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!
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)