Abstract
In this paper, we prove that the price of a defaultable bond, under a Vasicek short rate dynamics coupled with a Cox-Ingersoll-Ross default intensity model, is a real analytic function, in a neighborhood of the origin, of the correlation parameter between the Brownian motions driving the processes, used to express the dependence between the short rate and the default intensity of the bond issuer. Employing conditioning and a change of numéraire technique, we obtain a manageable representation of the bond price in this non-affine model which allows us to control its derivatives and assess the convergence of the series. By truncating the expansion at the second order, a quadratic approximation formula for the price is then provided. Finally, practical applications of the result are highlighted by performing a numerical comparison with alternative pricing methodologies.
Highlights
It has always been known that credit risk is one of the most important aspects of fixed income markets, for this reason bond pricing models must incorporate it in a meaningful way allowing, at the same time, for fast and efficient calibration of the model parameters to market data
We prove that the price of a defaultable bond, under a Vasicek short rate dynamics coupled with a Cox-Ingersoll-Ross default intensity model, is a real analytic function, in a neighborhood of the origin, of the correlation parameter between the Brownian motions driving the processes, used to express the dependence between the short rate and the default intensity of the bond issuer
Employing conditioning and a change of numéraire technique, we obtain a manageable representation of the bond price in this non-affine model which allows us to control its derivatives and assess the convergence of the series
Summary
It has always been known that credit risk is one of the most important aspects of fixed income markets, for this reason bond pricing models must incorporate it in a meaningful way allowing, at the same time, for fast and efficient calibration of the model parameters to market data. We study a market where the default-adjusted short rate process falls out of the affine class and so the previous implication breaks down This happens, when assuming that the short rate follows a Vasicek dynamics, while the intensity follows a CIR dynamics, with correlated driving Brownian motions. We denote by P d(t, T ) the current price of a defaultable bond (T being the maturity) with zero fractional recovery This price is going to depend on several parameters appearing in the equations describing the evolution of the state variables, the interest rate and the intensity. This opens up the possibility to evaluate the price P d(t, T ), employing a power series expansion in the correlation parameter around the origin If this series converges to the actual price, one can rightfully use it to derive an approximate formula up to any desired order of accuracy. The main strength of our approach lies in the possibility to improve the error estimate by increasing the order of the approximation, by virtue of the convergence result
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
