Estimating Bates Jump-Size Parameters from Returns

Summary

The document raises a parameter-estimation question for the Bates stochastic-volatility model with jumps. The author identifies candidate jump observations by thresholding absolute simple returns, defined as the price change divided by the previous price. For the jump-percentage mean, the author then proposes averaging those return percentages and asks whether this is correct, noting difficulty finding detailed references.

No answer, supporting derivation, or empirical result is included, so the proposed estimator is not validated in the document. The description also leaves important choices unspecified, including the threshold, sampling interval, and how ordinary price variation is distinguished from jumps. In practice, those choices affect which observations enter the estimate, and the model's jump-size convention must match the data transformation used. The discussion is therefore useful as a statement of the estimation problem and a possible threshold-based starting point, but it does not establish a reliable procedure for estimating the Bates jump mean or other jump parameters.

Key ideas

• The author identifies candidate jumps by thresholding the absolute simple return.
• The proposed jump-mean estimate is the average simple return among observations classified as jumps.
• The document provides no response or evidence confirming that this estimator is correct.
• Threshold choice and return sampling affect which observations count as jumps.
• Any estimator should use a jump-size definition consistent with the model specification.

Tags

# Bates Model Jump Percentage Parameters


# Bates Model Jump Percentage Parameters












I am trying to calculate the jump parameters for the Bates volatility jumps, specifically, the mean of the jump percentages, $\mu_j$. For the value of $J$, I am using jumps $|\frac{s_{i}-s_{i-1}}{s_{i-1}}| > jump_{thresh}$ for a given $jump_{thresh}$ and stock prices $s_i \in [s_0, ..., s_n]$.

For the value of $\mu_j$, I am simply taking the mean of $\frac{s_{i}-s_{i-1}}{s_{i-1}}$. I am struggling to find solid documentation and research papers that provide in-depth information on this. Am I computing this correctly?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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