Taylor Series Approximations (Solved Example)

1. Context

In this solved example, we explore how Taylor Series approximations work and how they are applied to the world of finance. We do not do a rigorous and formal proof of Taylor Series expansions (approximations). Rather, we follow a step-wise solved example that helps us rationalize how these approximations (and their functional form) are arrived at, so that we do not have to memorize anything.

2. Solved Example

A Zero Coupon Bond (ZCB) has the foll. features:

Face Value\$100
Yield (Continuously Compounded)5%
Maturity30 years

If the fair value of this ZCB at any time $t: 0 \leq t \leq 30$ is given by $f(t)$, based on the above:

  1. Calculate $𝑓(16), 𝑓’ (16), 𝑓” (16)$.
  2. A linear approximation to $𝑓(16.5)$.
  3. A quadratic approximation to $𝑓(16.5)$.

3. Video