Search results for "Market model"
showing 10 items of 10 documents
Initial Enlargement in a Markov chain market model
2011
Enlargement of filtrations is a classical topic in the general theory of stochastic processes. This theory has been applied to stochastic finance in order to analyze models with insider information. In this paper we study initial enlargement in a Markov chain market model, introduced by Norberg. In the enlarged filtration, several things can happen: some of the jumps times can be accessible or predictable, but in the original filtration all the jumps times are totally inaccessible. But even if the jumps times change to accessible or predictable, the insider does not necessarily have arbitrage possibilities.
Lecture Notes in Economics and Mathematical Systems: Preface
2007
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…
Role of noise in a market model with stochastic volatility
2006
We study a generalization of the Heston model, which consists of two coupled stochastic differential equations, one for the stock price and the other one for the volatility. We consider a cubic nonlinearity in the first equation and a correlation between the two Wiener processes, which model the two white noise sources. This model can be useful to describe the market dynamics characterized by different regimes corresponding to normal and extreme days. We analyze the effect of the noise on the statistical properties of the escape time with reference to the noise enhanced stability (NES) phenomenon, that is the noise induced enhancement of the lifetime of a metastable state. We observe NES ef…
Volatility Effects on the Escape Time in Financial Market Models
2008
We shortly review the statistical properties of the escape times, or hitting times, for stock price returns by using different models which describe the stock market evolution. We compare the probability function (PF) of these escape times with that obtained from real market data. Afterwards we analyze in detail the effect both of noise and different initial conditions on the escape time in a market model with stochastic volatility and a cubic nonlinearity. For this model we compare the PF of the stock price returns, the PF of the volatility and the return correlation with the same statistical characteristics obtained from real market data.
Hitting Time Distributions in Financial Markets
2006
We analyze the hitting time distributions of stock price returns in different time windows, characterized by different levels of noise present in the market. The study has been performed on two sets of data from US markets. The first one is composed by daily price of 1071 stocks trade for the 12-year period 1987-1998, the second one is composed by high frequency data for 100 stocks for the 4-year period 1995-1998. We compare the probability distribution obtained by our empirical analysis with those obtained from different models for stock market evolution. Specifically by focusing on the statistical properties of the hitting times to reach a barrier or a given threshold, we compare the prob…
The introduction of the Euro and its effects on portfolio decisions
2010
Abstract Examining investment behavior related to the Euro introduction, we address the relevance of different investment determinants. With the advent of the currency union two potential sources of portfolio reallocation can be distinguished: First, the diminishment of exchange rate risk and transaction costs within the EMU. Second, the increase of correlation of EMU returns so that diversification benefits decreased. We test for structural breaks in the holdings of German investors and estimate a market model to account for the two effects. A significant decrease in national and an increase in EMU and rest-of-the-world investments can be observed. Comparing the observed holdings with benc…
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.