No-arbitrage Model Research Articles

Macroeconomic determinants of the term structure: Long-run and short-run dynamics

Abstract We propose a no-arbitrage term structure model with a Taylor rule and two macroeconomic variables, real activity growth and inflation, that each contain long-run and short-run components. Variance decompositions indicate that the impact of macroeconomic variables on the term structure differs from existing models. For short maturities, inflation is relatively more important than real activity growth at short forecast horizons. For longer maturity yields, the long-run component of inflation explains most of the long-horizon forecast variance, but real activity growth matters for short forecast horizons. Unlike existing macro models, the model implies plausible term premia and expectations of short rates. The long-run components also improve the prediction of bond excess returns relative to information in the yield curve and macro variables. Measures of in-sample and out-of-sample fit confirm the benefits of allowing for long- and short-run components.

Mean-reverting no-arbitrage additive models for forward curves in energy markets

In this paper we present an additive no-arbitrage model for energy forward markets capable to exhibit mean-reversion. The model naturally incorporates term structures for both the mean-reversion level and the volatility of forward prices and it is able to reproduce the seasonalities empirically observed in gas and power markets. We also present a method to estimate the model parameters, based on quadratic variation/covariation for the volatility and on constrained maximum-likelihood estimation for the mean-reversion speed and level. We apply this technique to time series of Phelix Base forward products.

Interest rate trees: extensions and applications

This paper provides extensions to existing procedures for representing one-factor no-arbitrage models of the short rate in the form of a tree. It allows a wide range of drift functions for the short rate to be used in conjunction with a wide range of volatility assumptions. It shows that, if the market price of risk is a function only of the short rate and time, a single tree with two sets of probabilities on branches can be used to represent rate moves in both the real-world and risk-neutral world. Examples are given to illustrate how the extensions can provide modelling flexibility when interest rates are negative.

Volatility-of-Volatility Risk

We show that time-varying volatility of volatility is a significant risk factor which affects both the cross-section and the time-series of index and VIX option returns, above and beyond volatility risk itself. Volatility and volatility-of-volatility movements are identified in a model-free manner from index and VIX option prices, and correspond to the VIX and VVIX indices in the data. The VIX and VVIX have separate dynamics and are only weakly related in the data. Delta-hedged returns for index and VIX options are negative on average, and are more negative for strategies which are more exposed to volatility and volatility-of-volatility risks. In the time series, volatility and volatility of volatility significantly predict delta-hedged returns with a negative sign. The evidence in the data is consistent with a no-arbitrage model which features time-varying market volatility and volatility-of-volatility factors which are priced by investors. In particular, volatility and volatility of volatility have negative market prices of risk, so that investors dislike increases in volatility and volatility of volatility.

Forward Moments and Risk Premia Predictability

We estimate the term structures of risk-neutral forward variance and skewness, and examine their predictive power for equity market excess returns and variance. We use Partial Least Squares to extract a single predictive factor from each term structure that is motivated by the theoretical implications of affine no-arbitrage models. The empirical analysis shows that an increased forward variance factor, FVF (forward skewness factor, FSF) corresponds to a more negatively sloped forward variance (more U-shaped forward skewness) term structure, and significantly forecasts higher future market excess returns and variance. More importantly, FSF exhibits predictive power for market returns that is stronger than, and incremental to, that provided by FVF. However, it does not outperform FVF in terms of excess variance predictability.

Macroeconomic-Driven Prepayment Risk and the Valuation of Mortgage-Backed Securities

We develop a three-factor no-arbitrage model for valuing mortgage-backed securities in which we solve for the implied prepayment function from the cross-section of market prices. This model closely fits the cross-section of mortgage-backed security prices without needing to specify an econometric prepayment model. We find that implied prepayments are generally higher than actual prepayments, providing direct evidence of significant macroeconomic-driven prepayment risk premiums in mortgage-backed security prices. We also find evidence that mortgage-backed security prices were significantly affected by Fannie Mae credit risk and the Federal Reserve’s quantitative easing programs. Received May 10, 2016; editorial decision September 22, 2017 by Editor Stijn Van Nieuwerburgh.

