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Quantitative Analysis, Derivatives Modeling, and Trading Strategies
This book addresses selected practical applications and recent developments in the areas of quantitative financial modeling in derivatives instruments, some of which are from the authorsOCO own research and practice. While the primary scope of this book is the fixed-income market (with further focus on the interest rate market), many of the methodologies presented also apply to other financial markets, such as the credit, equity, and foreign exchange markets. This book, which assumes that the reader is familiar with the basics of stochastic calculus and derivatives modeling, is written from the point of view of financial engineers or practitioners, and, as such, it puts more emphasis on the ...
A Unified HJM Approach to Non-Markov Gaussian Dynamic Term Structure Models
Motivated by an extensive literature showing that government bond yields exhibit a strong non-Markov property, in the sense that moving averages of long-lagged yields significantly improve the predictability of excess bond returns. We then develop a systematic approach of constructing non-Markov Gaussian dynamic term structure models (GDTSMs) under the Heath-Jarrow-Morton (HJM) framework. Compared to the current literature, our approach is more flexible and parsimonious, enabling us to estimate an economically significant non-Markov effect that helps predict excess bond returns both in-sample and out-of-sample.
Multi-Curve HJM Modelling for Risk Management
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time-to-maturity buckets, we propose a modelling framework which is inherently discrete. In particular, we show how to approximate the HJM continuous time description of the multi-curve dynamics by a Vector Autoregressive process of order one. The resulting dynamics lends itself to a feasible estimation of the model volatility-correlation structure and market risk-premia. Then, resorting to the Principal Component Analysis we further simplify the dynamics reducing the number of covariance components. Applying the constant volatility version of our model on a sample of curves from the Euro area, we demonstrate its forecasting ability through an out-of-sample test.
The Study of the State
No detailed description available for "The Study of the State".
A General HJM Framework for Multiple Yield Curve Modeling
We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between (normalized) FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is specified as an affine process, we obtain a flexible Markovian structure which allows for tractable valuation formulas for most interest rate derivatives. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.
Empirical Tests of Two State-Variable HJM Models
Models for pricing interest rate claims, developed under the Heath-Jarrow-Morton paradigm, differ according to the volatility structure imposed on forward rates. For most general HJM structures the resultant path dependence creates implementation problems. Ritchken and Sankarasubramanian have recently identified necessary and sufficient conditions on the class of volatility structures of forward rates that enable the term structure dynamics to be captured by a finite set of state variables. The class is quite rich. The instantaneous spot rate volatility may be quite general, but the model curtails the structure of forward rate volatilities relative to this spot rate volatility. This paper provides empirical tests for this class of volatility structures. Unlike other studies, the volatility structure is examined over a broad section of maturities in the yield curve. Using Treasury data over the period 1982-1994, we find support for this class. Furthermore, unlike other studies, no evidence of a quot;volatilityquot; hump is identified.
