Estimating the implicit interest rate of a risky asset
type: Item
instance of: scholarly article
title: Estimating the implicit interest rate of a risky asset
zbMATH Open document ID: 0797.60036
DOI: 10.1016/0304-4149(94)90133-3
author: Raymond W. Rishel
author: Robert J. Elliott
published in: Stochastic Processes and their Applications
publication date: 1994-10-10T00:00:00Z
review text: Hidden Markov models characterize stochastic phenomena, where the Markov behavior is observed only noisily or indirectly. In a recent paper, the first author had studied filtering problems related to a Markov chain, and obtained finite-dimensional filters that provide revised estimates for the parameters in the model. In the present paper, these results are applied to a scalar model that arises in finance. The model is that of the price, \(S_ t\), of a risky asset, described by the stochastic differential equation \(dS_ t= S_ t(\rho_ t dt+ \sigma dw)\), where \(\rho_ t\) the implicit interest rate at time \(t\), behaving according to a finite state Markov chain, which is the quantity of interest for estimation. In this estimation problem, the logarithm of \(S_ t\) is used as the observation process. The results obtained allow a re-estimation of all the parameters of the model, except the volatility \(\sigma\) which is assumed to be a known constant. Among these parameters are the states of the Markov chain, and the elements of the rate matrix.
reviewed by: Tamer Başar
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 519766
zbMATH Keywords: hidden Markov models
zbMATH Keywords: finite-dimensional filters
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: finite state Markov chain
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)90133-3
OpenAlex ID: W1969786845
cites work: New finite-dimensional filters and smoothers for noisily observed Markov chains
cites work: Q3969647
cites work: Higher-order implicit strong numerical schemes for stochastic differential equations
cites work: Approximate Integration of Stochastic Differential Equations
cites work: Estimating variance from high, low and closing prices
description: scientific article; zbMATH DE number 519766