Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that are chosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.     

Negative Libor rates in the swap market model

We apply Stroock and Varadhan’s support theorem to show that there is a positive probability that within the Swap Market Model the implied Libor rates become negative in finite time. Mataix-Pastor received support from the Instituto Credito Oficial (ICO), Spain, and Fundación Caja Madrid.     

Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models

In this paper we propose a computationally efficient implementation of general one factor short rate models with a trinomial tree. We improve the Hull–Whites procedure to calibrate the tree to bond prices by circumventing the forward rate induction and numerical root search algorithms. Our calibration procedure is based on forward measure changes and is as general as the Hull–White procedure, but it offers a more efficient and flexible method of constructing a trinomial term structure model. It can be easily implemented and calibrated to both prices and volatilities. JEL classification G13, C6     

Volatility in the federal funds market and money market spreads during the financial crisis

We analyze the role of federal funds rate volatility in affecting risk premium as measured by various money market spreads during the 2007–2009 financial crisis. We find that volatility in the federal funds market contributed to elevated Overnight Index Swap (OIS) spreads of unsecured bank funding rates during the crisis. Using OIS as a proxy for market expectations, we also decompose London Inter-Bank Offered Rate (Libor) into its permanent and transitory components in a dynamic factor framework and show that increased volatility in the federal funds market contributed to substantial transitory movements of Libor away from its long-run trend during the financial crisis.     

Interest rate model comparisons for participating products under Solvency II

Under the Solvency II regulatory framework it is essential for life insurers to have an adequate interest rate model. In this paper, we investigate whether the choice of the interest rate model has an impact on the valuation of the best estimate of the liabilities. We use three well-known interest rate models; the CIR++-model, the G2++-model and the Libor Market model. Our numerical results show that for low to medium durations of the liabilities and a relatively low proportion of credit bonds in the asset portfolio, the three interest rate models produce quite similar values for the best estimate liabilities. However, for large durations of the liabilities, or a large bond proportion, or both, the differences can be quite large. There is no easy answer to the question of which model should be used in cases where the choice of interest rate model has a significant impact. Based on the study described in this paper, our advice is to use the G2++-model, which seems to represent an appropriate trade-off between accuracy and complexity.     

A Comparison of Unexplained Racial Disparities in Bank-Level and Market-Level Models of Mortgage Lending

Statistical models of mortgage lending have been used by both academics and regulators to assess the importance of racial discrimination in lending decisions. Models estimated by bank regulators are specified at a bank level, allowing regulators to focus on possible disparate treatment discrimination against minorities. In contrast, the academic literature has tended to estimate models combining data across many banks. We argue that the market-level approach uses a mis-specified model whose estimates do not clearly measure any well-defined concept of discrimination. Using data from eight banks, we find important differences between bank-level and market-level models, with market-level models producing larger estimated racial effects than bank-level models.     

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

Empirical Testing of Real Option-Pricing Models

This research is the first to examine the empirical predictions of a real option-pricing model using a large sample of market prices. We find empirical support for a model that incorporates the option to wait to develop land. The option model has explanatory power for predicting transactions prices over and above the intrinsic value. Market prices reflect a premium for the option to wait to invest that has a mean value of 6% in our sample. We also estimate implied standard deviations for individual commercial property prices ranging from 18 to 28% per year.     

Evaluation Periods and Asset Prices in a Market Experiment

We test whether the frequency of feedback information about the performance of an investment portfolio and the flexibility with which the investor can change the portfolio influence her risk attitude in markets. In line with the prediction of myopic loss aversion (Benartzi and Thaler (1995)), we find that more information and more flexibility result in less risk taking. Market prices of risky assets are significantly higher if feedback frequency and decision flexibility are reduced. This result supports the findings from individual decision making, and shows that market interactions do not eliminate such behavior or its consequences for prices.     

市场波动促使Libor走向完善

Libor一直是全球最为重要的利率基准之一。针对年初以来市场对于Libor可能偏离实际交易利率的担忧,英国银行家协会（BBA）迅速展开了调查和讨论,并公布了调查结果。从目前看,Libor在精确、透明和客观性上依然具有主导性和市场地位,市场尽管也提出了一些替代方案,但从实际看,继续完善Libor形成机制并加强监管也许是市场更好的选择。     

Correlation structure forecasting & ex ante portfolio selection strategies in the Japan market

Using monthly data for 160 stocks covering January 1977 to December 1991, we find that both the Historical Mean and the Industry Mean Models dominate the Global Mean and the Single Index Models. In theex-ante portfolio selection, the Historical Model dominates all other models when evaluated against the benchmark of the Global Minimum Variance Portfolio but a combination of historical correlation structure and Bayes-Stein Shrinkage expected returns dominates other models when the Optimal Tangency Portfolio is used as a benchmark for evaluation.     

