sabr-model

A repo with some selected R code, plots of fits to implied volatility smiles, and surface plots of implied volatility surfaces, conducted under a FAST grant received from the NYU Dean's Undergraduate Research Fund.

The materials here are part of the research I produced during the summer of 2019. In 2020 I decided to release the better parts of the material onto GitHub, to serve as a testament to my first "real" attempt at pricing options. Before, I had implemented the Cox binomial model in Python and compared its shortcomings to market prices, but I consider my implementation to be primitive and honestly not my best work. The code in this repository is not production quality, but is at least prototyping quality. Most of the code should work on versions of R >= 3.6.1.

Includes PDF slides accompanying my presentation video for NYU's 2020 Undergraduate Research Conference. Due to the COVID-19 outbreak in the United States, the conference was switched to a virtual format.

Directories

data

Contains the implied vol smile data for the models to fit. Implied vol data was downloaded from CME's QuikStrike Option Settlement Tool and copied by hand to the .csv files in the directory. Smile data is from European options on E-mini S&P 500 futures and options on Henry Hub natural gas futures.

Expirations are monthly from September 2019 to January 2020.

demos

Contains hh_test.R and spx_test.R, short demos that calibrate a model (specify within the script) to a particular smile (specify in the script). As noted in their heading comments, please run them from the R interpreter by source()ing them, as graphics problems seem to occur when using RScript. Currently configured to fit SABR.

*_fits

Contains .png files with sample fits of CEV forward and SABR model fits to implied vol data. hh_* directories contain fits to implied vol data from European options on Henry Hub natural gas futures, while spx_* directories contain fits to implied vol data from European options on E-mini S&P 500 futures. *_cevf_* indicates the CEV forward model is being fitted, while *_sabr_* indicates the SABR model is being fitted. Although not perfect, SABR fits are pretty good for the most part, while the CEV forward model fits tend to be much worse.

presentation

Contains PDF slides for accompanying my presentation video for NYU's 2020 Undergraduate Research Conference.

src

Contains the main R code used for the project formerly located in the top-level directory. File descriptions below.

cevf.R

Contains functions for calibrating the CEV forward model to market implied vol data by least squares fitting of the market smiles. Contains a fitting function, objective function for the fitting function, implied vol approximation for the CEV forward model, and a function to plot the model's fit on a smile.

ivol_util.R

Contains implied vol related utility functions, as well as data on ATM forward levels, times to expiration, and discount curve. Contains a discounting function, unused function for extracting Black volatilities, a function to plot an implied vol surface, functions to return Black call/put prices, and a useful strike sampling function. The end of the file contains several commented blocks code that I have kept as reference.

sabr.R

Contains functions for calibrating the SABR model to market implied vol data by least squares fitting. Contains the same functions as in cevf.R but modified for SABR.

vol_surfaces

Contains files vol_surface_hh_shared_crop.png and vol_surface_spx_shared_crop.png, which are plots of implied vol surfaces constructed from the Henry Hub and E-mini S&P 500 data respectively.