No-arbitrage Model Research Articles

Market co-movement between credit default swap curves and option volatility surfaces

We analyze the co-movement between the Credit Default Index (CDX) curve and the S&P 500 index's option volatility surface. We connect the reduced-form no-arbitrage model with the Nelson-Siegel (N-S) model on hazard rate implied from the CDX curve, and identify the levels, slopes, and curvatures from these two markets via the Unscented Kalman Filter (UKF). We find that the changes in the level, slope, and curvature in the CDX curve and those in the volatility surface are correlated due to the bridge of the S&P 500 index return. Finally, the co-movement between the CDX curve and S&P 500 index's volatility surface become stronger after the late 2000s global financial crisis.

Berry–Esseen inequalities for the fractional Black–Karasinski model of term structure of interest rates

Abstract The Black–Karasinski model is a one-factor non-affine interest rate model as it describes interest rate movements driven by a single source of randomness and the drift function is a nonlinear function of the interest rate. The drift parameters represent the level and the speed of mean reversion of the interest rate. It belongs to the class of no-arbitrage models. The paper introduces some new approximate minimum contrast estimators of the mean reversion speed parameter in the model based on discretely sampled data which are efficient and studies their asymptotic distributional properties with precise rates of convergence.

Information Jumps, Liquidity Jumps, and Market Efficiency

We formulate a measure of information efficiency in a general, no-arbitrage semimartingale model of the price process. The market quality measure is applied to a high-frequency dataset from the interdealer FX market to identify changes in market efficiency after a decimalization of tick size.

What does a term structure model imply about very long-term interest rates?

We address two empirical issues related to the long end of the yield curve based on euro swap rates. First, for maturities longer than 20 years we find evidence for an ‘excess’ downward slope that cannot be explained by convexity. Second, volatility at the very long end of the yield curve is larger than predicted by no-arbitrage models. We construct a model-based arbitrage-free extrapolation of the yield-curve and compare it to the regulatory discount curve. Because of near-zero mean reversion, there is no convergence towards an ‘ultimate forward rate’ and convexity effects cause the arbitrage-free extrapolations to have slightly downward sloping curves. The low level of mean-reversion also implies that the volatility of long-term rates does not decline relative to the 20-year volatility. Therefore, we conclude that the mean-reversion and resulting smoothing adopted by the regulatory curve is much too strong.

Zero-Coupon Yields and the Cross-Section of Bond Prices

Abstract I estimate a dynamic term structure model on an unbalanced panel of Treasury coupon bonds, without relying on an interpolated zero-coupon yield curve. A linearity-generating model, which separates the parameters that govern the cross-sectional and time-series moments of the model, takes about 8 min to estimate on a sample of over 1 million bond prices. The traditional exponential affine model takes about 2 hr, because of a convexity term in coupon-bond prices that cannot be concentrated out of the cross-sectional likelihood. I quantify the on-the-run premium and a “notes versus bonds” premium from 1990 to 2017 in a single, easy-to-estimate no-arbitrage model. (JEL G12, G14, C33) Received: April 30, 2018; editorial decision November 3, 2020 by Editor Nikolai Roussanov

Equilibrium short-rate models vs no-arbitrage models: Literature review and computational examples

In this paper equilibrium short-rate models are compared against no-arbitrage short-rate models. This article is composed of the introduction to this literature and a review, followed by numerical examples of one-factor short-rate models; the Cox-Ingersoll-Ross (CIR) model and the Vasicek model. No-arbitrage models were presented through the Hull-White (HW) model, the Binomial lattice model for bond pricing and interest rate modelling, the Black-Karasinski (BK) model, and the Heath-Jarrow-Morton (HJM) model. The results prove that no single interest rate model exists that can be used for all purposes. These models were compared in terms of volatility, mean reversion process and convergence. The end results confirm the dependence of volatility on the level rate as a determinant of the predictive success of these models.

Funding Liquidity and the Valuation of Mortgage-Backed Securities

We study the relationship between funding liquidity and the valuation of mortgage-backed securities. Most of the financing for mortgage-backed securities occurs through a trade known as a dollar roll, the simultaneous sale and purchase of forward contracts on mortgage-backed securities that is analogous to a repurchase agreement. We develop a four-factor no-arbitrage model for valuing mortgage-backed securities that allows for the valuation of dollar rolls. Unlike previous models of the dollar roll, we allow for the possibility of a prepayment risk premium. We develop a new model-implied measure of funding liquidity of MBS investors that is independent of prepayment risk premia and agency credit spreads. We find that our implied funding liquidity spread is strongly related to measures of intermediary balance sheet constraints and primary dealer positions in mortgage-backed securities.

