Consider the following general formulation of the quadratic term structure model (Jamshidian, 1996), where the short rate is defined by 

for some smooth deterministic vector α(t), matrices β(t) and σ(t). 

(a) Show that the governing partial differential equation for the price of a contingent claim C(x,t) is given by

(b) Show that the price of a T -maturity discount bond admits the following exponential affine form 

where the matrix BT (t), vector bT (t) and scalar cT (t) are governed by the following coupled system of ordinary differential equations: 

Transcribed Image Text:

= ½x(t)" Q(1)x(1) +g(t)” x(t)+ ƒ (1), r(t) =