The Heath Jarrow Morton is used for modelling fixed income markets and has closed form solutions for specific volatilities. The known methods are different such that the approximation of the integral arbitrage-free drift is constructed using Euler-type approach schemes discretization. A Java applet is developed to price a caplet using a different numerical approach based on a functional backward Kolmogorov equation with two proportional volatility models. Students pursuing financial engineering and interest rate derivative traders can use this book as a manual for pricing instruments, specifically ,caplets and floorlets.