In general, the logarithmic returns of asset prices are not normally distributed. Brownian motion and normal distribution have been widely used in the Black-Scholes-Merton bond framework to model the return of assets. Merton has provided a formula for the valuation of a zero coupon bond where the asset price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. This paper applies jump diffusion processes to derive some bond parameters, these are equity and default probability, when the asset prices have extreme values.