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capbyblk - Price caps using Black option pricing model

Syntax

[CapPrice, Caplets] = capbyblk(RateSpec, Strike, Settle, Maturity, Volatility) [CapPrice, Caplets] = capbyblk(RateSpec, Strike, Settle, Maturity, Volatility, 'Name1', Value1...)

Arguments

`RateSpec`	The annualized, continuously compounded rate term structure. For more information, see `intenvset`.
`Strike`	`NINST`-by-`1` vector of rates at which the cap is exercised, as a decimal number.
`Settle`	Scalar representing the settle date of the cap.
`Maturity`	Scalar representing the maturity date of the cap.
`Volatility`	`NINST`-by-`1` vector of volatilities.
`Reset`	(Optional) `NINST`-by-`1` vector representing the frequency of payments per year. Default is `1`.
`Principal`	(Optional) `NINST`-by-`1` vector representing the notional principal amount. Default is `100`.
`Basis`	`NINST`-by-`1` vector representing the basis used when annualizing the input forward rate. 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
`ValuationDate`	(Optional) Scalar representing the observation date of the investment horizons. The default is the `Settle` date.

Note All optional inputs are specified as matching parameter name/value pairs. The parameter name is specified as a character string, followed by the corresponding parameter value. You can specify parameter name/value pairs in any order. Names are case-insensitive and partial string matches are allowed provided no ambiguities exist.

Description

[CapPrice, Caplets] = capbyblk(RateSpec, Strike, Settle,Maturity, Volatility)

[CapPrice, Caplets] = capbyblk(RateSpec, Strike, Settle,Maturity, Volatility, 'Name1', Value1...)

Use capbyblk to price caps using the Black option pricing model.

The outputs are:

CapPrice — NINST-by-1 expected prices of the cap.
Caplets — NINST-by-NCF array of caplets, padded with NaNs.

Examples

Consider an investor who gets into a contract that caps the interest rate on a $100,000 loan at 8% quarterly compounded for 3 months, starting on January 1, 2009. Assuming that on January 1, 2008 the zero rate is 6.9394% continuously compounded and the volatility is 20%, use this data to compute the cap price.

Calculate the RateSpec:

ValuationDate = 'Jan-01-2008';
EndDates ='April-01-2010';
Rates = 0.069394;
Compounding = -1; 
Basis = 1;

RateSpec = intenvset('ValuationDate', ValuationDate, ...
'StartDates', ValuationDate,'EndDates', EndDates, ...
'Rates', Rates,'Compounding', Compounding,'Basis', Basis);

Compute the price of the cap:

Settle = 'Jan-01-2009'; % cap starts in a year
Maturity = 'April-01-2009';
Volatility = 0.20;
CapRate = 0.08;
CapReset = 4;
Principal=100000;

CapPrice = capbyblk(RateSpec,  CapRate, Settle, Maturity, Volatility,...
'Reset',CapReset,'ValuationDate',ValuationDate,'Principal', Principal,...
'Basis', Basis)

CapPrice =

   51.6125

capbyblk - Price caps using Black option pricing model

Syntax

Arguments

Description

Examples

See Also