what is the heath jarrow morton hjm model 
the heath jarrow morton model hjm model is used to model forward interest rates these rates are then modeled to an existing term structure of interest rates to determine appropriate prices for interest rate sensitive securities formula for the hjm modelin general the hjm model and those that are built on its framework follow the formula 1df t t t t dt t t dw t where df t t the instantaneous forward interest rate ofzero coupon bond with maturity t is assumed to satisfythe stochastic differential equation shown above adaptedw a brownian motion random walk under therisk neutral assumption begin aligned text d f t t alpha t t text d t sigma t t text d w t textbf where text d f t t text the instantaneous forward interest rate of text zero coupon bond with maturity t is assumed to satisfy text the stochastic differential equation shown above alpha sigma text adapted w text a brownian motion random walk under the text risk neutral assumption end aligned df t t t t dt t t dw t where df t t the instantaneous forward interest rate ofzero coupon bond with maturity t is assumed to satisfythe stochastic differential equation shown above adaptedw a brownian motion random walk under therisk neutral assumption 