[Price,PriceTree]
= capbyhw(HWTree,Strike,Settle,Maturity) computes
the price of a cap instrument from a Hull-White interest-rate tree. capbyhw computes
prices of vanilla caps and amortizing caps.
Load the file deriv.mat, which provides HWTree. The HWTree structure contains the time and interest-rate information needed to price the cap instrument.
load deriv.mat;
Set the required values. Other arguments will use defaults.
Interest-rate tree structure, specified by using hwtree.
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 | cell array of date character vectors
Settlement date for the cap, specified as a NINST-by-1 vector
of serial date numbers or date character vectors. The Settle date
for every cap is set to the ValuationDate of the
HW tree. The cap argument Settle is ignored.
Data Types: double | char | cell
Maturity — Maturity date for cap serial date number | date character vector | cell array of date character vectors
Maturity date for the cap, specified as a NINST-by-1 vector
of serial date numbers or date character vectors.
Data Types: double | char | cell
CapReset — Reset frequency payment per year 1 (default) | numeric
(Optional) Reset frequency payment per year, specified as a
NINST-by-1 vector.
Data Types: double
Basis — Day-count basis of instrument 0 (actual/actual) (default) | integer from 0 to 13
(Optional) Day-count basis representing the basis used when annualizing the input
forward rate, specified as a NINST-by-1 vector
of integers.
Principal — Notional principal amount 100 (default) | numeric
(Optional) Notional principal amount, specified as a
NINST-by-1 of notional principal amounts, or a
NINST-by-1 cell array, where each element is a
NumDates-by-2 cell array where the first
column is dates and the second column is 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.
Expected price of the cap at time 0, returned as a NINST-by-1 vector.
PriceTree — Tree structure with values of cap at each node vector
Tree structure with values of the cap at each node, returned
as a MATLAB® structure of trees containing vectors of instrument
prices and a vector of observation times for each node:
PriceTree.PTree contains cap prices.
PriceTree.tObs contains the observation
times.
PriceTree.Connect contains the connectivity vectors. Each
element in the cell array describes how nodes in that level connect to the next.
For a given tree level, there are NumNodes elements in the
vector, and they contain the index of the node at the next level that the middle
branch connects to. Subtracting 1 from that value indicates where the up-branch
connects to, and adding 1 indicated where the down branch connects to.
PriceTree.Probs contains the probability arrays. Each
element of the cell array contains the up, middle, and down transition
probabilities for each node of the level.
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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