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In order to simulate an interest rate yield curve, can I just estimate a covariance matrix of historical key rate data, simulate with a normal copula, spline my simulated key rates, then price my assets as a function of the simulated yield curves?

Alternatively, could I just spline historical key rate values and estimate risk as a function of those values?

Why is this insufficient? / Where does the need for stochastic models arise?

Thanks

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One reason is that your system needs to correctly price today's yield curve and interest rate options market , otherwise it is not arbitrage free versus existing instruments. Historical data will not in general achieve that.

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  • $\begingroup$ "need" is very strong. In some cases, yes your model should price the market correctly, but it's not a necessary condition for all possible uses. The approach described is very useful in risk management for example. $\endgroup$
    – crunch
    Commented Aug 17, 2017 at 14:08
  • $\begingroup$ ok, since the OP referred to pricing of assets I assumed that consistency with the market would be important. $\endgroup$
    – dm63
    Commented Aug 18, 2017 at 2:11

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