A Class of Heath-jarrow-morton Models in Which the Unbiased Expectations Hypothesis Holds
نویسنده
چکیده
The unbiased expectations hypothesis states that forward rates are unbiased estimates for future short rates. Cox, Ingersoll and Ross 1] conjectured that this hypothesis should be inconsistent with the absence of arbitrage possibilities. Using the framework of Heath, Jar-row and Morton 4] we show that this is not always the case. The unbiased expectations hypothesis together with the existence of an equivalent martingale measure is equivalent to a certain condition on the volatilities of the forward rates.
منابع مشابه
A Class of Heath-jarrow-morton Term Structure Models with Stochastic Volatility
This paper considers a class of Heath-Jarrow-Morton term structure models with stochastic volatility. These models admit transformations to Markovian systems, and consequently lend themselves to well-established solution techniques for the bond and bond option prices. Solutions for certain special cases are obtained, and compared against their non-stochastic counterparts.
متن کاملThe Heath - Jarrow - Morton Framework
The Heath-Jarrow-Morton framework refers to a class of models that are derived by directly modeling the dynamics of instantaneous forward-rates. The central insight of this framework is to recognize that there is an explicit relationship between the drift and volatility parameters of the forward-rate dynamics in a no-arbitrage world. The familiar short-rate models can be derived in the HJM fram...
متن کاملTerm Structure Models Driven by Wiener Process and Poisson Measures: Existence and Positivity
In the spirit of [4], we investigate term structure models driven by Wiener process and Poisson measures with forward curve dependent volatilities. This includes a full existence and uniqueness proof for the corresponding Heath–Jarrow–Morton type term structure equation. Furthermore, we characterize positivity preserving models by means of the characteristic coefficients, which was open for jum...
متن کاملMarkovian Term Structure Models in Discrete Time
In this article we discuss Markovian term structure models in discrete time and with continuous state space. More precisely, we are concerned with the structural properties of such models if one has the Markov property for a part of the forward curve. We investigate the two cases where these parts are either a true subset of the forward curve, including the short rate, or the entire forward cur...
متن کاملExplicit Bond Option and Swaption Formula in Heath-jarrow-morton One Factor Model
We present an explicit formula for European options on coupon bearing bonds and swaptions in the Heath-Jarrow-Morton (HJM) one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds. We provide also an explicit way to compute the hedging ratio (∆) to hedge the option with its underlying.
متن کامل