Gravity in FX Rsquared: Understanding the Factor Structure in Exchange Rates

Exchange rates strongly co-vary against their base currency. We uncover a gravity equation in this factor structure: the key determinant of a country’s exchange rate beta on the common base factor is the country’s distance from the base country. The farther the country, the larger the beta. For example, the beta of the CHF/USD exchange rate on the dollar factor is determined by the distance between Switzerland and the United States. Shared language, legal origin, shared border, resource similarity and colonial linkages also significantly lower the betas. On average, the exchange rates of peripheral countries tend to have high Rsquareds in factor regressions, while central countries have low Rsquareds. A no-arbitrage model of exchange rates replicates this distance-dependent factor structure when the exposure of pricing kernels to global risk factors is more similar for closer country pairs.

Interest Rate Trees: Extensions and Applications

This paper provides extensions to existing procedures for representing one-factor no-arbitrage models of the short rate in the form of a tree. It allows a wide range of drift functions for the short rate to be used in conjunction with a wide range of volatility assumptions. It shows that, if the market price of risk is a function only of the short rate and time, a single tree with two sets of probabilities on branches can be used to represent rate moves in both the real-world and risk-neutral world. Examples are given to illustrate how the extensions can provide modeling flexibility when interest rates are negative.

International correlation risk

We show that the cross-sectional dispersion of conditional foreign exchange (FX) correlation is countercyclical and that currencies that perform badly (well) during periods of high dispersion yield high (low) average excess returns. We also find a negative cross-sectional association between average FX correlations and average option-implied FX correlation risk premiums. Our findings show that while investors in spot currency markets require a positive risk premium for exposure to high dispersion states, FX option prices are consistent with investors being compensated for the risk of low dispersion states. To address our empirical findings, we propose a no-arbitrage model that features unspanned FX correlation risk.

The cross-section and time series of stock and bond returns

Bond factors which predict future U.S. economic activity at business cycle horizons are priced in the cross-section of U.S. stock returns. High book-to-market stocks have larger exposures to these bond factors than low book-to-market stocks, because their cash flows are more sensitive to the business cycle. Because of this new nexus between stock and bond markets, a parsimonious three-factor dynamic no-arbitrage model can be used to jointly price book-to-market-sorted portfolios of stocks and maturity-sorted bond portfolios, while reproducing the time-series variation in expected bond returns. The business cycle itself is a priced state variable in stock and bond markets.

Implementation of Short-Rate Models - A Case Study of the Black-Derman-Toy Model of Interest Rate

In order to value a bond with one or more embedded options, one must consider the volatility of interest rates, as changes in volatility will affect the possibility of the option being exercised. The valuation of bonds with embedded options can be achieved by constructing a binomial or trinomial interest rate tree that models the random evolution of future interest rates and then by using backward-induction to generate the value of the bond at each node. No-arbitrage models such as the Black-Derman-Toy (BDT) model are more commonly used in practice to price financial instruments with embedded options or contingent claims. In this paper therefore, we explore how one of the no-arbitrage short rate models, the BDT model, can be implemented in a practical and reproducible manner. This is the first in our series of discussions on short-rate models. In future essays, we will discuss the implementation of other short-rate models namely the Hull-White, Ho-Lee, Kalotay-Fabozzi-Williams and the Black-Karansinski models of interest rates.

Economic and Financial Determinants of Credit Risk Premiums in the Sovereign CDS Market*

We specify and estimate no-arbitrage models for sovereign CDS contracts by assuming that the country’s default intensity depends on observable economic and …nancial indicators. We estimate these models using a sample of twenty-eight countries, three CDS maturities, and over a decade of daily data. The models provide a good …t. The impact of the economic and …nancial variables on spreads is consistent with economic intuition. Spreads increase as a function of stock market and exchange rate volatility, but decrease as a function of interest rates and stock market returns. The magnitudes of these impacts vary substantially across countries and over time. Estimated risk premiums are also highly time-varying and peak during the 2008 …nancial crisis for nearly all countries. For European countries, the risk premiums are also high during the Eurozone debt crisis. In periods of market stress and high CDS spreads, the increase in market risk premiums is even larger than the increase in default probabilities. The cross-sectional variation in risk premiums across countries is high, also in non-crisis periods.

