RQuantLib (version 0.4.3)

DiscountCurve: Returns the discount curve (with zero rates and forwards) given times

Description

DiscountCurve constructs the spot term structure of interest rates based on input market data including the settlement date, deposit rates, futures prices, FRA rates, or swap rates, in various combinations. It returns the corresponding discount factors, zero rates, and forward rates for a vector of times that is specified as input.

Usage

DiscountCurve(params, tsQuotes, times, legparams)

Arguments

params

A list specifying the tradeDate (month/day/year), settleDate, forward rate time span dt, and two curve construction options: interpWhat (with possible values discount, forward, and zero) and interpHow (with possible values linear, loglinear, and spline). spline here means cubic spline interpolation of the interpWhat value.

tsQuotes

Market quotes used to construct the spot term structure of interest rates. Must be a list of name/value pairs, where the currently recognized names are:

flat

rate for a flat yield curve

d1w

1-week deposit rate

d1m

1-month deposit rate

d3m

3-month deposit rate

d6m

6-month deposit rate

d9m

9-month deposit rate

d1y

1-year deposit rate

s2y

2-year swap rate

s3y

3-year swap rate

s4y

4-year swap rate

s5y

5-year swap rate

s6y

6-year swap rate

s7y

7-year swap rate

s8y

8-year swap rate

s9y

9-year swap rate

s10y

10-year swap rate

s12y

12-year swap rate

s15y

15-year swap rate

s20y

20-year swap rate

s25y

25-year swap rate

s30y

30-year swap rate

s40y

40-year swap rate

s50y

50-year swap rate

s60y

60-year swap rate

s70y

70-year swap rate

s80y

80-year swap rate

s90y

90-year swap rate

s100y

100-year swap rate

fut1--fut8

3-month futures contracts

fra3x6

3x6 FRA

fra6x9

6x9 FRA

Here rates are expected as fractions (so 5% means .05). If flat is specified it must be the first and only item in the list. The eight futures correspond to the first eight IMM dates. The maturity dates of the instruments specified need not be ordered, but they must be distinct.

times

A vector of times at which to return the discount factors, forward rates, and zero rates. Times must be specified such that the largest time plus dt does not exceed the longest maturity of the instruments used for calibration (no extrapolation).

legparams

A list specifying the dayCounter the day count convention for the fixed leg (default is Thirty360), and fixFreq, fixed coupon frequecny (defualt is Annual), floatFreq, floating leg reset frequency (default is Semiannual).

Value

DiscountCurve returns a list containing:

Details

This function is based on QuantLib Version 0.3.10. It introduces support for fixed-income instruments in RQuantLib. Forward rates and zero rates are computed assuming continuous compounding, so the forward rate $f$ over the period from $t1$ to $t2$ is determined by the relation $$d_1/d_2 = e^{f (t_2 - t_1)},$$ where $d1$ and $d2$ are discount factors corresponding to the two times. In the case of the zero rate $t1$ is the current time (the spot date).

Curve construction can be a delicate problem and the algorithms may fail for some input data sets and/or some combinations of the values for interpWhat and interpHow. 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.)

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

BermudanSwaption

Examples

savepar <- par(mfrow=c(3,3), mar=c(4,4,2,0.5))

## This data is taken from sample code shipped with QuantLib 0.9.7
## from the file Examples/Swap/swapvaluation
params <- list(tradeDate=as.Date('2004-09-20'),
               settleDate=as.Date('2004-09-22'),
               dt=.25,
               interpWhat="discount",
               interpHow="loglinear")
setEvaluationDate(as.Date("2004-09-20"))

## We get numerical issue for the spline interpolation if we add
## any on of these three extra futures -- the original example
## creates different curves based on different deposit, fra, futures
## and swap data
## Removing s2y helps, as kindly pointed out by Luigi Ballabio
tsQuotes <- list(d1w = 0.0382,
                 d1m = 0.0372,
                 d3m = 0.0363,
                 d6m = 0.0353,
                 d9m = 0.0348,
                 d1y = 0.0345,
                 fut1=96.2875,
                 fut2=96.7875,
                 fut3=96.9875,
                 fut4=96.6875,
                 fut5=96.4875,
                 fut6=96.3875,
                 fut7=96.2875,
                 fut8=96.0875,
#                 s2y = 0.037125,
                 s3y = 0.0398,
                 s5y = 0.0443,
                 s10y = 0.05165,
                 s15y = 0.055175)

times <- seq(0,10,.1)

# Loglinear interpolation of discount factors
curves <- DiscountCurve(params, tsQuotes, times)
plot(curves,setpar=FALSE)

# Linear interpolation of discount factors
params$interpHow="linear"
curves <- DiscountCurve(params, tsQuotes, times)
plot(curves,setpar=FALSE)

# Spline interpolation of discount factors
params$interpHow="spline"
curves <- DiscountCurve(params, tsQuotes, times)
plot(curves,setpar=FALSE)

par(savepar)