CHAPTER 5
An Essay on Stochastic
Volatility and the
Yield Curve
Raymond Théoret, Pierre Rostan and,
Abdeljalil El-Moussadek∗5.1 INTRODUCTION
In this chapter we consider the issue of forecasting the stochastic volatility
and the yield curve. These two concepts are very important in financial
engineering, especially in risk management. Forecasting stochastic volatility
is indeed an essential ingredient in VaR computations, and for immunizing
bond portfolios a prediction of the yield curve is asine qua non.
Volatility has many avatars. Financial theory has evolved from the con-
cept of historical volatility to the concept of stochastic volatility. Between
these concepts, the apparition of conditional volatility, introduced by Engle
(1982) to forecast the volatility of inflation, among others, was perhaps
an accident in financial theory. Anyway, there is a relation between con-
ditional volatility and stochastic volatility which is confusing, even in
financial theory. Nelson (1990) was the first to show that ARCH models con-
verge weakly in distribution to continuous stochastic volatility diffusion
∗The authors want to thank Mr François-Éric Racicot, PhD, Professor of Finance in the Depart-
ment of Administrative Sciences at the University of Quebec (Outaouais) for his help and
numerous suggestions.
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