The Hull-White convertible bond pricing model assumes that the short-term interest rate process follows a SDE of the Hull-White form, and that the stock’s price process follows geometric Brownian motion with drift.

The Brownian bridge algorithm generates points on a path sequentially, starting from the initial point and progressing toward the end. However, the symmetry of the formula for the intermediate point with respect to the initial and final points and the recursive nature of the algorithm suggest that the generator may work better.

A convertible bond with exchangeable feature, which can be converted into a stock issued by a party different from the bond issuer. Assume that the stock conversion is vulnerable. If the bond-issuer has defaulted by a time, t , then the stock price is zero. If, on the other hand, the bond-issuer has not defaulted by time t , then the stock price is given by St or 0.

An early amortization event is a set of circumstances specified in the offering memorandum, which if it were to occur, would effectively move the liquidation date forward to the time of its occurrence. Generally, early amortization is triggered by the failure of the pool assets to remain within a certain range of value or quality