STATISTICAL ARBITRAGE IN THE MULTI-ASSET BLACK–SCHOLES ECONOMY

In this study, we consider the statistical arbitrage definition given in Hogan, S, R Jarrow, M Teo and M Warachka (2004). Testing market efficiency using statistical arbitrage with applications to momentum and value strategies, Journal of Financial Economics, 73, 525–565 and derive the statistical arbitrage condition in the multi-asset Black–Scholes economy building upon the single asset case studied in Göncü, A (2015). Statistical arbitrage in the Black Scholes framework. Quantitative Finance, 15(9), 1489–1499. Statistical arbitrage profits can be generated if there exists at least one asset in the economy that satisfies the statistical arbitrage condition. Therefore, adding a no-statistical arbitrage condition to no-arbitrage pricing models is not realistic if not feasible. However, with an example we show that what excludes statistical arbitrage opportunities in the Black–Scholes economy, and possibly in other complete market models, is the presence of uncertainty or stochasticity in the model parameters. Furthermore, we derive analytical formulas for the expected value and probability of loss of the statistical arbitrage portfolios and compute optimal boundaries to sell the risky assets in the portfolio by maximizing the expected return with a constraint on the probability of loss.

The Cross-Section of Currency Volatility Premia

We identify a global risk factor that drives the cross-section of volatility excess returns in the foreign exchange market. We show that a zero-cost strategy that buys forward volatility agreements with downward sloping volatility curves and sells those with upward slopes - the volatility carry strategy - earns on average 5.15% per month. When we form slope-sorted portfolios, the covariation with volatility carry returns fully explains the cross-sectional variation of our portfolios. The lower the slope of the volatility curve, the more the forward volatility agreement is exposed to volatility carry risk. A standard no-arbitrage model of exchange rates with two types of factor - a set of country specifi c factors and a global one - provides intuition for the findings. The state variables determining the exposure to the global risk factor are empirically related to squared deviations of changes in economic growth. In the cross-section, the returns to volatility carry strategy are only weakly related to traditional currency risk factors, like carry, global imbalance, global volatility and global liquidity risk.

A New Class of Probability Distortion Operators with an Application to CAT Bonds

The current paper provides a general approach to construct distortion operators that can price financial and insurance risks. Our approach generalizes the Wang (2000) transform and recovers multiple distortions proposed in the literature as particular cases. This approach enables designing distortions that are consistent with various pricing principles used in finance and insurance such as no-arbitrage models, equilibrium models and actuarial premium calculation principles. Such distortions allow for the incorporation of risk-aversion, distribution features (e.g., skewness and kurtosis) and other considerations that are relevant to price contingent claims. The pricing performance of multiple distortions obtained through our approach is assessed on CAT bonds data. The current paper is the first to provide evidence that jump-diffusion models are appropriate for CAT bonds pricing, and that natural disaster aversion impacts empirical prices. A simpler distortion based on a distribution mixture is finally proposed for CAT bonds pricing to facilitate the implementation.

A PRICING METHOD OF HYBRID DLS WITH GPGPU

We develop an efficient numerical method for pricing the Derivative Linked Securities (DLS). The payoff structure of the hybrid DLS consists with a standard 2-Star step-down type ELS and the range accrual product which depends on the number of days in the coupon period that the index stay within the pre-determined range. We assume that the 2-dimensional Geometric Brownian Motion (GBM) as the model of two equities and a no-arbitrage interest model (One-factor Hull and White interest rate model) as a model for the interest rate. In this study, we employ the Monte Carlo simulation method with the Compute Unified Device Architecture (CUDA) parallel computing as the General Purpose computing on Graphic Processing Unit (GPGPU) technology for fast and efficient numerical valuation of DLS. Comparing the Monte Carlo method with single CPU computation or MPI implementation, the result of Monte Carlo simulation with CUDA parallel computing produces higher performance.

