Financial Derivatives Toolbox

Sensitivity

The Financial Derivatives Toolbox can calculate two types of derivative price sensitivities, namely delta and gamma. Delta represents the dollar sensitivity of prices to shifts in the observed forward yield curve. Gamma represents the dollar sensitivity of delta to shifts in the observed forward yield curve.

The intenvsens function computes instrument sensitivities as well as instrument prices. If you need both the prices and sensitivity measures, use intenvsens. A separate call to intenvprice is not required.

Here is the syntax

• [Delta, Gamma, Price] = intenvsens(RateSpec, InstSet)
  

where, as before:

• RateSpec is the interest rate term structure.
• InstSet is the name of the portfolio.

Example: Sensitivities and Prices

Here is an example of using intenvsens to calculate both sensitivities and prices.

• format long
  load deriv.mat;
  [Delta, Gamma, Price] = intenvsens(ZeroRateSpec, ZeroInstSet);
  

Display the results in a single matrix in long format.

• All = [Delta Gamma Price]
  
  All =
  
    1.0e+003 *
  
    -0.27264034403478   1.02984451401241   0.09871593902758
    -0.34743857788527   1.62265027222659   0.09753338552637
    -0.27264034403478   1.02984451401241   0.09871593902758
    -0.00104445683331   0.00330878190894   0.10055293001355
    -0.28204045553455   1.05962355119047   0.00369230914950
  

To view the per-dollar sensitivity, divide the first two columns by the last one.

• [Delta./Price, Gamma./Price, Price]
  
  ans =
  
    1.0e+002 *
  
    -0.02761867503065   0.10432403562759   0.98715939027581
    -0.03562252822561   0.16636870169834   0.97533385526369
    -0.02761867503065   0.10432403562759   0.98715939027581
    -0.00010387134748   0.00032905872643   1.00552930013547
    -0.76385926561057   2.86981265188338   0.03692309149502
  

Pricing

Heath-Jarrow-Morton (HJM) Model