Financial Derivatives Toolbox

Using treeviewer to View Instrument Prices Through Time

You can use the function treeviewer to display a graphical representation of the tree, allowing you to examine interactively the prices on the nodes of the tree until maturity. With treeviewer you select each instrument individually in the instrument portfolio for display. For example, the command

• treeviewer(PriceTree, HJMInstSet)
  

with the 4% bond instrument selected in the Instrument window shows prices for this bond instrument along the price tree from the valuation date until maturity.

Example: Valuation Date Prices

You can use treeviewer instrument-by-instrument to observe instrument prices through time. For the first 4% bond in the 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 6.2831. Use treeviewer on this instrument to confirm this price.

Example: Additional Observation Times

The second node represents the first rate observation time, tObs = 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.

• PriceTree.PBush{2}(:,:,1)
  
  ans =
  
    100.1563
     99.7309
      0.1007
    100.1563
    100.3782
      3.2594
      0.1007
      3.5597
  

As before, you can use treeviewer, this time to examine the price for the 4% bond on the up branch. treeviewer displays a price of 100.2 for the first node of the up branch, as expected.

Now examine the corresponding down branch.

• PriceTree.PBush{2}(:,:,2)
  
  ans =
  
     96.3041
     94.1986
           0
     96.3041
    100.3671
      8.6342
           0
     -0.3923
  

Use 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.

Pricing and Sensitivity from HJM

HJM Pricing Options Structure