Evaluating The Use Of Taylor’s Formula To Approximate Bond Value.

Evaluating the use of Taylor’s Formula to approximate bond value.

This essay will explore the formulation and how the formula is used to approximate bond value,

answering the question ’How do we approximate a function to properly estimate the behaviour it

describes?’ (Dym, 2004, pg. 71).

The formulation of Taylor’s formula branches from the idea of approximating any continuous

function, with derivatives. In this case, the function would be the change in price of the bond

(∆;P ).A bond, in simple words, is a loan that you give to an organisation, and in return, they pay

back the initial loan and a certain percentage of it as interest. The term ’derivatives’ comes from

the concept of differentiation and are represented as ∂;P

∂;y and ∂;2P ∂;y2 . ;

It is necessary here to clarify what is meant by differentiation, it is a mathematical concept that describes how a function changes

when the input value (∆;y) in Figure 1 changes by a minimal amount.

A use of Taylor’s Formula is to approximate the value of a bond at the end of the duration

period. Kaur (2020) uses the term ’crucial’ to describe the importance of Taylor’s formula when

used to approximate the change in price of a bond. This is supported by calculations performed to

produce the percentage change in the value of the bond. The change in price calculated using Tay-

lor’s formula is −;8.99%, compared to the actual change of −;9.01% whereas using another method, a

change of −;9.54% was predicted suggesting that the use of Taylor’s Formula was much more precise.

On the contrary, Taylor’s Formula may understate the change in the price of a bond (Winkel-

mann, 1989). Essentially, when the interest rate increases, the value of the bond should decrease

and vice versa. Figure 2 shows that for a shock of −;300, representing a decrease in the interest rate

by −;3.00%, Taylor’s formula underestimates the change in the price of the bond when compared

to the Valuation Formula. The main reason for this is that Taylor’s Formula is not able to handle

significant changes in the interest rate. However, ’It is not immediately clear that the qualitative

judgments provided ... are necessarily invalid’ (Winkelmann, 1989). This means that both Kaur

(2020) and Winkelmann (1989) signify that the use of Taylor’s Formula has both advantages and

disadvantages. Therefore the use of Taylor’s Formula to calculate bond value would produce a

feasible solution in some cases.

To conclude, Taylor’s Formula has its strengths and weaknesses, but it still is a great option for

estimating the value of a bond, allowing for risk management to some extent. It would be optimal

to use in cases where the interest rate is constant.