Keeping Bates Model Parameters Consistent with Data Frequency

Summary

The document asks how to interpret and scale parameters estimated for a Bates stochastic volatility model from daily log returns, using the mean reversion parameter κ as an example. It distinguishes estimates under the real-world probability measure from parameters calibrated under the pricing measure, then assumes for discussion that the market price of risk is zero.

The response advises keeping all pricing inputs on a consistent time scale. If returns, interest rates, and time to maturity are expressed in daily units, parameter estimates should be used in that same daily convention. The answer does not recommend converting κ by multiplying by 100, by the square root of the number of trading days, or by that number itself. It also does not provide a conversion derivation or address calendar conventions and model-specific discretization, so it is a concise consistency rule rather than a full treatment of parameter estimation or annualization.

Key ideas

• Parameter estimates depend on the time frequency used for the data.
• Pricing inputs such as rates and maturity should use a time unit consistent with the estimates.
• The response recommends retaining daily units when returns, rates, and maturity are all expressed daily.
• The source does not give a general annualization formula for the Bates parameters.
• The real-world and pricing probability measures are distinct unless additional assumptions connect them.

Tags

# Pricing with estimated parameters


# Pricing with estimated parameters












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?

## Answer by Stéphane (score 1)

https://quant.stackexchange.com/a/53021

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.