New solutions to the bond-pricing equation via Lieʹs classical method

Using Lieʹs classical method of group invariants, we provide new and simple solutions to the bond-pricing partial differential equation. All of our solutions satisfy the final condition for the bond price. In finding these solutions, we used one-factor interest-rate modelling, in which our short-term interest rate follows a random walk which allows the volatility of interest rate changes to be highly sensitive to the level of riskless rate, and the market price of risk is arbitrary. As well, in one of our simple solutions, the nonlinear drift of our risk-neutral interest rate contains an arbitrary function of time, which may be freely chosen.