Skip to content
All library documents

Choosing Data for Testing Merton Jump-Diffusion Models

Article Quant Q&A · Author: Oop
Read the original

Summary

The discussion suggests testing a Merton jump-diffusion model on broad equity benchmarks and their exchange-traded funds, naming the Nasdaq, S&P 500, Russell 2000, and examples such as QQQ, SPY, and IWM. It notes that these liquid benchmarks can help compare large-cap, technology, and smaller-company behavior. Historical option data may be costly, so the proposed starting point is underlying price data and an implementation of the model in MATLAB, with an option-pricing reference as a guide.

For pronounced jumps, one answer points to short-term power prices, while cautioning that long historical records may be hard to obtain. Another recommends examining research that models jumps in both the underlying asset and its volatility. The thread offers candidate markets and data considerations rather than a tested comparison, and it does not specify a calibration procedure, sample design, or empirical results. Its suggestions therefore serve as starting points for investigation, not evidence that one asset or period is best.

Key ideas

  • Broad equity indices and related ETFs are suggested as accessible underlyings for jump-diffusion experiments.
  • Historical options data may be expensive, so underlying price series can be a practical starting point.
  • Short-term power prices may exhibit pronounced jumps, although long historical datasets can be difficult to obtain.
  • Researchers may compare models with jumps in both asset prices and volatility.

Tags

OptionsEquitiesCommoditiesVolatilityDerivatives pricing
Full text
# I just got Matlab, what are some options that I should model in a jump diffusion


# I just got Matlab, what are some options that I should model in a jump diffusion












Don't worry I understand mathematics: ito's calc, martingales, etc. I am just curious what options I should test, and from what indices. Is there stuff I can test from the 2008 crash to measure their effects, or from COVID-19. Or data preloaded into Matlab. What type of options would be best to model their behavior using a Merton jump-diffusion?

## Answer by Con Fluentsy (score 1)

https://quant.stackexchange.com/a/55886

The bellwether Indices for testing, are NASDAQ, Technology sector, S & P 500 Big 500 capital weighted Stocks, Russell 2000, MID sector stocks and some small stocks. It is better to use the data fro their relative, ETF's eg. QQQ, SPY, IWM. The Dow is covered by the Nasdaq and the S&P 500, it is the 20 biggest stocks on the market and is not useful. Getting historic option data costs money, it is not free like stocks, futures and commodities data. You will have to create your own Jump diffusion model in matlab to apply on the data, you can refer to Espen Haug's complete Book of Option Pricing models, he implements the formula in a concise algorithm in VBA in the book, but it should be easier in Matlab, on the disk that accompanied the 2003, & 2007 editions he did all the models in C++ as well.

## Answer by kurtosis (score 0)

https://quant.stackexchange.com/a/55882

Short-term power options have very high volatility and kurtosis. If you can find power data from, say, 2001... that would have jumps. However, those data are likely difficult to come by.

If you are going to model jumps, you might do better by looking into work by Todorov and Tauchen. They find jumps in both the underlier and in volatility itself. Their work will also show you data to look at with jumps; and, that would allow you to compare results.

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.