Title page for ETD etd-11082001-094650


Type of Document Dissertation
Author Park, Tae Young
Author's Email Address tapark@vt.edu
URN etd-11082001-094650
Title Efficiency and Accuracy of Alternative Implementations of No-Arbitrage Term Structure Models of the Heath-Jarrow-Morton Class
Degree PhD
Department Finance, Insurance, and Business Law
Advisory Committee
Advisor Name Title
Mozumdar, Abon Committee Chair
Chance, Donald M. Committee Member
Day, Martin V. Committee Member
Kumar, Raman Committee Member
Morgan, George E. Committee Member
Keywords
  • Term Structure of Interest Rates
  • Eurodollar Futures Options
  • Implied Volatility
  • Interest Rate Derivatives
  • No-Arbitrage Models
Date of Defense 2001-10-25
Availability unrestricted
Abstract
EFFICIENCY AND ACCURACY OF ALTERNATIVE IMPLEMENTATIONS OF NO-ARBITRAGE TERM STRUCTURE MODELS OF THE HEATH-JARROW-MORTON CLASS

Tae Young Park

Abstract

Models of the term structure of interest rates play a central role in the modern theory of pricing bonds and other interest rate claims. Term structure models based on the principle of no-arbitrage, especially those of the Heath-Jarrow-Morton (1992) class, have become very popular recently, both with academics and practitioners. Surprisingly however, although the implied volatility function plays a crucial role in these no-arbitrage term structure models, there is little systematic evidence to guide optimal model specification within this broad class.

We study the implied volatility in the Heath-Jarrow-Morton framework using Eurodollar futures options data. We estimate a daily time series of forward rates within the HJM framework such that, by construction, the predicted futures prices from our model exactly match the observed futures prices. Next, we estimate a daily time series of volatility parameters such that the sum of squared errors between futures options prices predicted by the model and observed futures options prices is minimized. We use the six different volatility specifications suggested by Amin and Morton (1994) within the HJM class of models to price interest rate claims. Since the volatilities are the only unobservables, we use these models to infer the volatilities from the market prices of Eurodollar futures options over the 1987-1998 periods. The minimized sum of squared errors in the option prices is used as the measure of accuracy of each specific model. Each model differs from the others in its ability to match the market option prices and the time required for the computation. We compare the performances of the six volatility specifications in the accuracy-versus-computation time tradeoff. We document the systematic biases between the model and market prices as a function of option type, maturity, and moneyness.

We also examine alternative numerical implementations of HJM models using the six volatility specifications. In particular, we analyze the impact on accuracy and computation time of using different numbers of time-steps. We also examine the effect of using time-steps of varying lengths within the same estimation procedure, and of ordering the time-steps in different ways.

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