Calibration of Gaussian heath, Jarrow and Morton and random field interest rate term structure models

We show how the recently introduced Gaussian random field interest rate term structure models can be calibrated accurately and quickly to market caps and swaptions prices. We show how the calibrated random field model can be approximated arbitrarily closely with a multi-factor Gaussian Heath, Jarrow and Morton model. We argue that the Gaussian random field model is easier to calibrate and can be used as an indirect way to calibrate multi-factor Gaussian Heath, Jarrow and Morton interest rate models.This work was carried out when the author was at the Financial Options Research Centre, Warwick Business School, University of Warwick. I wish to thank Stewart Hodges for many helpful discussions and comments and Martin Cooper of Tokai Bank, Europe, for supplying the data used in this paper. I also wish to thank the Economic and Social Research Council and FORC for funding. An earlier version of this paper entitled Multi-Factor Gaussian HJM Approximation to Kennedy and Calibration to Caps and Swaptions Prices was presented at the 9th Annual Conference, FORC., Warwick Business School, September 1996. Another version also appears in the author's Ph.D. thesis. I am grateful to the helpful comments provided by Marti Subrahmanyam and the two anonymous referees. All errors are my own and the views expressed in no way reflect the opinion of my employer.     

Building multivariate Sato models with linear dependence

The increased trading in multi-name financial products has required the development of state-of-the-art multivariate models. These models should be computationally tractable and, at the same time, flexible enough to explain the stylized facts of asset log-returns and of their dependence structure. The popular class of multivariate Lévy models provides a variety of tractable models, but suffers from one major shortcoming: Lévy models can replicate single-name derivative prices for a given time-to-maturity, but not for the whole range of quoted strikes and maturities, especially during periods of market turmoil. Moreover, there is a significant discrepancy between the moment term structure of Lévy models and the one observed in the market. Sato processes on the other hand exhibit a moment term structure that is more in line with empirical evidence and allow for a better replication of single-name option price surfaces. In this paper, we propose a general framework for multivariate models characterized by independent and time-inhomogeneous increments, where the asset log-return processes at unit time are modeled as linear combinations of independent self-decomposable random variables, where at least one self-decomposable random variable is shared by all the assets. As examples, we consider two general subclasses within this new framework, where we assume a normal variance-mean mixture with a one-sided tempered stable mixing density or a difference of one-sided tempered stable laws for the distribution of the risk factors. Particular attention is given to the models' ability to explain the asset dependence structure. A numerical study reveals the advantages of these new types of models.     

Pricing credit default swaps with bilateral value adjustments

The aim of this work is to examine the influence of mutual fund flows on market timing models, thus providing unbiased timing coefficients. However, as this control is motivated by the existing relationship between mutual fund flows and market returns, we first analyse this relationship, considering previous and concurrent market returns. However, unlike existing studies, we do not consider future returns, since investors do not observe them when making investment decisions. Thus, we feel it is more appropriate to consider expected market returns. We construct the expected market returns by running an AR model and considering the available public information about the macro-economy. The relationship is analysed under different conditions, considering a variety of different mutual fund flow measures, and considering (or not) the sensitivity of mutual fund flows to positive and negative market returns. We also propose different controls for the traditional timing models, and we further analyse the reverse-causality problem. The study demonstrates, for a sample of equity mutual funds registered for sale in the USA, that the poor market timing performance found in this and other prior studies can be completely attributed to the perverse effect of the fund managers’ liquidity service.     

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.     

Stochastic duration and fast coupon bond option pricing in multi-factor models

Generalizing Cox, Ingersoll, and Ross (1979), this paper defines the stochastic duration of a bond in a general multi-factor diffusion model as the time to maturity of the zero-coupon bond with the same relative volatility as the bond. Important general properties of the stochastic duration measure are derived analytically, and the stochastic duration is studied in detail in various well-known models. It is also demonstrated by analytical arguments and numerical examples that the price of a European option on a coupon bond (and, hence, of a European swaption) can be approximated very accurately by a multiple of the price of a European option on a zero-coupon bond with a time to maturity equal to the stochastic duration of the coupon bond. This revised version was published online in June 2006 with corrections to the Cover Date.     

