BermudanSwaption {RQuantLib} | R Documentation

## Bermudan swaption valuation using several short-rate models

### Description

`BermudanSwaption` prices a Bermudan swaption with specified strike and maturity (in years), after calibrating the selected short-rate model to an input swaption volatility matrix. Swaption maturities are in years down the rows, and swap tenors are in years along the columns, in the usual fashion. It is assumed that the Bermudan swaption is exercisable on each reset date of the underlying swaps.

### Usage

    BermudanSwaption(params, tsQuotes, swaptionMaturities, swapTenors,
    volMatrix)

### Arguments

`params` | A list specifying the `tradeDate` (month/day/year), `settlementDate`, `payFixed` flag, `strike`, pricing `method`, and curve construction options (see Examples section below). Curve construction options are `interpWhat` (possible values are `discount`, `forward`, and `zero`) and `interpHow` (possible values are `linear`, `loglinear` , and `spline`). Both `interpWhat` and `interpHow` are ignored when a flat yield curve is requested, but they must be present nevertheless. The pricing method can be one of the following (all short-rate models):
`G2Analytic` | G2 2-factor Gaussian model using analytic formulas.
`HWAnalytic` | Hull-White model using analytic formulas.
`HWTree` | Hull-White model using a tree.
`BKTree` | Black-Karasinski model using a tree.
`tsQuotes` | Market observables needed to construct the spot term structure of interest rates. A list of name/value pairs. See the help page for `DiscountCurve` for details.
`swaptionMaturities` | A vector containing the swaption maturities associated with the rows of the swaption volatility matrix.
`swapTenors` | A vector containing the underlying swap tenors associated with the columns of the swaption volatility matrix.
`volMatrix` | The swaption volatility matrix. Must be a 2D matrix stored by rows. See the example below.

### Details

This function is based on `QuantLib` Version 0.3.10. It introduces support for fixed-income instruments in `RQuantLib`.

At present only a small number of the many parameters that can be set in `QuantLib` are exposed by this function. Some of the hard-coded parameters that apply to the current version include: day-count conventions, fixing days (2), index (Euribor), fixed leg frequency (annual), and floating leg frequency (semi-annual). Also, it is assumed that the swaption volatility matrix corresponds to expiration dates and tenors that are measured in years (a 6-month expiration date is not currently supported, for example).

Given the number of parameters that must be specified and the care with which they must be specified (with no defaults), it is not practical to use this function in the usual interactive fashion.

The simplest approach is simply to save the example below to a file, edit as desired, and `source` the result. Alternatively, the input commands can be kept in a script file (under Windows) or an Emacs/ESS session (under Linux), and selected parts of the script can be executed in the usual way.

Fortunately, the C++ exception mechanism seems to work well with the R interface, and `QuantLib` exceptions are propagated back to the R user, usually with a message that indicates what went wrong. (The first part of the message contains technical information about the precise location of the problem in the `QuantLib` code. Scroll to the end to find information that is meaningful to the R user.)

### Value

`BermudanSwaption` returns a list containing calibrated model paramters (what parameters are returned depends on the model selected) along with:

`price` | Price of swaption in basis points (actual price equals `price` times notional divided by 10,000)
`ATMStrike` | At-the-money strike
`params` | Input parameter list

### Author(s)

Dominick Samperi

### References

Brigo, D. and Mercurio, F. (2001) Interest Rate Models: Theory and Practice, Springer-Verlag, New York.

For information about `QuantLib` see http://quantlib.org.

For information about `RQuantLib` see http://dirk.eddelbuettel.com/code/rquantlib.html.

### See Also

`DiscountCurve`

### Examples

    # This data is taken from sample code shipped with QuantLib 0.3.10.
    params <- list(tradeDate=as.Date('2002-2-15'),
                   settleDate=as.Date('2002-2-19'),
                   payFixed=TRUE,
                   strike=.06,
                   method="G2Analytic",
                   interpWhat="discount",
                   interpHow="loglinear")

    # Market data used to construct the term structure of interest rates
    tsQuotes <- list(d1w  =0.0382,
                     d1m  =0.0372,
                     fut1=96.2875,
                     fut2=96.7875,
                     fut3=96.9875,
                     fut4=96.6875,
                     fut5=96.4875,
                     fut6=96.3875,
                     fut7=96.2875,
                     fut8=96.0875,
                     s3y  =0.0398,
                     s5y  =0.0443,
                     s10y =0.05165,
                     s15y =0.055175)

    # Use this to compare with the Bermudan swaption example from QuantLib
    #tsQuotes <- list(flat=0.04875825)

    # Swaption volatility matrix with corresponding maturities and tenors
    swaptionMaturities <- c(1,2,3,4,5)

    swapTenors <- c(1,2,3,4,5)

    volMatrix <- matrix(
                        c(0.1490, 0.1340, 0.1228, 0.1189, 0.1148,
                          0.1290, 0.1201, 0.1146, 0.1108, 0.1040,
                          0.1149, 0.1112, 0.1070, 0.1010, 0.0957,
                          0.1047, 0.1021, 0.0980, 0.0951, 0.1270,
                          0.1000, 0.0950, 0.0900, 0.1230, 0.1160),
                        ncol=5, byrow=TRUE)

    # Price the Bermudan swaption
    pricing <- BermudanSwaption(params, tsQuotes,
                                swaptionMaturities, swapTenors, volMatrix)
    summary(pricing)

[Package RQuantLib version 0.2.7 Index]