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# Bond

## Description

A bond is a **debt security** in which the authorized issuer owes the holder a debt and is obliged to pay the principal and interest (also known as the coupon) at some fixed dates. There is a large set of different bond types that vary in terms of both the principal and coupon payments.

We will look at regular bonds that pay coupon and principal according to a fixed schedule.

## ThetaML implementation for coupon bond prices

The model `CouponBond` prices a coupon paying bond. The discount numeraire `EUR` can be computed with either constant interest rates as in Discounting or stochastic interest rates simulated with the CIR model, Vasicek model or the Hull-White model.

model CouponBond import c_r "Coupon rate" import N "Notional principal" import EUR "Discount numeraire" import T "Bond maturity" export P "Bond price" %at current time, set the bond value to have the same expected discounted %value as the variable 'V'; the ThetaML future operator '!' accompanying the %variable 'V' acts like a function on 'V', such that the values of 'V' %at current time remain to be determined at a later instance when 'V' %is assigned some values P = E(V!) %initialize the variable 'sum' to 0 sum = 0 %loop 'T' times loop T %the ThetaML command 'theta' passes time by '1' years theta 1 %update the sum sum = sum + c_r * N * EUR end V = sum end