Research Projects in Volatility Modeling and Option Pricing

Summary

The document presents possible master’s thesis directions in option pricing, aimed at a beginner seeking a manageable empirical or model-comparison project. One suggestion is to fit a GARCH volatility model to market data, use it in Monte Carlo option pricing, and compare classical with quasi-Monte Carlo simulation for computational speed. Another proposal is to explore machine-learning methods for estimating volatility models or fitting a volatility surface.

The answer also points toward local stochastic volatility models, where fitting the implied-volatility skew can require numerical methods such as PDEs or particle methods. That direction may be more technically demanding but relevant to derivatives research. These are project suggestions, not reported experiments: the document provides no dataset, implementation details, evaluation criteria, or findings. A thesis would need to define the instruments, data period, calibration procedure, benchmark models, and measures of pricing accuracy or computation time before the comparisons could support conclusions.

Key ideas

• A thesis can fit GARCH volatility to market data and use the estimates in Monte Carlo option pricing.
• Classical and quasi-Monte Carlo methods can be compared by computational speed.
• Machine-learning methods may be studied for estimating volatility models or volatility surfaces.
• Local stochastic volatility models offer a more advanced direction focused on fitting the implied-volatility skew.
• The suggestions provide no empirical results or detailed experimental design.

Tags

# Suggestions for a Master thesis in option pricing models


# Suggestions for a Master thesis in option pricing models












I am willing to do my Master Thesis about option pricing. Do you have any suggestions? I would like it to be something simple, like comparing methods, e.g. compare ARCH and GARCH approaches for volatility estimates and their impact options pricing . Or this could be some empiriacl study using data from the Market. Any suggestions of something simple? Please try to detail a little bit because I am a beginner in the subject - I've fully read Hull and I'm starting to read Schreve. Thanks!

## Answer by Drew (score 4, accepted)

https://quant.stackexchange.com/a/32101

In option pricing, the entire game is fitting the skew with a fairly robust model. All the research right now is in LSV (Local Stochastic Vol) Models. Fitting these is a challenge (with PDE or Particle Methods), maybe a study on that will be ideal if you're looking for a derivatives job after.

Alternately, you could also test ML techniques in obtaining the vol surface (or even estimating vol models)

## Answer by Qbik (score 1)

https://quant.stackexchange.com/a/32100

- Fit GARCH to data.

- Use obtained GARCH model and Monte Carlo simulation method for pricing options.

- Compare speed of classical and quasi-Monte Carlo algorithms.

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.