我国利率市场化的目标、障碍和对策探讨

利率市场化的实现表现在两个层面上:一是在宏观层面上,表现为借贷市场资金的供求均衡决定利率总水平;二是在微观层面上,表现为具体融资项目的当事人根据项目的特点,通过协商或讨价还价,自主决定融资项目的利率.目前,我国整个利率体系的基准利率确定困难、商业银行风险定价能力不足以及利率市场化之后可能出现的存贷利差缩小是推进利率市场化进程的主要障碍.本文认为:我们应根据现有市场条件构建基准利率指标,为各具特点的融资项目提供合理的定价基础;商业银行应在市场建设的同时积极实践,以提高风险定价能力;商业银行之间应避免过度竞争,以保持合理利差.     

Option pricing for GARCH-type models with generalized hyperbolic innovations

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets being modeled by Garch-type models with generalized hyperbolic innovations and the pricing kernel is an exponential affine function of the state variables, we show that the risk-neutral distribution is unique and again implies a generalized hyperbolic dynamics with changed parameters. We provide an empirical test for our pricing methodology on two data sets of options, respectively written on the French CAC 40 and the American SP 500. Then, using our theoretical result associated with Monte Carlo simulations, we compare this approach with natural competitors in order to test its efficiency. More generally, our empirical investigations analyse the ability of specific parametric innovations to reproduce market prices in the context of an exponential affine specification of the stochastic discount factor.     

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.     

The Term Structure of Interest Rates: Bounded or Falling?

This short paper resolves an apparent contradiction betweenFeldman's (1989) and Riedel's (2000) equilibrium models of theterm structure of interest rates under incomplete information.Feldman (1989) showed that in an incomplete information versionof Cox, Ingersoll, and Ross (1985), where the stochastic productivityfactors are unobservable, equilibrium term structures are ‘interior’and bounded. Interestingly, Riedel (2000) showed that an incompleteinformation version of Lucas (1978), with an unobservable constantgrowth rate, induces a ‘corner’ unbounded equilibriumterm structure: it decreases to negative infinity. This paperdefines constant and stochastic asymptotic moments, clarifiesthe apparent conflict between Feldman's and Riedel's equilibria,and discusses implications. Because productivity and growthrates are not directly observable in the real world, the questionwe answer is of particular relevance. JEL Classification codes:E43, G12, D92, D80, D51.     

The Term Structure of Interest Rates: Bounded or Falling?

This short paper resolves an apparent contradiction between Feldman's (1989) and Riedel's (2000) equilibrium models of the term structure of interest rates under incomplete information. Feldman (1989) showed that in an incomplete information version of Cox, Ingersoll, and Ross (1985), where the stochastic productivity factors are unobservable, equilibrium term structures are ``interior' and bounded. Interestingly, Riedel (2000) showed that an incomplete information version of Lucas (1978), with an unobservable constant growth rate, induces a ``corner' unbounded equilibrium term structure: it decreases to negative infinity. This paper defines constant and stochastic asymptotic moments, clarifies the apparent conflict between Feldman's and Riedel's equilibria, and discusses implications. Because productivity and growth rates are not directly observable in the real world, the question we answer is of particular relevance.     

Volatility transmission patterns and terrorist attacks

The objective of this study is to analyse volatility transmission between the US and Eurozone stock markets considering the financial market responses to the September 11, March 11 and July 7 terrorist attacks. In order to do this, we use a multivariate GARCH model and take into account the asymmetric volatility phenomenon, the non-synchronous trading problem and the turmoil periods themselves. Moreover, a graphical analysis of the Asymmetric Volatility Impulse-Response Functions (AVIRF) is introduced, which takes into consideration the financial market responses to the terrorist attacks. Results suggest that there is bidirectional and asymmetric volatility transmission and show the different impacts that terrorist attacks had on both markets.     

Continuous-time term structure models: Forward measure approach

The problem of term structure of interest rates modelling is considered in a continuous-time framework. The emphasis is on the bond prices, forward bond prices and so-called LIBOR rates, rather than on the instantaneous continuously compounded rates as in most traditional models. Forward and spot probability measures are introduced in this general set-up. Two conditions of no-arbitrage between bonds and cash are examined. A process of savings account implied by an arbitrage-free family of bond prices is identified by means of a multiplicative decomposition of semimartingales. The uniqueness of an implied savings account is established under fairly general conditions. The notion of a family of forward processes is introduced, and the existence of an associated arbitrage-free family of bond prices is examined. A straightforward construction of a lognormal model of forward LIBOR rates, based on the backward induction, is presented.