Macroeconomic Implications of Term Structures of Interest Rates Under Stochastic Differential Utility with Non-Unitary EIS

This paper proposes a continuous-time term-structure model under stochastic differential utility with non-unitary elasticity of intertemporal substitution (EIS, henceforth) in a representative-agent endowment economy with mean-reverting expectations on real output growth and inflation. Using this model, we make clear structural relationships among a term structure of real and nominal interest rates, utility form and underlying economic factors (in particular, inflation expectation). Notably, we show that, if (1) the EIS is less than one, (2) the agent is comparatively more risk-averse relative to time-separable utility, (3) short-term interest rates are pro-cyclical, and (4) the rate of expected inflation is negatively correlated with the rate of real output growth and its expected rate, then a nominal yield curve can have a low instantaneous riskless rate and an upward slope.     

Interest Rates and Exchange Rate Movements: Analyzing Short-term Investments in Long-term Bonds

Tests of the uncovered interest rate parity (UIP) are subject to various data problems when long-term interest rates are applied: due to the long investment period, time intervals for measuring exchange rate movements are usually overlapping and therefore not independent. This shortfall can be prevented by considering short-term investments in long-term bonds instead of investments to maturity. This article analyzes the explanatory power of long-term interest rates with regard to 1- and 3-month exchange rate movements by relating return differences from 1- and 3-month investments in domestic and foreign 10-year government bonds to nine different exchange rates. From a Swiss perspective, there is only weak support for an interrelation between return differences and the corresponding exchange rate movements, whereas from a US perspective, the resulting estimates are much more in line with UIP.The reader may for instance consider Engel (1996) and Froot and Thaler (1990).     

Global asset prices and FOMC announcements

This paper analyzes the impact of U.S. monetary policy announcement surprises on foreign equity indexes, short- and long-term interest rates, and exchange rates in 49 countries. We use two proxies for monetary policy surprises: the surprise change to the current target federal funds rate (target surprise) and the revision to the expected path of future monetary policy (path surprise). We find that different asset classes respond to different components of the monetary policy surprises. Global equity indexes respond mainly to the target surprise; exchange rates and long-term interest rates respond mainly to the path surprise; and short-term interest rates respond to both surprises. On average, a hypothetical surprise 25-basis-point cut in the federal funds target rate is associated with about a 1 percent increase in foreign equity indexes and a 5 basis point decline in foreign short-term interest rates. A surprise 25-basis-point downward revision in the expected path of future policy is associated with about a ½ percent decline in the exchange value of the dollar against foreign currencies and 5 and 8 basis point declines in short- and long-term interest rates, respectively. We also find that asset prices’ responses to FOMC announcements vary greatly across countries, and that these cross-country variations in the response are related to a country’s exchange rate regime. Equity indexes and interest rates in countries with a less flexible exchange rate regime respond more to U.S. monetary policy surprises. In addition, the cross-country variation in the equity market response is strongly related to the percentage of each country’s equity market capitalization owned by U.S. investors. This result suggests that investors’ asset holdings may play a role in transmitting monetary policy surprises across countries.     

International money and stock market contingent claims

We develop a unified approach with closed-form solutions for pricing bonds, stocks, currencies and their derivatives. The specification assumes a fundamental risk factor represented by a stochastic positive definite matrix following a Wishart autoregressive (WAR) process. By assuming a volatility-in-mean specification for the domestic stock returns and the relative changes of exchange rates, and a domestic stochastic discount factor exponential affine with respect to the fundamental risk, it is possible to derive closed form solutions for the term structures of interest rates and for the risk-neutral probabilities while keeping the flexibility of the model. In particular:

i) The domestic and foreign term structures are jointly affine and correspond to Wishart quadratic term structures, which can ensure the positivity of interest rates;

ii) In this framework where the stock price follows a model with stochastic volatility, we obtain explicit or quasi-explicit formulas for futures and forward contracts, swaps and options. This extends results by

Heston (1993)

and

Ball and Roma (1994)

.

Options on realized variance and convex orders

Realized variance option and options on quadratic variation normalized to unit expectation are analysed for the property of monotonicity in maturity for call options at a fixed strike. When this condition holds the risk-neutral densities are said to be increasing in the convex order. For Lévy processes, such prices decrease with maturity. A time series analysis of squared log returns on the S&P 500 index also reveals such a decrease. If options are priced to a slightly increasing level of acceptability, then the resulting risk-neutral densities can be increasing in the convex order. Calibrated stochastic volatility models yield possibilities in both directions. Finally, we consider modeling strategies guaranteeing an increase in convex order for the normalized quadratic variation. These strategies model instantaneous variance as a normalized exponential of a Lévy process. Simulation studies suggest that other transformations may also deliver an increase in the convex order.     

