Graphical Representation of Trees
You can use the function
treeviewer to display a
graphical representation of a tree, allowing you to examine interactively the prices
and rates on the nodes of the tree until maturity. To get started with this process,
first load the data file
deriv.mat included in this
treeviewer price tree diagrams follow the convention that
increasing prices appear on the upper branch of a tree and, consequently,
decreasing prices appear on the lower branch. Conversely, for interest rate
displays, decreasing interest rates appear on the upper
branch (prices are rising) and increasing interest rates on
the lower branch (prices are falling).
For information on the use of
treeviewer to observe interest
rate movement, see Observing Interest Rates.
For information on using
treeviewer to observe the
movement of prices, see Observing Instrument Prices.
Observing Interest Rates
If you provide the name of an interest rate tree to the
treeviewer function, it displays
a graphical view of the path of interest rates. For example, here is the
treeviewer representation of all
the rates along both the up and down branches of
FRates = bushpath(HJMTree.FwdTree, [1 2 2])
FRates = 1.0356 1.0364 1.0526 1.0674
treeviewer function you can
display the identical information by clicking along the same sequence of nodes, as
Next is a
treeviewer representation of
interest rates along several branches of
treeviewer with recombining trees,
such as BDT, BK, and HW, you must click each node in succession from the
beginning to the end. Because these trees can recombine,
treeviewer is unable to
complete the path automatically.
FRates = treepath(BDTTree.FwdTree, [1 2 2])
FRates = 1.1000 1.0979 1.1377 1.1606
You can display the identical information by clicking along the same sequence of nodes, as shown next.
Observing Instrument Prices
load deriv.mat [Price, PriceTree] = hjmprice(HJMTree, HJMInstSet); treeviewer(PriceTree, HJMInstSet)
treeviewer you select
each instrument individually in the instrument portfolio
You can use an analogous process to view instrument prices based on the BDT
interest rate tree included in
load deriv.mat [BDTPrice, BDTPriceTree] = bdtprice(BDTTree, BDTInstSet); treeviewer(BDTPriceTree, BDTInstSet)
Valuation Date Prices
You can use
instrument-by-instrument to observe instrument prices through time. For the
first 4% bond in the HJM instrument portfolio,
treeviewer indicates a
valuation date price of 98.72, the same value obtained by accessing the
PriceTree structure directly.
As a further example, look at the sixth instrument in the price vector, the 3%
cap. At the valuation date, its value obtained directly from the structure is
treeviewer on this
instrument to confirm this price.
Additional Observation Times
The second node represents the first-rate observation time,
1. This node displays two states, one representing the branch
going up and the other one representing the branch going down.
Examine the prices of the node corresponding to the up branch.
ans = 100.1563 99.7309 0.1007 100.1563 100.3782 3.2594 0.1007 3.5597
Now examine the corresponding down branch.
ans = 96.3041 94.1986 0 96.3041 100.3671 8.6342 0 -0.3923
treeviewer once again, now
to observe the price of the 4% bond on the down branch. The displayed price of
96.3 conforms to the price obtained from direct access of the
PriceTree structure. You may continue this process as far
along the price tree as you want.
- Overview of Interest-Rate Tree Models
- Pricing Using Interest-Rate Term Structure
- Pricing Using Interest-Rate Tree Models
- Understanding Interest-Rate Tree Models
- Understanding the Interest-Rate Term Structure