Bootstrapping Yield Curve

Bootstrap the yield curve, discount curve and forward curve from bond market prices. Plot results.

Bootstrap the yield curve, discount curve and the forward curve from market data

***************** BOOTSTRAPPING RESULTS **********************

Time (Years)| Yield Curve | Discount Curve| Forward Curve |
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0.51 | 1.2404% | 0.9938 | 1.2366% |
1.01 | 1.1857% | 0.9881 | 1.1282% |
1.52 | 1.4177% | 0.9788 | 1.8735% |
2.03 | 1.8191% | 0.9641 | 3.0081% |
2.54 | 2.2704% | 0.9447 | 4.0628% |
3.04 | 2.6798% | 0.9226 | 4.6925% |
3.55 | 3.0091% | 0.9001 | 4.9538% |
4.06 | 3.2662% | 0.8777 | 5.0182% |
4.56 | 3.4694% | 0.8559 | 5.0521% |
5.07 | 3.6464% | 0.8339 | 5.1832% |
5.58 | 3.8090% | 0.8117 | 5.3740% |
6.09 | 3.9591% | 0.7895 | 5.5457% |
6.59 | 4.0913% | 0.7676 | 5.6195% |
7.10 | 4.1997% | 0.7466 | 5.5403% |
7.61 | 4.2799% | 0.7270 | 5.3424% |
8.12 | 4.3337% | 0.7087 | 5.0797% |
8.62 | 4.3650% | 0.6919 | 4.8105% |
9.13 | 4.3803% | 0.6761 | 4.5880% |
9.64 | 4.3876% | 0.6611 | 4.4698% |
10.15 | 4.3963% | 0.6462 | 4.5122% |
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[YieldCurve, DiscountCurve, ForwardCurve] = Bootstrap( Bond, Schedule, Solver )

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INPUTS:

Bond

  Bond.CashFlows - Matrix of all cash-flows of all bonds
one column represents one bond. one row represents one cash-flow date

  Bond.BondMarketPrices - Vector of bond market prices

Schedule

  Schedule.CashFlowSchedule - Times where future cash flows are paid.
This is common to all bonds. This needs inputing in years from today and accounting for the right day count convention.

Solver

  Solver.InterpolationMethod - Interpolation method to bootstrap the forward curve (the curve that is solved for). The valid inputs are:
'nearest' Nearest neighbor interpolation
'linear' Linear interpolation (default)
'spline' Cubic spline interpolation
'pchip' Piecewise cubic Hermite interpolation

Graph

  Graph - If graph = 'on', the bootstrapping automatically generates a graph that consists in four subplots: the yield curve (yield to maturity), the discount to par value curve, the discount curve and the forward curve.

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OUTPUTS: 

ForwardCurve - Vector of forward rates.
There are as many forward rates output as cash flow dates input. For a given date t, the forward rate at this date represents the rate tarting from the previous date t-1 and maturing at the given date t.

DiscountCurve - Vector of discount factors. There are as many discount factors output as cash flow dates input.

YieldCurve - Vector of bond yields to maturity.
There are as many bond yields output as cash flow dates input.