Abstract
We perform Lie symmetry analysis to a zero-coupon bond pricing equation whose price evolution is described in terms of a partial differential equation (PDE). As a result, using the computer software package SYM, run in conjunction with Mathematica, a new family of Lie symmetry group and generators of the aforementioned pricing equation are derived. We furthermore compute the exact invariant solutions which constitute the pricing models for the bond by making use of the derived infinitesimal generators and the associated similarity reduction equations. Using known solutions, we again compute more solutions via group point transformations.
Highlights
In order to raise capital, firms and governments normally do so by issuing financial instruments known as bonds
We focus our attention on Lie symmetry analysis that have played a vital role in solving partial differential equation (PDE) models arising in the field of mathematical finance
Lie symmetry analysis has been performed on a zero-coupon bond pricing equation in mathematical finance
Summary
In order to raise capital, firms and governments normally do so by issuing financial instruments known as bonds. The Black–Scholes Merton model, which it was later called due to the contribution made by Merton [5], have been used as the main vehicle for pricing many financial products whose price dynamics were expressed in terms of partial differential equations After this discovery, Black–Scholes valuation framework was extended to price many other financial products, among them: bond options and other interest rate derivatives. This interest rate model embeds most known interest rate models that can be deduced for different choices of f , η, e and σ Using this functional interest rate model, it can be shown that, for an interest rate derivative such as a zero-coupon bond, its price dynamics are described in terms of the following partial differential equation vt ( x, t) +.
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