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

black-scholes calibration finance fourier heston levy levy-processes option-pricing options-pricing pricing python quant quantitative-finance quantitative-trading sabr stochastic-volatility variance-gamma

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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.

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README 

        

# 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



```python



"""

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()

```