Time consistency of Lévy models

Time consistency of the models used is an important ingredient to improve risk management. The empirical investigation in this article gives evidence for some models driven by Lévy processes to be highly consistent. This means that they provide a good statistical fit of empirical distributions of returns not only on the timescale used for calibration but on various other timescales as well. As a result these models produce more reliable risk numbers and derivative prices.     

The volatility term structure in a lognormal process for the short rate

One-factor Markov models are widely used by practitioners for pricing financial options. Their simplicity facilitates their calibration to the intial conditions and permits fast computer Implementations. Nevertheless, the danger remains that such models behave unrealistically, if the calibration of the volatility is not properly done. Here, we study a lognormal process and investigate how to specify the volatility constraints in such a way that the term structure of volatility at future times, as implied by the short rate process, has a realistic and stable shape. However, the drifting down of the volatility term structure is unavoidable. As a result, there is a tendency to underestimate option prices.     

Valuing Fixed-Income Options and Mortgage-Backed Securities with Alternative Term Structure Models

To value mortgage-backed securities and options on fixed-income securities, it is necessary to make assumptions regarding the term structure of interest rates. We assume that the multi-factor fixed parameter term structure model accurately represents the actual term structure of interest rates, and that the values of mortgage-backed securities and discount bond options derived from such a term structure model are correct. Differences in the prices of interest rate derivative securities based on single-factor term structure models are therefore due to pricing bias resulting from the term structure model. The price biases that result from the use of single-factor models are compared and attributed to differences in the underlying models and implications for the selection of alternative term structure models are considered.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

Switching VARMA Term Structure Models

The purpose of this article is to propose a global discrete-timemodeling of the term structure of interest rates which is ableto capture simultaneously the following important features:(i) a historical dynamics of the factor driving term structureshapes involving several lagged values, and switching regimes;(ii) a specification of the stochastic discount factor (SDF)with time-varying and regime-dependent risk-premia; (iii) explicitor quasi explicit formulas for zero-coupon bond (ZCB) and interestrate derivative prices. We develop the switching autoregressivenormal (SARN) and the switching vector autoregressive normal(SVARN) Factor-Based Term Structure Models of order p. The factoris considered as a latent variable or an observable variable:in the second case the factor is a vector of several yields.Regime shifts are described by a Markov chain with (historical)nonhomogeneous transition probabilities. An empirical analysisof bivariate VAR(p) and SVARN(p) Factor-Based Term StructureModels, using monthly observations of the U.S. term structureof interest rates, and a goodness-of-fit and expectation hypothesispuzzle comparison with competing models in the literature, showsthe determinant role played by the observable nature of thefactor, lags, and switching regimes in the term structure modeling.     

Deep learning volatility: a deep neural network perspective on pricing and calibration in (rough) volatility models

We present a neural network-based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models—including second-generation stochastic volatility models and the rough volatility family—and a range of derivative contracts. Neural networks in this work are used in an off-line approximation of complex pricing functions, which are difficult to represent or time-consuming to evaluate by other means. The form in which information from available data is extracted and used influences network performance: The grid-based algorithm used for calibration is inspired by representing the implied volatility and option prices as a collection of pixels. We highlight how this perspective opens new horizons for quantitative modelling. The calibration bottleneck posed by a slow pricing of derivative contracts is lifted, and stochastic volatility models (classical and rough) can be handled in great generality as the framework also allows taking the forward variance curve as an input. We demonstrate the calibration performance both on simulated and historical data, on different derivative contracts and on a number of example models of increasing complexity, and also showcase some of the potentials of this approach towards model recognition. The algorithm and examples are provided in the Github repository GitHub: NN-StochVol-Calibrations.     

Aggressive Orders and the Resiliency of a Limit Order Market

We analyze the resiliency of a pure limit order market by investigating the limit order book (bid and ask prices, spreads, depth and duration), order flow and transaction prices in a window of best limit updates and transactions around aggressive orders (orders that move prices). We find strong persistence in the submission of aggressive orders. Aggressive orders take place when spreads and depths are relatively low, and they induce bid and ask prices to be persistently different after the shock. Depth and spread remain also higher than just before the order, but do return to their initial level within 20 best limit updates after the shock. Relative to the sample average, depths stay around their mean before and after aggressive orders, whereas spreads return to their mean after about twenty best limit updates. The initial price impact of the aggressive order is partly reversed in the subsequent transactions. However, the aggressive order produces a long-term effect as prices show a tendency to return slowly to the price of the aggressive order.We thank Theo Nijman, Erik Theissen, Rob van den Goorbergh, Josef Zechner (editor) and an anonymous referee for valuable comments on an earlier draft as well as seminar participants at the EEA-conference in Venice, the CFS Conference on Market Design in Eltville, CORE, Leuven and Tilburg. The first and last authors gratefully acknowledge financial assistance from FWO-Flanders under contract G.0333.