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plots
plots
 
 
results
results
 
 
.gitignore
.gitignore
 
 
LICENSE
LICENSE
 
 
README.md
README.md
 
 
SPX_all.csv
SPX_all.csv
 
 
black_scholes.py
black_scholes.py
 
 
cev.py
cev.py
 
 
models.md
models.md
 
 
option_chain_fetch.py
option_chain_fetch.py
 
 
option_plots.py
option_plots.py
 
 
option_pricing.py
option_pricing.py
 
 
option_summary.py
option_summary.py
 
 
option_utils.py
option_utils.py
 
 
sabr.py
sabr.py
 
 
ssvi.py
ssvi.py
 
 
svi.py
svi.py
 
 
timing_util.py
timing_util.py
 
 
xbachelier_implied_vols.py
xbachelier_implied_vols.py
 
 
xcev.py
xcev.py
 
 
xcev_implied_vols.py
xcev_implied_vols.py
 
 
xget_option_prices.py
xget_option_prices.py
 
 
ximplied_vols.py
ximplied_vols.py
 
 
xsabr.py
xsabr.py
 
 
xssvi.py
xssvi.py
 
 
xsummarize_options.py
xsummarize_options.py
 
 
xsvi.py
xsvi.py
 
 
xsynthetic_sabr.py
xsynthetic_sabr.py
 
 
xsynthetic_ssvi.py
xsynthetic_ssvi.py
 
 
xsynthetic_svi.py
xsynthetic_svi.py
 
 

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Implied-Vol-Surface

Tools to build and visualize implied-volatility smiles and surfaces from option chain data. The interpolation models are defined here. The most important programs are xget_option_prices.py ximplied_vols.py xsvi.py xssvi.py xsabr.py.

Programs

xget_option_prices.py

Download option chain data and save to CSV for use by the other tools. It is taken from my Yahoo-Option-Prices project and documented more extensively there.

Key features:

  • Fetches option chains (per expiry or expiry range).
  • Saves a combined CSV with calls and puts and summary stats.
  • Optional plot of implied vol vs strike.

Usage:

python xget_option_prices.py SYMBOL [--expiry YYYYMMDD|YYYYMMDD:YYYYMMDD] [--exp-range N:M]
    [--plot [file.png]] [--summary] [outfile.csv]

Example: python xget_option_prices.py "^SPX"

downloads the option chain for SPX to SPX_all.csv and gives summary data.

ximplied_vols.py

Compute implied vols by expiry from option chain data (CSV or freshly downloaded from Yahoo Finance).

Key features:

  • Infer forward and discount factor using put-call parity.
  • Compute implied vols for calls/puts and summarize ATM vols by tenor.
  • Optional plotting of vol curves and ATM vol vs tenor.
  • Supports American options with Bjerksund-Stensland (default) or CRR.

Usage (CSV):

python ximplied_vols.py options.csv [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--plot [file.png]] [--plot-atm [file.png]] [--both-sides]
    [--american] [--american-method bjerksund|crr] [--tree-steps N] [--spot S]

Usage (download + compute):

python ximplied_vols.py --symbol SYMBOL [--expiry YYYYMMDD|YYYYMMDD:YYYYMMDD] [--exp-range N:M]
    [--fwd-range L:U] [--plot [file.png]] [--plot-atm [file.png]] [--american]

Example: python ximplied_vols.py spx_all.csv --expiry 20260206 20260213 20260220 --fwd-range 0.9:1.1 --plot creates raw implied vol plots and tables.

xbachelier_implied_vols.py

Compute implied vols using the Bachelier (normal) model from option chain data.

Key features:

  • Uses normal implied vols (absolute vol units) instead of lognormal.
  • Optional plotting of vol curves and ATM vol vs expiry.

Usage:

python xbachelier_implied_vols.py options.csv [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--plot [file.png]] [--plot-atm [file.png]] [--both-sides]

xcev_implied_vols.py

Compute implied CEV sigma for a fixed beta from option chain data.

Key features:

  • Solves for the CEV sigma that matches each option price.
  • Beta controls the diffusion power (beta=1 is lognormal; beta=0 is normal-like).
  • Optional plotting of sigma curves and ATM sigma vs expiry.

Usage:

python xcev_implied_vols.py options.csv --beta B [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--plot [file.png]] [--plot-atm [file.png]] [--both-sides]

xsvi.py

Fit SVI smiles per expiry from European option data.

Key features:

  • Fits SVI parameters per expiry and prints RMSE.
  • Outputs fitted vols by strike (optional).
  • Plots fitted IV curves and implied densities.
  • Infers symbol from contractSymbol in the input file for plot titles (when available).

Usage:

python xsvi.py options.csv [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--both-sides] [--outfile out.csv]
    [--plot [file.png]] [--plot-density [file.png]] [--plot-density-log-s [file.png]]

Example: python xsvi.py spx_all.csv --expiry 20260202 20260206 20260213 20260220 --fwd-range 0.9:1.1 --plot creates SVI implied vol curves.

xssvi.py

Fit a surface SVI (SSVI) or eSSVI across expiries from European option data.

Key features:

  • Global SSVI fit across tenors.
  • Optional eSSVI with theta(T)=a+b*T^c and constant rho/eta/gamma.
  • Plots fitted curves and implied densities (linear or log stock scale).
  • Infers symbol from contractSymbol in the input file for plot titles (when available).

