Yield Curve Construction Models – Tools & Techniques

Yield Curve

Yield curve models are used to price a wide variety of interest rate-contingent claims.  The existence of several different competing methods of curve construction available and there is no single standard method for constructing yield curves and alternate procedures are adopted in different business areas to suit local requirements and market conditions.  This fragmentation has often led to confusion amongst some users of the models as to their precise functionality and uncertainty as to which is the most appropriate modeling technique. In addition, recent market conditions, which inter-alia have seen elevated levels of LIBOR basis volatility, have served to heighten concerns amongst some risk managers and other model users about the output of the models and the validity of the underlying modeling methods.

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The purpose of this review, which was carried out in conjunction with research analyst Xu Bai, now at Morgan Stanley, was to gain a thorough understanding of current methodologies, to validate their theoretical frameworks and implementation, identify any weaknesses in the current modeling methodologies, and to suggest improvements or alternative approaches that may enhance the accuracy, generality and robustness of modeling procedures.

Yield Curve Construction Models

Modeling Asset Processes

Introduction

Over the last twenty five years significant advances have been made in the theory of asset processes and there now exist a variety of mathematical models, many of them computationally tractable, that provide a reasonable representation of their defining characteristics.

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While the Geometric Brownian Motion model remains a staple of stochastic calculus theory, it is no longer the only game in town.  Other models, many more sophisticated, have been developed to address the shortcomings in the original.  There now exist models that provide a good explanation of some of the key characteristics of asset processes that lie beyond the scope of models couched in a simple Gaussian framework. Features such as mean reversion, long memory, stochastic volatility,  jumps and heavy tails are now readily handled by these more advanced tools.

In this post I review a critical selection of asset process models that belong in every financial engineer’s toolbox, point out their key features and limitations and give examples of some of their applications.


Modeling Asset Processes