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I used daily log-returns to estimate the parameters in the Bates model, and I want to price a contingent claim using these estimates. I know that I have to distinguish between parameters estimated under $P$ and parameters calibrated under $Q$. But let us for a moment assume market price of risk is zero, and these to measures is the same.

My question is the following;

  • Lets say I estimated $\kappa$ to 0.30. Is this percentage? Do I have to multiply it with 100%.

  • $\kappa$ is daily, then do I have to multiply it with $\sqrt{252}$ or 252 to make it yearly? $\kappa$ is a parameter appearing in the volatility process, so do I have to scale it like the volatility?

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The only important thing with all the parameters you use for pricing is that they all refer to the same frequency. If in your data, you work with daily returns, daily interest rates and days to maturity, your estimates will reflect daily values. It's usually what people do.

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