Usage:

python xssvi.py options.csv [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--both-sides] [--essvi]
    [--plot [file.png]] [--plot-density [file.png]] [--plot-density-log-s [file.png]]
    [--outfile out.csv]

Example: python xssvi.py spx_all.csv --expiry 20260202 20260206 20260213 20260220 --fwd-range 0.9:1.1 --plot creates SSVI implied vol curves.

xsabr.py

Fit SABR smiles per expiry from European option data.

Key features:

  • Hagan SABR implied-vol approximation.
  • Beta defaults to 1.0 (lognormal); optional --fit-beta.
  • Plots fitted IV curves and implied densities.
  • Infers symbol from contractSymbol in the input file for plot titles (when available).

Usage:

python xsabr.py options.csv [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--both-sides] [--beta B] [--fit-beta]
    [--outfile out.csv] [--plot [file.png]]
    [--plot-density [file.png]] [--plot-density-log-s [file.png]]

Example: python xsabr.py spx_all.csv --expiry 20260202 20260206 20260213 20260220 --fwd-range 0.9:1.1 --plot creates SABR implied vol curves.

xcev.py

Fit CEV smiles per expiry from European option data.

Key features:

  • CEV prices via noncentral chi-square formula.
  • Fits sigma and beta by default (use --fixed-beta to hold beta fixed).
  • Optional --beta-grid to scan beta values and report RMSE by beta.
  • Plots fitted IV curves and implied densities.
  • Infers symbol from contractSymbol in the input file for plot titles (when available).

Usage:

python xcev.py options.csv [--expiry YYYY-MM-DD|YYYYMMDD:YYYYMMDD] [--as-of YYYY-MM-DD]
    [--fwd-range L:U] [--both-sides] [--beta B] [--fixed-beta] [--beta-grid spec]
    [--outfile out.csv] [--plot [file.png]]
    [--plot-density [file.png]] [--plot-density-log-s [file.png]]

Example: python xcev.py spx_all.csv --expiry 20260206 20260220 --fwd-range 0.9:1.1 --plot

xsummarize_options.py

Print a per-expiry summary from an option chain CSV.

Usage:

python xsummarize_options.py options.csv

xsynthetic_svi.py

Generate synthetic prices from SVI and optionally fit SVI back, to test the fitting algorithm.

Key features:

  • Generates option prices from a known SVI parameterization.
  • Adds absolute price noise (supports multiple noise levels).
  • Optional fit and plot of true vs fitted IVs.

Usage:

python xsynthetic_svi.py --outfile out.csv [--fit] [--plot [file.png]]
    [--as-of YYYY-MM-DD] [--expiry YYYYMMDD ... | --tenor-days D ...]
    [--fwd F] [--df DF] [--rate R] [--fwd-range L:U] [--n-strikes N]
    [--a A] [--b B] [--rho RHO] [--m M] [--sigma S]
    [--noise N ...] [--spread S] [--both-sides] [--symbol SYM]
    [--fit-vol | --fit-price]

Example:

python xsynthetic_svi.py --outfile synth.csv --tenor-days 30 --noise 0.10 0.25 --fit --plot

xsynthetic_ssvi.py

Generate synthetic prices from SSVI/eSSVI and optionally fit back, to test the fitting algorithm.

Key features:

  • Generates option prices from SSVI or eSSVI parameters across tenors.
  • Adds absolute price noise (supports multiple noise levels).
  • Optional fit and plot of true vs fitted IVs.

Usage:

python xsynthetic_ssvi.py --outfile out.csv [--fit] [--plot [file.png]]
    [--as-of YYYY-MM-DD] [--expiry YYYYMMDD ... | --tenor-days D ...]
    [--fwd F] [--df DF] [--rate R] [--fwd-range L:U] [--n-strikes N]
    [--theta TH] [--rho RHO] [--eta ETA] [--gamma G] [--essvi]
    [--a A] [--b B] [--c C] [--noise N ...] [--spread S] [--both-sides]
    [--fit-vol | --fit-price]

Example:

python xsynthetic_ssvi.py --outfile synth.csv --tenor-days 30 60 --noise 0.0 0.04 --fit --plot

xsynthetic_sabr.py

Generate synthetic prices from SABR and optionally fit back, to test the fitting algorithm.

Key features:

  • Generates option prices from SABR parameters.
  • Adds absolute price noise (supports multiple noise levels).
  • Optional fit and plot of true vs fitted IVs.

Usage:

python xsynthetic_sabr.py --outfile out.csv [--fit] [--plot [file.png]]
    [--as-of YYYY-MM-DD] [--expiry YYYYMMDD ... | --tenor-days D ...]
    [--fwd F] [--df DF] [--rate R] [--fwd-range L:U] [--n-strikes N]
    [--alpha A] [--beta B] [--rho RHO] [--nu NU] [--fit-beta]
    [--noise N ...] [--spread S] [--both-sides]
    [--fit-vol | --fit-price]

Example:

python xsynthetic_sabr.py --outfile synth.csv --tenor-days 30 --noise 0.0 0.10 --fit --plot

Input CSV format

All programs expect a CSV with at least:

  • expiration (YYYY-MM-DD)
  • strike
  • option_type (call or put)
  • Either bid/ask or a column containing price (case-insensitive, e.g., lastPrice or price)

Optional:

  • volume, openInterest

Notes

  • Use quotes for symbols starting with ^ (e.g., "^SPX").
  • Density plots are computed via second derivatives of fitted Black-Scholes call prices; they can be sensitive to noisy fits.

About

Fit implied vol curves to option prices using SVI and SABR

Topics

options calibration option-pricing quantitative-finance american-options yahoo-finance black-scholes sabr implied-volatility stock-options svi sabr-model yfinance volatility-smile bjerksund-stensland

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