Description
General Interest derivatives pricing framework: set contract, set
vol/price/interest models and run MC. We also cover: Treasury's, Price/Yield,
Zero Curve, Fixed-Interest bonds, Forward rates/FRAs, Duration and Convexity.
Product Details
WebCab Bonds implements the following functionality:
General Interest Derivatives Pricing Framework
General Pricing Framework offers the following predefined Models and
Contracts:
- Contracts: Asian Option, Binary Option, Cap, Coupon Bond, Floor, Forward Start stock option,
Lookback Option, Ladder Option, Vanilla Swap, Vanilla Stock Option, Zero Coupon Bond, Barrier Option,
Parisian Option, Parasian Option, Forward and Future.
- Interest Rate Models: Constant Spot Rate, Constant (in time) Yield curve,
One factor stochastic models (Vasicek, Black-Derman-Toy (BDT), Ho & Lee, Hull and White),
Two factor stochastic models (Breman & Schwartz, Fong & Vasicek, Longstaff & Schwartz),
Cox-Ingersoll-Ross Equilibrium model, Spot rate model with automatic yield (Ho & Lee, Hull & White),
Heath-Jarrow-Morton forward rate model, Brace-Gatarek-Musiela (BGM) LIBOR market model.
- Price Models: Constant price model, General deterministic price model,
Lognormal price model, Poisson price model.
- Volatility Models: Constant Volatility Models, General Deterministic Volatility model,
Hull & White Stochastic model of the Variance, Hoston Stochastic Volatility model.
Once the contract and the price/interest/vol model combination has been set you
able to run the Monte Carlo Pricing Engine which allows:
- Evaluate Price: Evaluate price estimate accordance to number of iterations or maximum expected error
- Estimate Error: Evaluate the standard deviation of the price estimate, and the minimum/maximum expected
price for a given confidence level.
Fundamental Theory of Bonds
- Price 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.
Interest Calculations
- Exponents and Series - Law of Exponents, Arithmetic Progression, Finite/Infinite Geometric Series
- Simple interest - a deposits value, Real worth, Real return
- Compound interest - Accumulated values, Real worth, Real return, Depreciation
- Effective and nominal interest - Real return, Force of interest
- Accumulated values of annuity-certain - Accumulated annuity certain in arrears, Accumulated annuity
certain in advance
- Present values
- Present value of annuity-certain
- Yield - Internal rate, Real and nominal
- Real returns - Bonds, Rate of return
Technology Aspects
This product also contains the following features:
- GUI Bundle - we bundle a suite of graphical user interface JavaBean
components allowing the developer to plug-in a wide range of GUI functionality
(including charts/graphs) into their client applications.
- JDBC Mediator - A J2SE Component which mediates between a J2SE component,
its J2SE Clients and the Database server. The JDBC Mediator J2SE classes are
a convenient way of enhancing all financial and mathematical specific
methods with JDBC-based functionality. Check the jdbc subpackage of
every J2SE class for JavaDocs documentation.
- Web Application Example - A Java WAR file which contains a JSP example that
makes use of the functionality provided by our J2SE Component.
- Synthetic JDBC - The JDBC functionality provided by the Web Application
example included within this package. This Web Application is an example of
how to make a JSP client using our J2SE Component while manually
implementing the JDBC code. The JSP Application applies J2SE methods to
certain rows from the database and lists the output in HTML format.
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