Instrument prices and sensitivities from Heath-Jarrow-Morton interest-rate tree
[Delta, Gamma, Vega, Price] = hjmsens(HJMTree,
InstSet,
Options)
| Heath-Jarrow-Morton tree sampling a forward-rate process.
See |
| Variable containing a collection of instruments. Instruments are categorized by type. Each type can have different data fields. The stored data field is a row vector or character vector for each instrument. |
| (Optional) Derivatives pricing options structure created
with |
[Delta, Gamma, Vega, Price] = hjmsens(HJMTree,
InstSet,
computes instrument sensitivities
and prices for instruments using an interest-rate tree created with
Options)hjmtree
. NINST
instruments
from a financial instrument variable, InstSet
,
are priced. hjmsens
handles instrument types: 'Bond'
, 'CashFlow'
, 'OptBond'
, 'OptEmBond'
, 'OptEmBond'
, 'OptFloat'
, 'OptEmFloat'
, 'Fixed'
, 'Float'
, 'Cap'
, 'Floor'
, 'RangeFloat'
, 'Swap'
.
See instadd
for information
on instrument types.
Delta
is an NINST
-by-1
vector
of deltas, representing the rate of change of instrument prices with
respect to changes in the interest rate. Delta
is
computed by finite differences in calls to hjmtree
.
See hjmtree
for information on the observed yield
curve.
Gamma
is an NINST
-by-1
vector
of gammas, representing the rate of change of instrument deltas with
respect to the changes in the interest rate. Gamma
is
computed by finite differences in calls to hjmtree
.
Vega
is an NINST
-by-1
vector
of vegas, representing the rate of change of instrument prices with
respect to the changes in the volatility $$\sigma \left(t,T\right)$$. Vega
is
computed by finite differences in calls to hjmtree
.
See hjmvolspec
for information
on the volatility process.
Note All sensitivities are returned as dollar sensitivities. To find the per-dollar sensitivities, divide by the respective instrument price. |
Price
is an NINST
-by-1
vector
of prices of each instrument. The prices are computed by backward
dynamic programming on the interest-rate tree. If an instrument cannot
be priced, NaN
is returned.
Delta
and Gamma
are calculated
based on yield shifts of 100 basis points. Vega
is
calculated based on a 1% shift in the volatility process.
hjmprice
| hjmtree
| hjmvolspec
| instadd