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# Bond Option

The models for European Option or American Option in the equity market can, in most cases, be used to price bond options without significan changes. We show how to price a bond option using ThetaML, when bond prices are observed readily or obtained analytically using a particular interest rate model.

## A European Bond Option

Consider a European put on a zero-coupon bond. We will now assume that the bond price is given (for that an interest rate model also need be defined) and design an option on the bond similar to the European Option for stocks.

model EuropeanPut_Bond
import K    "Option strike price"
import L    "Bond principal"
import Topt "Option time to maturity"
import EUR  "Discount numeraire"
import P    "underlying bond prices"
export Popt "Option Price, Empiric"

%at current time, set the option 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
Popt = E(V!)
%the ThetaML command 'theta' passes time by 'Topt' years
theta Topt
%at option maturity time T, set the option payoffs;
%the option payoffs are discounted to time 0 by the discount numeraire 'EUR'
V = max(K - L*P, 0) * EUR
end