Search results for "Forward rate"
showing 5 items of 5 documents
International evidence on alternative models of the term structure of volatilities
2009
The term structure of instantaneous volatilities (TSV) of forward rates for different monetary areas (euro, U.S. dollar and British pound) is examined using daily data from at-the-money cap markets. During the sample period (two and a half years), the TSV experienced severe changes both in level and shape. Two new functional forms of the instantaneous volatility of forward rates are proposed and tested within the LIBOR Market Model framework. Two other alternatives are calibrated and used as benchmarks to test the accuracy of the new models. The two new models provide more flexibility to adequately calibrate the observed cap prices, although this improved accuracy in replicating cap prices …
A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures
1997
The lognormal distribution assumption for the term structure of interest is the most natural way to exclude negative spot and forward rates. However, imposing this assumption on the continuously compounded interest rate has a serious drawback: rates explode and expected rollover returns are infinite even if the rollover period is arbitrarily short. As a consequence, such models cannot price one of the most widely used hedging instruments on the Euromoney market, namely the Eurodollar futures contract. The purpose of this note is to show that the problems with lognormal models result from modeling the wrong rate, namely the continuously compounded rate. If instead one models the effective an…
Toward Pricing Financial Derivatives with an IBM Quantum Computer
2021
Pricing interest-rate financial derivatives is a major problem in finance, in which it is crucial to accurately reproduce the time evolution of interest rates. Several stochastic dynamics have been proposed in the literature to model either the instantaneous interest rate or the instantaneous forward rate. A successful approach to model the latter is the celebrated Heath-Jarrow-Morton framework, in which its dynamics is entirely specified by volatility factors. In its multifactor version, this model considers several noisy components to capture at best the dynamics of several time-maturing forward rates. However, as no general analytical solution is available, there is a trade-off between t…
THE CARMA INTEREST RATE MODEL
2014
In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.
A Reconsideration of the Role of Forward-Market Arbitrage in Keynes’s and Hicks’s Theories of the Term Structure of Interest Rates
2014
International audience; This paper develops the relationship between Hicks’s and Keynes’s writings on the theory of the term structure of interest rates, and shows in detail how Hicks built on and extended Keynes’s account. According to this theory, the level of the long-term interest rate is determined by expectations of future short-term rates. Keynes’s thinking contained several notions – such as the preferred habitat of lenders, the theory of forward markets, and risk-premiums – which Hicks used to give a more complete theory of the term structure of interest rates. Besides implementing these notions in his own theory, Hicks introduced the concepts of the preferred habitat of borrowers,…