vanilla-option-pricing 0.1.0

Stochastic model for vanilla option pricing

Vanilla Option Pricing

A Python package implementing stochastic models to price financial options.
The theoretical background and a comprehensive explanation of models and their parameters can be found is the paper Fast calibration of two-factor models for energy option pricing by Emanuele Fabbiani, Andrea Marziali and Giuseppe De Nicolao, freely available on arXiv.

Installing

The preferred way to install the package is using pip, but you can also download the code and install from source

To install the package using pip:

pip install vanilla_option_pricing

Quickstart

Let's create a call option.

from datetime import datetime, timedelta
from vanilla_option_pricing.option import VanillaOption

option = VanillaOption(
    spot=100,
    strike=101,
    dividend=0,
    date=datetime.today(),
    maturity=datetime.today() + timedelta(days=30),
    option_type='c',
    price=1,
    instrument='TTF'
)

We can compute the implied volatility and create a Geometric Brownian Motion model with it. Of course, if now we ask price the option using the Black framework, we'll get back the initial price.

from vanilla_option_pricing.models import GeometricBrownianMotion

volatility = option.implied_volatility_of_undiscounted_price
gbm_model = GeometricBrownianMotion(volatility)
gbm_price = gbm_model.price_option_black(option)
print(f'Actual price: {option.price}, model price: {gbm_price}')

But, if we adopt a different model, say a Log-spot price mean reverting to generalised Wiener process model (MLR-GW), we will get a different price.

import numpy as np
from vanilla_option_pricing.models import LogMeanRevertingToGeneralisedWienerProcess

p_0 = np.eye(2)
model = LogMeanRevertingToGeneralisedWienerProcess(p_0, 1, 1, 1)
lmrgw_price = model.price_option_black(option)
print(f'Actual price: {option.price}, model price: {lmrgw_price}')

In the previous snippet, the parameters of the LMR-GW model were chosen at random. We can also calibrate the parameters of a model against listed options.

from datetime import date
from vanilla_option_pricing.option import VanillaOption
from vanilla_option_pricing.models import OrnsteinUhlenbeck, GeometricBrownianMotion
from vanilla_option_pricing.calibration import ModelCalibration

data_set = [
    VanillaOption('TTF', 'c', date(2018, 1, 1), 2, 101, 100, date(2018, 2, 1)),
    VanillaOption('TTF', 'p', date(2018, 1, 1), 2, 98, 100, date(2018, 2, 1)),
    VanillaOption('TTF', 'c', date(2018, 1, 1), 5, 101, 100, date(2018, 5, 31))
]

models = [
    GeometricBrownianMotion(0.2),
    OrnsteinUhlenbeck(p_0=0, l=100, s=2)
]
calibration = ModelCalibration(data_set)

print(f'Implied volatilities: {[o.implied_volatility_of_undiscounted_price for o in data_set]}\n')

for model in models:
    result, trained_model = calibration.calibrate_model(model)
    print('Optimization results:')
    print(result)
    print(f'Calibrated parameters: {trained_model.parameters}\n\n')