Why Historical Yield Curves May Not Price Interest Rate Options Consistently

Summary

The question considers simulating an interest rate curve from historical key rate changes, using a covariance matrix and a normal copula, then interpolating the simulated rates and repricing assets. It also asks whether historical curves can be interpolated directly to estimate risk, and why a stochastic model might be needed.

The response identifies a key limitation: a model should reproduce today’s yield curve and the interest rate options market so that its prices are consistent with traded instruments and do not create arbitrage opportunities. Historical observations alone generally will not ensure that consistency. Thus, a historical simulation can be useful for representing past rate behavior, but the short answer does not specify a complete model, calibration procedure, or risk framework. It focuses on market consistency as a reason to use models calibrated to current instruments, rather than presenting evidence comparing simulation methods or detailing how to construct such a model.

Key ideas

• Historical key rate data can be used to generate plausible curve scenarios, but may not match current market prices.
• A pricing framework should reproduce the current yield curve and interest rate option prices.
• Consistency with traded instruments matters for avoiding arbitrage in modeled prices.
• The response identifies a limitation but does not provide a full model specification or calibration method.

Tags

# Interest rate risk using copulas


# Interest rate risk using copulas












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

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/35665

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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