FyPy

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.

Currently Supported

Models

• 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

Pricing Methods

• 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) ...

Model Calibration

• 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

Contract types supported (single underlying):

• 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

Coming Soon !

• 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

User installation

pip install git+https://github.com/jkirkby3/fypy.git

Dependencies

fypy requires:

• Python (>= 3.7)
• NumPy (tested with 1.20.2)
• py_lets_be_rational (implied volatility)

Source code

You can check the latest sources with the command

git clone https://github.com/jkirkby3/fypy.git

Test Suite

You can run the full test suite with this command,

python tests/test_runner.py

Example: Price Variance Gamma / Black-Scholes Models with PROJ (Fourier) Method

"""
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()