Estimating Discrete-Time Gaussian Term Structure Models in Canonical Companion Form

This article formally introduces a convenient parametrization for the popular class of discrete-time essentially-affine term structure models in the spirit of Duffee (2002), and Ang and Piazzesi (2003). First, I show that if the term structure is spanned by N_f latent state variables, all pricing information must also be contained in N_f shortest-maturity forward rates. Every no-arbitrage model of the type studied is therefore observationally equivalent to a unique canonical model in which these forward rates act as factors. Second, the risk-neutral transition matrix of the canonical model is conveniently parametrized by N_f unrestricted real numbers, and the risk neutral drift is a function of factor covariance matrix, plus one extra parameter. Third, although it may appear restrictive to specify the shortest-maturity forward rates as factors, the model can be estimated using all information in observed bond prices, either by Kalman filter, or assuming perfect observability of certain combinations of yields. Monte-Carlo evidence suggests that both approaches lead to similar out-of-sample forecasting performance in artificial data sets. Finally, by using unique insights offered by the canonical companion form, I discuss some difficulties in fitting term structure models of the essentially-affine class to the standard set of Fama-Bliss discount bonds. The problems stem from the existence of factors seemingly inconsistent with the assumption of no arbitrage. This discussion may have implications for interpreting the evidence of bond return predictability, and for the question of whether imposing no arbitrage can improve yield forecasts.

Affine Term Structure Modeling and Macroeconomic Risks at the Zero Lower Bound

This paper exploits the term structures of treasury yields to extract information about macroeconomic dynamics during the effective lower bound period (ELB). I introduce a new no-arbitrage macro-finance affine model jointly representing stochastic inflation trend and volatility with a short-term nominal yield that can be persistently stuck at its lower bound. The model consistently attributes movements in the long-end of treasury curves to the pricing of macroeconomic shocks, providing a tighter identification of inflation components. Estimation performed on U.S. real and nominal treasuries reveals that the ELB period coincides with lower inflation trend and elevated inflation volatility. These adverse inflation outcomes produce significant deflation fears, leading investors to be averse to tightening monetary policy shocks and justifying an ELB embrace by the monetary authority. Lifting off can have destabilizing effects depending on the anchoring of expectations of a binding ELB, leaving room for unconventional monetary policy effectiveness.

An International Examination of the Role of Default and Liquidity Risks in the Interbank Market.

We estimate a no-arbitrage model of the term structure of international interbank spreads, and attempt to disentangle credit and liquidity risk premium in the interbank market. We study the consistency of the spreads’ movements across major currencies and assess the effectiveness of monetary policy actions on the deterioration of credit and liquidity risks. We find that at the core of the financial crisis, the interbank spread is clearly driven by liquidity risk. The effect is stronger in the US market, where liquidity pressures were severe. Our analysis suggests that the establishment of the unconventional policy programs, led to the deterioration of liquidity risk in the interbank market. Furthermore, the policy of major Central banks to substantially cut interest rates, kept credit pressures at low levels. By early 2009, the dominant driver of the spread is credit risk. This effect is stronger in the Euro and UK markets, due to the escalation of the European sovereign debt crisis. This is not the case for the Japanese market, which experienced remarkably low credit pressures during the core of the crisis. Moreover, we decompose the spread into an expectation hypothesis component and a time-varying risk premia component and find that the hypothesis of constant risk premia is rejected.

Can No-Arbitrage SDF Models with Regime Shifts Explain the Correlations between Commodity, Stock, and Bond Returns?

We investigate whether it is possible to find a Stochastic Discount Factor (SDF) that jointly prices the cross-section of eight U.S. portfolios of stocks, Treasuries, corporate bonds, and commodities and replicates their observed moments, and especially correlations. We use the first three principal components extracted from a set of 112 U.S. macro variables as pricing factors. We also introduce commodity-based factors in the SDF, motivated by commodity pricing theories and we use them either separately or in conjunction with the macro-based ones. We report that it is not impossible to find a set of macroeconomic factors able to jointly price the cross section of stocks, bonds, and commodities; however, this task is accomplished by a small set of commodity-based factors. Observed correlations for commodities are perfectly matched by a parsimonious, single state, diagonal factor VAR model where only three commodity-based factors enter the SDF. While introducing regimes does not improve the performance in all cases, they could be beneficial to replicating correlations among commodity and bond portfolios.