Vanilla and exotic option pricing library to support quantitative R&D. Focus on pricing interesting/useful models and contracts (including and beyond Black-Scholes), as well as calibration of financial models to market data.
This library is under active development, although the currently posted features are relatively stable.
- Black-Scholes
- Jump Diffusions: Merton, Kou (Double Exponential)
- Levy: (VG, NIG, CGMY/KoBoL, MJD, Kou, Tempered-Stable, Bilateral Gamma, etc)
- Stochastic Volatility: Heston
- SVJ: Bates, Heston + Double Expo Jumps
- SLV: SABR
- Analytical: closed form pricing when available, e.g. Black Scholes
- Fourier: PROJ (Frame Projection), Lewis, Gil-Peleaz, Carr-Madan, Hilbert Transform
- More in progress (PDE, Monte Carlo, etc) ...
- Levy Model Calibration (VG, NIG, CGMY, MJD, Kou, Tempered-Stable, Bilateral Gamma, etc)
- Heston Stochastic Volatility Model Calibration
- Stochastic Volatility with Jumps Model Calibration
- SABR Model calibration
- European Options
- Barrier Options (Single/Double barrier, and rebates)
- Asian Options (Discrete/Continuous)
- Discrete Variance Swaps, Variance/Volatility Options
- Bermudan/American early-exercise Options
- Parisian Options (Cumulative and resetting Parisian barrier options)
- Cliquets/Equity Indexed Annuities (Additive/Multiplicative)
- Step (Soft Barrier) Options
- Lookback/Hindsight Options
- Fader/Range-Accrual Options
- More Exotic Option Pricing
- Models: Stochastic Volatility, Stochastic Local Vol
- Additional pricing methods, such as Mellin Series, PDE, Monte Carlo, etc.
- Regime Switching Calibration
- Many of the exotic pricing algorithms will be translated into python from: https://github.com/jkirkby3/PROJ_Option_Pricing_Matlab
pip install git+https://github.com/jkirkby3/fypy.git
fypy requires:
- Python (>= 3.7)
- NumPy (tested with 1.20.2)
- py_lets_be_rational (implied volatility)
You can check the latest sources with the command
git clone https://github.com/jkirkby3/fypy.git
You can run the full test suite with this command,
python tests/test_runner.py
"""
This example shows how to price using a Fourier pricing method (PROJ)
We include two examples: 1) Black Scholes 2) Variance Gamma
"""
from fypy.pricing.fourier.ProjEuropeanPricer import ProjEuropeanPricer
from fypy.model.levy.BlackScholes import *
from fypy.model.levy.VarianceGamma import *
from fypy.termstructures.DiscountCurve import DiscountCurve_ConstRate
from fypy.termstructures.EquityForward import EquityForward
from fypy.volatility.implied.ImpliedVolCalculator import ImpliedVolCalculator_Black76
import matplotlib.pyplot as plt
# ============================
# Set Common Parameters
# ============================
S0 = 100 # Initial stock price
r = 0.01 # Interest rate
q = 0.03 # Dividend yield
T = 1 # Time to maturity of option
# ============================
# Set Term Structures
# ============================
disc_curve = DiscountCurve_ConstRate(rate=r)
div_disc = DiscountCurve_ConstRate(rate=q)
fwd = EquityForward(S0=S0, discount=disc_curve, divDiscount=div_disc)
# ============================
# Create Black-Scholes Model
# ============================
model = BlackScholes(sigma=0.2, forwardCurve=fwd, discountCurve=fwd.discountCurve)
pricer = ProjEuropeanPricer(model=model, N=2 ** 10)
# Price a set of strikes
strikes = np.arange(50, 150, 1)
prices = pricer.price_strikes(T=T, K=strikes, is_calls=np.ones(len(strikes), dtype=bool))
# Plot
plt.plot(strikes, prices, label='Black Scholes')
# ============================
# Create Variance Gamma Model
# ============================
model = VarianceGamma(sigma=0.2, theta=0.1, nu=0.8, forwardCurve=fwd, discountCurve=fwd.discountCurve)
pricer = ProjEuropeanPricer(model=model, N=2 ** 10)
# Price a set of strikes
strikes = np.arange(50, 150, 1)
is_calls = np.ones(len(strikes), dtype=bool)
prices = pricer.price_strikes(T=T, K=strikes, is_calls=is_calls)
# Plot
plt.plot(strikes, prices, label='Variance Gamma')
plt.legend()
plt.xlabel(r'strike, $K$')
plt.ylabel('price')
plt.show()
# Compute Implied Volatilities
ivc = ImpliedVolCalculator_Black76(disc_curve=disc_curve, fwd_curve=fwd)
vols = ivc.imply_vols(strikes=strikes, prices=prices, is_calls=is_calls, ttm=T)
# Plot Implied Vols
plt.plot(strikes, vols, label='Variance Gamma')
plt.legend()
plt.xlabel(r'strike, $K$')
plt.ylabel('implied vol')
plt.show()