BermudanSwaption: 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, ts, swaptionMaturities, swapTenors,
volMatrix)

Value

BermudanSwaption , if there are sufficient swaption vols to fit an affine model, 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

If there are insufficient swaption vols to calibrate it throws a warning and returns NULL

Arguments

params

A list specifying the tradeDate (month/day/year), settlementDate, startDate, maturity, 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.

ts

A term structure built with DiscounCurve or 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.

Author

Dominick Samperi

Details

This function was update for QuantLib Version 1.7.1 or later. It introduces support for fixed-income instruments in RQuantLib. It implements the full function and should work in most cases as long as there are suuficient swaption vol data points to fit the affine model. At least 5 unique points are required. The data point search attempts to find 5 or more points with one being the closet match in terms in of expiration and maturity.

See the SabrSwaption function for an alternative.

References

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

For information about QuantLib see https://www.quantlib.org/.

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

Examples

Run this code

if (FALSE) {
# This data replicates sample code shipped with QuantLib 0.3.10 results
params <- list(tradeDate=as.Date('2002-2-15'),
               settleDate=as.Date('2002-2-19'),
               startDate=as.Date('2003-2-19'),
               maturity=as.Date('2008-2-19'),
               dt=.25,
               payFixed=TRUE,
               strike=.05,
               method="G2Analytic",
               interpWhat="discount",
               interpHow="loglinear")
setEvaluationDate(as.Date('2002-2-15'))
# Market data used to construct the term structure of interest rates
tsQuotes <- list(d1w  =0.05,
                 # 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  =0.05,
                 s5y  =0.05,
                 s10y =0.05,
                 s15y =0.05)

times=seq(0,14.75,.25)
swcurve=DiscountCurve(params,tsQuotes,times)
# 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)

volMatrix <- matrix(
    c(rep(.20,25)),
    ncol=5, byrow=TRUE)
# Price the Bermudan swaption
pricing <- BermudanSwaption(params, ts=.05,
                            swaptionMaturities, swapTenors, volMatrix)
summary(pricing)
}

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