Package webcab.lib.finance.bonds

Model the pricing and risk analytics of interest rate cash and derivative products.

See:
Description

Class Summary

CalculatingZeroRates	Within this class we offer: Evaluation of the zero rate for a given maturity from the corresponding zero bond.
DurationConvexity	Provides methods for the evaluation and application of the notions of the duration and convexity of a bond.
FixedInterestBonds	Within this class we consider what is generally referred to as fixed-interest bonds.
ForwardRates	Within this class we provide methods for the evaluation of forward rates and forward rate agreements.
Interest	Evaluation of interest bearing investments and convertion between compounded conventions.
TreasuryPrice	Offers functionality related to the evaluation of the price and yield of a government backed bond issued in the local currency.

Exception Summary

NoSolutionException

This is an exception thrown when a solution to the equation cannot be found.

Package webcab.lib.finance.bonds Description

Model the pricing and risk analytics of interest rate cash and derivative products. We cover the fundamental theory of bonds including: Treasury bonds, Yield/Pricing, Zero Curve, Forward rates/FRAs, Duration and Convexity. We also cover the topics of Fixed-Interest bonds and interest based calculations.

Details of the Functionality Offered

The Bonds module implements the following functionality:

Fundamental Theory of Bonds

• Pricing and Yield
• Pricing - Discounted cash flows model in accordance with the risk free interest rate. We include an implementation of the pricing market convention as offered within Excel's PRICE function and the DEC page of a Bloomberg Terminal.
• Yield to Maturity (YTM) - the YTM (also known as the Internal rate of Return (IRR) can be evaluated for any bond where the market price and the coupon payments until maturity are known. We include an implementation of the YTM market convention as offered within Excel's YIELD function and used within Bloomberg Terminals.
• Treasury Price - evaluate the price of a Treasury bond from the Treasury zero rates.
• Bond Yield - returns the yield of a Treasury bond when the price and coupons are known.
• Par Yield - we provide methods for calculating the Par Yield where the number of yearly payments and the annuity may vary.
• Constructing the Zero Rate Curve - using the technique known as bootstrapping and linear interpolation we our able to construct the zero rate curve.
• Forward Rates and FRAs
• Evaluation of Forward Rates - the forward rate for a given period can be evaluated from the zero rates at the start and end of that period.
• Forward Rate Agreements (FRAs) - we provide a method which shows to value of a FRA and the cash flows when the contract is settled.
• Duration and Convexity
• Duration - the Duration of a bond, bond portfolio, interest rate future and the rescaling of Duration according to different interest compounding conventions.
• Duration based hedging - Duration-Hedge Ratio, Convexity and its use in hedging interest rate risk.

Yield of Fixed-Interest Bonds on Interest payment dates

• Simple Yield to Maturity - As used in Japanese bond markets to calculate the yield to maturity (simple yield to maturity) rather than the usual compound interest method (redemption yield).
• Gross Redemption Yield - For an interest payment date the gross redemption yield is given. We follow the convention in the US and UK to calculate and express redemption yield as a yield per annum, convertible half-yearly.
• Net Redemption Yield - The gross redemption yield on an interest payment date taking into account the investors income tax position.
• Holding period return - The yield over the period the stock was held by the investor according to US and UK interest payment conventions.
• Rate of Payments - Knowing the series of payments of one per interval payable in arrears for a number of intervals.
• Series of Payments - Knowing the rate of interest per interval and the number of intervals.

In implementing the above procedures it has often be necessary to find solutions of polynomial equations. In order to find these solutions we have used the following techniques:

• Interval Bisection Method - A robust method that always finds a solution or a singularity inside a bracketed interval.
• Newton-Raphson Method - Given a first approximation to a root and the differential of the function this procedure will always produce a solution. We implement this procedure for polynomial functions of one variable.

Business Classes contained with the Future module

• CalculatingZeroRates - Evaluation of the zero rate from discrete set of known zero rates, Bootstrap methods, and the construction of the zero rate curve.
• DurationConvexity - We provide methods for the evaluation and application of the duration and convexity of a bond.
• FixedInterestBonds - Considers (in general) situations where there exists closed formulae for the redemption yield, holding period, interest yield, yield to maturity and current price of a fixed-interest bond.
• ForwardRates - We provide methods for the evaluation of forward rates and forward rate agreements.
• TreasuryPrice - We offer functionality related to the evaluation of the price and yield of a government backed bond (i.e. Treasury bond) issued in the local currency.