外汇储备增长与通货膨胀关系研究

在现行外汇体制下,外汇储备增长与通货膨胀之间的关系是个值得探讨的问题。文章使用1998～2010年的月度数据,采用理论分析和实证分析相结合的方法分析外汇储备增长与通货膨胀的关系,得出：外汇储备增长对通货膨胀具有单向因果关系,外汇储备间接导致了通货膨胀。     

International order flows: Explaining equity and exchange rate returns

Macroeconomic models of equity and exchange rate returns perform poorly at high frequencies. The proportion of daily returns that these models explain is essentially zero. Instead of relying on macroeconomic determinants, we model equity price and exchange rate behavior based on a concept from microstructure–order flow. The international order flows are derived from belief changes of different investor groups in a two-country setting. We obtain a structural relationship between equity returns, exchange rate returns and their relationship to home and foreign equity market order flow. To test the model we construct daily aggregate order flow data from 800 million equity trades in the U.S. and France from 1999 to 2003. Almost 60% of the daily returns in the S&P100 index are explained jointly by exchange rate returns and aggregate order flows in both markets. As predicted by the model, daily exchange rate returns and order flow into the French market have significant incremental explanatory power for the daily S&P returns. The model implications are also validated for intraday returns.     

Pricing via recursive quantization in stochastic volatility models

We provide the first recursive quantization-based approach for pricing options in the presence of stochastic volatility. This method can be applied to any model for which an Euler scheme is available for the underlying price process and it allows one to price vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein [Rev. Financ. Stud. 1991, (4), 727–752] model and the SABR model introduced in Hagan et al. [Wilmott Mag., 2002, 84–108]. A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.     

A New Spin on the Jumbo/Conforming Loan Rate Differential

This article uses house-price transaction data to estimate volatility in house prices. The volatility parameter is an input into a mortgage-pricing model that is used to simulate the contract interest rate that balances the mortgage contract. By segmenting the house-price transaction into high- and low-valued homes, we are able to estimate a theoretical jumbo/conforming loan rate differential. Simulation results demonstrate that the differences in volatility between high- and low-priced homes can produce a contract loan rate differential, holding all else constant. The article also presents a discussion of the problems inherent to estimating volatilities form assets with infrequent trades and long holding periods.     

Are there nonlinearities in short‐term interest rates?

The present paper investigates the characteristics of short‐term interest rates in several countries. We examine the importance of nonlinearities in the mean reversion and volatility of short‐term interest rates. We examine various models that allow the conditional mean (drift) and conditional variance (diffusion) to be functions of the current short rate. We find that different markets require different models. In particular, we find evidence of nonlinear mean reversion in some of the countries that we examine, linear mean reversion in others and no mean reversion in some countries. For all countries we examine, there is strong evidence of the need for the volatility of interest rate changes to be highly sensitive to the level of the short‐term interest rate. Out‐of‐sample forecasting performance of one‐factor short rate models is poor, stemming from the inability of the models to accommodate jumps and discontinuities in the time series data.     

Stochastic interest rate modelling using a single or multiple curves: an empirical performance analysis of the Lévy forward price model

In current financial markets negative interest rates have become rather persistent, while in theory it is often common practice to discard such rates as incredible and irrelevant. However, from a risk management perspective, it is crucially important to financial institutions to properly account for this phenomenon in their Asset Liability Management (ALM) studies. In this paper, we develop a coherent framework on how to best incorporate negative interest rates in these studies through a single curve stochastic term structure model and compare it to its multiple curve analogue. It turns out that, from the wide range of available single curve models, especially the Lévy Forward Price model (LFPM) of Eberlein and Özkan [The Lévy LIBOR model. Financ. Stoch., 2005, 9, 327–348] seems appropriate for ALM purposes. This paper describes an optimisation routine for calibrating this LFPM under the risk-neutral measure in both the single and multiple curve framework to the market prices of interest rate caplets with different strike rates, maturities and tenors. In addition, an empirical performance analysis is made of the single and multiple curve LFPM, where we include four deterministic volatility specifications and provide an explicit parametrisation of a piecewise homogeneity restriction with both deterministic and random breakpoints. This comparative analysis indicates that both the single and multiple curve LFPM is best adopted with the Linear-Exponential Volatility (LEV) specification and that deterministic breakpoints should be included, rather than random breakpoints.     

关于中国外汇储备多与少的思考

本文认为,外汇储备的增长既是我国经济实力增强的必然结果,又对我国经济健康发展具有重要保障作用;我国外汇储备尽管已逾8000亿美元,但并没有足够证据表明外汇储备已经“过多”;外汇储备的增减有其自身的规律性,只要外汇储备增长的同时,国内经济运行状态良好,就应当认为这种增长是正常的、合理的;外汇储备增长并不是通货膨胀、汇率升值的决定因素,也不存在资源浪费问题。