Premium
VOLATILITY STRUCTURES OF FORWARD RATES AND THE DYNAMICS OF THE TERM STRUCTURE 1
Author(s) -
Ritchken Peter,
Sankarasubramanian L.
Publication year - 1995
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.1995.tb00101.x
Subject(s) - volatility (finance) , markov chain , state variable , term (time) , markov process , yield curve , short rate , stochastic volatility , econometrics , statistical physics , mathematics , computer science , interest rate , economics , statistics , finance , physics , quantum mechanics , thermodynamics
For general volatility structures for forward rates, the evolution of interest rates may not be Markovian and the entire path may be necessary to capture the dynamics of the term structure. This article identifies conditions on the volatility structure of forward rates that permit the dynamics of the term structure to be represented by a two‐dimensional state variable Markov process. the permissible set of volatility structures that accomplishes this goal is shown to be quite large and includes many stochastic structures. In general, analytical characterization of the terminal distributions of the two state variables is unlikely, and numerical procedures are required to value claims. Efficient simulation algorithms using control variates are developed to price claims against the term structure.