Bond Pricing

I have coded the mathematics in C. Call the code in Python.

For the curious reader...

What Is a Bond?

A bond is a loan made by an investor to a borrower. The borrower is usually a business or a government.

When you buy a bond, you're just lending money in exchange for interest payments and the return of the amount you paid for the bond at an agreed future date.

Key Components:

Face Value ( $F$ ): The amount repaid at the agreed future date. This agreed future date is when the bond matures.
Coupon Rate ( $c$ ): The interest rate which the bond pays you.
Coupon Payment ( $C$ ): $C = c \times F$ This is just the face value of the bond multiplied by the interest rate offered. These are typically made semi-annually. If so, then we tweak our formula ever so slightly:

C = \frac{c}{2} \times F

Maturity ( $T$ ): Number of years until repayment.
Yield to Maturity (YTM) ( $r$ ): Effective annual return if held to maturity. This is used to calculate something financial geeks know as the discount rate.

Bond Pricing Formula

The value of a bond is the present value of all future coupon payments and the face value:

P = \sum_{t=1}^{T} \frac{C}{(1 + r)^t} + \frac{F}{(1 + r)^T}

Where:

$P$ = price of the bond
$C$ = coupon payment
$F$ = face value
$r$ = discount rate / yield
$T$ = time to maturity

Prices of bonds and their yields move inversely:

If interest rates rise, bond prices fall.
If interest rates fall, bond prices rise.

Think about it.

Take a bond which is priced at £1000.

Let’s say interest rates in the economy rise to 7%, but before they were 5%.

You purchased a bond at 5% interest.

But since interest rates are now 7%...

Newly issued bonds now offer £70 per year instead of your £50.

So ask yourself:

Why would someone buy your bond paying £50 when they can get £70 from a new one?

They won’t.

Unless your bond is cheaper.

Why are Bonds such a big deal?

Bonds are famous for being a nice diversification of risk in a portfolio.

Bonds guarantee returns.

Stocks and other high-risk investments, such as options, do not.

What Bonds exist?

Government Bonds (e.g. U.S. Treasuries, UK Gilts, German Bunds)
Corporate Bonds

These two are the most common. Others that are not so common, but exist, are:

Municipal Bonds (issued by local governments)
Zero-Coupon Bonds (sold at a discount, no coupons)

Bonds are very important. They are useful for governments to fund infrastructure, for companies to grow, and for investors to earn steady, guaranteed returns.

Go get yourself a Bond. Not James Bond.