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Chapter 11: stochastic model calibration

P

Phani Vasantarao

Member
Hello,
Could someone please explain stochastic model calibration (both risk-neutral and real-world), with examples? I see an example in the core reading text but I still feel muddled conceptually. The example discusses the price of bonds - what are the parameters in question here? Is there any other example that can help clarify?

Thanks,
Phani
 
Hi Phani

The aim of risk-neutral calibration is to calibrate the model to reproduce the market value of assets using risk-neutral rates. We can then use these cashflows to value liabilities (and other assets without a market value) that have the same cashflows (as they must have the same value if the cashflows are the same).

For a real-world calibration, instead of reproducing the market value of assets, we want the model to reproduce the long-term expected value for the assets. So, we’ll set the assumptions such that this is what the model does. We can then use these same assumptions to determine the value for the assets and liabilities.

The example given in the notes says that if bonds and equities both had a market value of 100, the risk-neutral calibration would value both these assets (and any liabilities that share the same cashflows) with a value of 100.

Using the real-world method, in the long-term we expect equities to have a higher market value than bonds, so the model might give a value of 110 to the equity and 100 to the bond. We would then use the model set up with the same assumptions that derived this result to determine the value of the assets and liabilities (the value of these will obviously depend on what assumptions lead to the model giving these results and how these affect the value of assets/liabilities).

Hope this helps,
Sarah
 
Thanks, Sarah, that helps. It seems to me that you are saying that calibration is essentially the process of setting assumptions that give us a certain value for one variable that seems reasonable (here, for example, the price of a bond), and then using those same assumptions to determine the value of another variable (let us say, future claims outgo or reserves, as mentioned in the core reading). Is this correct?
 
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