[CapPrice,Caplets]
= capbynormal(RateSpec,Strike,Settle,Maturity,Volatility) prices
caps using the Normal (Bachelier) pricing model for negative rates. capbynormal computes
prices of vanilla caps and amortizing caps.
Consider an investor who gets into a contract that caps the interest rate on a $100,000 loan at –.08% quarterly compounded for 3 months, starting on January 1, 2009. Assuming that on January 1, 2008 the zero rate is .069394% continuously compounded and the volatility is 20%, use this data to compute the cap price. First, calculate the RateSpec, and then use capbynormal to compute the CapPrice.
Interest-rate term structure (annualized and continuously compounded),
specified by the RateSpec obtained from intenvset. For information on the interest-rate
specification, see intenvset.
Data Types: struct
Strike — Rate at which cap is exercised decimal
Rate at which cap is exercised, specified as a NINST-by-1 vector
of decimal values.
Data Types: double
Settle — Settlement date for cap serial date number | date character vector | datetime object | string object
Settlement date for the cap, specified as a NINST-by-1 vector
of serial date numbers, date character vectors, datetime objects,
or string objects.
Data Types: double | char | datetime | string
Maturity — Maturity date for cap serial date number | date character vector | datetime object | string object
Maturity date for the cap, specified as a NINST-by-1 vector
of serial date numbers, date character vectors, datetime objects,
or string objects.
Data Types: double | char | datetime | string
Volatility — Normal volatilities values numeric
Normal volatilities values, specified as a NINST-by-1 vector
of numeric values.
Specify optional
comma-separated pairs of Name,Value arguments. Name is
the argument name and Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
Name1,Value1,...,NameN,ValueN.
'Reset' — Reset frequency payment per year 1 (default) | numeric
Reset frequency payment per year, specified as the comma-separated
pair consisting of 'Reset' and a NINST-by-1 vector.
Data Types: double
'Principal' — Notional principal amount 100 (default) | numeric
Notional principal amount, specified as the comma-separated
pair consisting of 'Principal' and a NINST-by-1 of
notional principal amounts, or a NINST-by-1 cell
array. Each element in the NINST-by-1 cell
array is a NumDates-by-2 cell
array, where the first column is dates, and the second column is the
associated principal amount. The date indicates the last day that
the principal value is valid.
Use Principal to pass a schedule to compute
the price for an amortizing cap.
Data Types: double | cell
'Basis' — Day-count basis of instrument 0 (actual/actual) (default) | integer from 0 to 13
Day-count basis of instrument representing the basis used when
annualizing the input forward rate, specified as the comma-separated
pair consisting of 'Basis'and a NINST-by-1 vector
of integers. Values are:
'ValuationDate' — Observation date of investment horizon if ValuationDate is not specified,
then Settle is used (default) | serial date number | date character vector | datetime object | string object
Observation date of the investment horizon, specified as the comma-separated pair consisting
of 'ValuationDate' and a serial date number, date character
vector, datetime object, or string array.
Data Types: double | char | datetime | string
'ProjectionCurve' — Rate curve used in generating future cash flows if ProjectionCurve is not
specified, then RateSpec is used both for discounting
cash flows and projecting future cash flows (default) | structure
The rate curve to be used in projecting the future cash flows,
specified as the comma-separated pair consisting of 'ProjectionCurve' and
rate curve structure. This structure must be created using intenvset. Use this optional input if
the forward curve is different from the discount curve.
A cap is a contract that includes a guarantee
that sets the maximum interest rate to be paid by the holder, based on an otherwise floating
interest rate.
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