No-arbitrage one-factor term structure models in zero- or negative-lower-bound environments

One-factor no-arbitrage term structure models where the instantaneous interest rate follows either the process proposed by Vasicek (1977) or by Cox, Ingersoll, and Ross (1985), commonly known as CIR, are parsimonious and analytically tractable. Models based on the original CIR process have the important characteristic of allowing for a time-varying conditional interest rate volatility but are undefined in negative interest rate environments. A Shifted-CIR no-arbitrage term structure model, where the instantaneous interest rate is given by the sum of a constant lower bound and a non-negative CIR-like process, allows for negative yields and benefits from similar tractability of the original CIR model. Based on the U.S. and German yield curve data, the Vasicek and Shifted-CIR specifications, both considering constant and time-varying risk premia, are compared in terms of information criteria and forecasting ability. Information criteria prefer the Shifted-CIR specification to models based on the Vasicek process. It also provides similar or better in-sample and out-of-sample forecasting ability of future yield curve movements. Introducing a time variation of the interest rate risk premium in no-arbitrage one-factor term structure models is instead not recommended, as it provides worse information criteria and forecasting performance.

Model of corporate bond spread based on improved neural network

The reasons for credit spreads can be divided into enterprise-specific non-systematic risks and widespread macroeconomic systemic risks. The previous traditional research mainly focused on the perspective of unsystematic risk. However, at present, more and more scholars are beginning to focus on systemic risks. Based on the neural network algorithm, this paper constructs an improved neural network-based corporate bond spread model to explore the impact of macro systemic risks on credit spreads. Based on the multi-factor no-arbitrage model, the linear relationship between the credit spread and the risk premium of each factor is obtained. At the same time, based on previous research results and observations of the current market reality, this paper identifies five important macroeconomic factors: actual economic output factors, inflation factors, stock market volatility factors, stock market return factors and inter-bank funding factors. The research results show that the model constructed in this paper has excellent performance.

Sovereign credit risk and exchange rates: Evidence from CDS quanto spreads

Sovereign credit default swap quanto spreads tell us how financial markets view the interaction between a country’s likelihood of default and associated currency devaluations (the Twin Ds). A no-arbitrage model applied to the term structure of eurozone quanto spreads can isolate the Twin Ds and can gauge the associated risk premiums. Conditional on the occurrence of default, the true and risk-adjusted one-week probabilities of devaluation are 42% (2%) and 90% (55%) for the core (periphery) countries. The weekly risk premium for euro devaluation in case of default for the core (periphery) exceeds the regular currency premium by up to 18 (13) basis points.

Model migration and rough edges: British actuaries and the ontologies of modelling.

The existing literature on modelling provides two main ways of viewing model migration: a modular view, which seeks to decompose models in their constitutive elements, and thus provides a view on what it is that migrates; and a practice-based view, which focuses on modelling as an activity, and understands a model as intricately entangled with its context of use. This article brings together these two sensitivities by focusing on ontologies of modelling. The paper presents a case study of the appropriation of modern finance theory’s ‘no-arbitrage’ models by British actuaries – a process that gradually unfolded at around the turn of the century and led to significant friction within the UK’s insurance industry. We can distinguish two main modelling ontologies: a ‘risk-neutral ontology’, which underpins no-arbitrage models and holds that the value of financial instruments is determined by ‘arbitrage’; and, a ‘real-world ontology’, which assumes that the economic world consists of real probabilities that may be approximated through a combination of archival-statistical methods and expert judgment. The appropriation of the risk-neutral modelling ontology was made possible by the declining legitimacy of actuarial expertise as ‘financial stewards’ of life insurance companies. The risk-neutral modelling ontology provided an ‘objective’ alternative to the traditional actuarial models, which explicitly required actuaries to make ‘prudent’ judgments. Despite the fact that the no-arbitrage modelling was considered an ‘objective’ affair, the valuation models that insurers use today are strongly shaped by political compromises, a result of the ‘rough edges’ of models.

