jump, leading to non-normal return innovations. Second, return volatilities vary stochastically over time. Third, returns and their volatilities are correlated, often negatively for equities. Time-changed Lévy processes can simultaneously address these three issues. We show that our framework encompasses almost all of the models proposed in the option pricing literature, and it is straightforward to select and test a particular option pricing model through the use of characteristic function technology.

This paper proposes a top-down linear option pricing model that unifies the pricing of different option contracts not by assuming common dynamics but by imposing common pricing on each risk source in proportion to decentralized risk estimates. The model generates significantly better pricing performance than existing bottom-up models. Its high-dimensional risk structure effectively explains the options return variation, allowing for the seamless integration of option pricing with risk management. The market price of risk estimate from the model strongly predicts the future excess return of the corresponding risk-targeting option portfolio, an important dimension of attribute completely absent from prior literature.

We develop a simple robust link between deep out-of-the-money American put options on a company's stock and a credit insurance contract on the company's bond. We assume that the stock price stays above a barrier B before default but drops below a lower barrier A after default, thus generating a default corridor [A,B] that the stock price can never enter. Given the presence of this default corridor, a spread between two co-terminal American put options struck within the corridor replicates a pure credit contract, paying off when and only when default occurs prior to the option expiry.