LMMDiscountFactors = squeeze(cumprod(1./(1 + LMMZeroRates(:,1,:)*.5)))
TenYearRates = squeeze(G2PP_SimZeroRates(:,Tenor = 7,:))
TwoYearRates = squeeze(G2PP_SimZeroRates(:,Tenor = 2,:)) % Compute mortgage rates from interest rate paths Calibration remains a complex task, and while the plot below indicates that the best fit parameters seem to do a reasonably good job of reproducing the Cap prices, it should be noted that the procedure outlined here simply represents one approach. The remaining mean reversion and volatility parameters are constrained to be between 0 and. 7 to ensure that the parameters represent a truly two-factor model. Therefore, r h o is constrained to be between -.7 and. As Brigo and Mercurio discuss, the correlation parameter, r h o, can often be close to -1 when fitting a G2++ model to interest-rate cap prices. Upper and lower bounds for the model parameters are set to be relatively constrained. The function capbylg2f computes the analytic values for the caps given parameter values. The Optimization Toolbox™ function lsqnonlin is used in this example, although other approaches (for example, Global Optimization) may also be applicable.
To calibrate the model parameters, a parameter set will be found that minimizes the sum of the squared differences between the G2++ predicted Cap values and the observed Black Cap values.
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