how the vasicek interest rate model works
predicting how interest rates evolve can be difficult investors and analysts have many tools available to help them figure out how they ll change over time in order to make well informed decisions about how their investments and the economy the vasicek interest rate model is among the models that can be used to help estimate where interest rates will go as noted above the vasicek interest rate model which is commonly referred to as the vasicek model is a mathematical model used in financial economics to estimate potential pathways for future interest rate changes as such it s considered a stochastic model which is a form of modeling that helps make investment decisions it outlines the movement of an interest rate as a factor composed of market risk time and equilibrium value the rate tends to revert toward the mean of these factors over time the model shows where interest rates will end up at the end of a given period of time by considering current market volatility the long run mean interest rate value and a given market risk factor 1the vasicek interest rate model values the instantaneous interest rate using the following equation drt a b rt dt dwtwhere w random market risk represented bya wiener process t time perioda b rt expected change in the interest rateat time t the drift factor a speed of the reversion to the meanb long term level of the mean volatility at time t begin aligned dr t a b r t dt sigma dw t textbf where w text random market risk represented by text a wiener process t text time period a b r t text expected change in the interest rate text at time t text the drift factor a text speed of the reversion to the mean b text long term level of the mean sigma text volatility at time t end aligned drt a b rt dt dwt where w random market risk represented bya wiener process t time perioda b rt expected change in the interest rateat time t the drift factor a speed of the reversion to the meanb long term level of the mean volatility at time t the model specifies that the instantaneous interest rate follows the stochastic differential equation where d refers to the derivative of the variable following it in the absence of market shocks i e when dwt 0 the interest rate remains constant rt b when rt b the drift factor becomes positive which indicates that the interest rate will increase toward equilibrium the vasicek model is often used in the valuation of interest rate futures and may also be used in solving for the price of various hard to value bonds special considerationsas mentioned earlier the vasicek model is a one or single factor short rate model a single factor model is one that only recognizes one factor that affects market returns by accounting for interest rates in this case market risk is what affects interest rate changes this model also accounts for negative interest rates 2 rates that dip below zero can help central bank authorities during times of economic uncertainty although negative rates aren t commonplace they have been proven to help central banks manage their economies for instance denmark s central banks lowered interest rates below zero in 2012 european banks followed two years later followed by the bank of japan boj which pushed its interest rate into negative territory in 2016 3vasicek interest rate model vs other modelsthe vasicek interest rate model isn t the only one factor model that exists the following are some of the other common models 