Core and ‘Crust’: Consumer Prices and the Term Structure of Interest Rates

Abstract We propose a no-arbitrage model of the nominal and real term structures that accommodates the different persistence and volatility of distinct inflation components. Core, food, and energy inflation combine into a single total inflation measure that ties nominal and real risk-free bond prices together. The model successfully extracts market participants’ expectations of future inflation from nominal yields and inflation data. Estimation uncovers a factor structure common to core inflation and interest rates and downplays the pass-through effect of short-lived food and energy shocks on inflation and interest rates. Model forecasts systematically outperform survey forecasts and other benchmarks. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Pricing structured products with economic covariates

We introduce a top-down no-arbitrage model for pricing structured products. Losses are described by Cox processes whose intensities depend on economic variables. The model provides economic insight into the impact of structured products on financial institutions’ risk exposure and systemic risk. We estimate the model using CDO data and find that spreads decrease with higher interest rates and increase with volatility and leverage. Volatility is the primary determinant of variation in tranche spreads. Leverage and interest rates are more closely associated with rare credit events. Model-implied risk premiums and the probabilities of tranche losses increase substantially during the financial crisis.

The information content of forward moments

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.

A 'Bad Beta, Good Beta' Anatomy of Currency Risk Premiums and Trading Strategies

We test a two-beta currency pricing model that features betas with risk-premium news and real-rate news of the currency market. Unconditionally, with currency market risk-premium news is because of a significantly positive price of risk of 2.52% per year; with global real-rate news is because of the negative price of risk. The price of risk-premium-beta risk is countercyclical, whereas the price of the real-rate-beta risk is procyclical. Most prevailing currency trading strategies have either excessive bad beta or too little good beta, thus fail to deliver abnormal performance. Our empirical results can be delivered by a no-arbitrage model with precautionary savings and a pricing kernel characterized by two separate global shocks.

Forecasting U.K. Yield Curve Dynamics Using Macroeconomic and Asset Pricing Factors: A No-Arbitrage Approach

We propose a no-arbitrage affine Gaussian model that links term structure dynamics to the evolution of asset pricing measures along with conventional macroeconomic and latent factors. In contrast to generic factors in FAVAR-type models, our economic factors exploit concept-specific rich data. For the U.K. economy, we find that medium and long-term yields respond more to shocks in asset pricing than real activity. The out-of-sample predictive analysis reveals that the proposed model outperforms traditional no-arbitrage affine Gaussian approaches with conventional macroeconomic and latent factors during the 2007-2010 crisis and post-crisis periods; the contribution of asset pricing measures to forecast accuracy is most pronounced at intermediate and long forecasting horizons. However, models with concept-specific factors only outperform models with generic FAVAR-type factors in the crisis and post-crisis periods, indicating that investors pay closer attention to specific sources of economic risks during periods of heightened economic uncertainty.

The Two-Pillar Policy for the RMB

We document stylized facts about China's recent exchange rate for its currency, the renminbi (RMB). Our empirical findings suggest that a policy is in place, aiming to balance RMB index stability and exchange rate flexibility. We then develop a tractable no-arbitrage model of the RMB under the two-pillar policy. Using derivatives data on the RMB and the U.S. dollar index, we estimate the model to assess financial markets' views about the fundamental exchange rate and sustainability of the policy. Our model is able to predict the modification of the two-pillar in May 2017, when a discretion-based countercyclical factor was introduced for the first time. We also examine the model's ability to forecast RMB movements.

A general class of distortion operators for pricing contingent claims with applications to CAT bonds

ABSTRACTThe 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.

The Two-Pillar Policy for the RMB

We document stylized facts about China's recent exchange rate for its currency, the renminbi (RMB). Our empirical findings suggest that a \two-pillar policy is in place, aiming to balance RMB index stability and exchange rate flexibility. We then develop a tractable no-arbitrage model of the RMB under the two-pillar policy. Using derivatives data on the RMB and the U.S. dollar index, we estimate the model to assess financial markets' views about the fundamental exchange rate and sustainability of the policy. Our model is able to predict the modification of the two-pillar in May 2017, when a discretion-based \countercyclical factor was introduced for the first time. We also examine the model's ability to forecast RMB movements.

The Term Structure of Expected Recovery Rates

There is widespread agreement that corporate debts’ recovery rates are time varying, but empirical work in this area is limited. We show that the joint information from the term structure of senior and subordinate credit default swaps can identify the level and the dynamics of recovery rates. We estimate a reduced-form no-arbitrage model on 46 firms across different industries. We find that the term structure of expected recovery rates is, on average, downward sloping. However, an inversion occurs during the 2008 crisis, suggesting the market expects higher recoveries conditional on short-term survival. The inversion is more pronounced for firms in distressed industries.