Master Thesis project files for the completion of the MSc in Mathematical Finance at Birkbeck College of London.

Main Objective

Main question: How accurate are new stochastic volatility models in calculating implied volatility? A research that will go trogh a bried history of implied volatility over the last decades, as well as a in depth statistical research on effectiveness on models such as the Heston stochastic volatility, SABR free, normal and shifted models. Graphical and statistical analysis of the models using volatility smiles and surfaces. To add to the main topic, how good are these models with respect to negative interest rates environonments?

Usage

Download the folder and use the notebook file for showing the results. Change the initial variable data in initialize.py to "GOLD", "SILVER" or "COFFEE" to load related dataset. Restart the kernel and run cells to update results.

Main

• Plot implied option prices against market prices with respect to each model
• Organise thesis theoretical structure. Write down general concept
• Test using negative interest rates
• Write a clear, non-empirical statistical process for comparing models
• General Review: check Cit. for each formula
• General Review: double check fommulas derivations amd possibly add full to appendix.

Optional

• [NO] Add Obloj's refinement model for SABR
• Add Dupire's Local Volatility Model Surface (now returning negative variance)
• Add mixed SABR models
• [] Add visualised PDF
• [] Delta Hedging
• [] Greeks explanation