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bkcaplet - Price interest-rate caplet using Black's model

Syntax

CapPrices = bkcaplet(CapData, FwdRates, ZeroPrice, Settle, 
StartDate, EndDate, Sigma)

Arguments

CapData

Number of caps (NCAP)-by-2 matrix containing cap rates and bases: [CapRates Basis].

Values for bases may be:

  • 0 = actual/actual (default)

  • 1 = 30/360 (SIA)

  • 2 = actual/360

  • 3 = actual/365

  • 4 = 30/360 (BMA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

FwdRates

Scalar or NCAP-by-1 vector containing forward rates in decimal. FwdRates accrue on the same basis as CapRates.

ZeroPrice

Scalar or NCAP-by-1 vector containing zero coupon prices with maturities corresponding to those of each cap in CapData, per $100 nominal value.

Settle

Scalar or NCAP-by-1 vector of identical elements containing settlement date of caplets.

StartDate

Scalar or NCAP-by-1 vector containing start dates of the caplets.

EndDate

Scalar or NCAP-by-1 vector containing maturity dates of caplets.

Sigma

Scalar or NCAP-by-1 vector containing volatility of forward rates in decimal, corresponding to each caplet.

Description

CapPrices = bkcaplet(CapData, FwdRates, ZeroPrice, Settle, StartDate, EndDate, Sigma) computes the prices of interest-rate caplets for every $100 face value of principal.

Examples

Given a notional amount of $1,000,000, compute the value of a caplet on October 15, 2002 that starts on October 15, 2003 and ends on January 15, 2004.

CapData = [0.08, 1];
FwdRates = 0.07;
ZeroPrice = 100*exp(-0.065*1.25);
Settle = datenum('15-Oct-2002');
BeginDates = datenum('15-Oct-2003');
EndDates = datenum('15-Jan-2004');
Sigma = 0.20;

Because the caplet is $100 notional, divide $1,000,000 by $100.

Notional   = 1000000/100; 

CapPrice = Notional*bkcaplet(CapData, FwdRates, ZeroPrice, ...
Settle, BeginDates, EndDates, Sigma)

CapPrice =

  519.0046

See Also

bkfloorlet

  

 

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