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Q-Fin

A Python library for mathematical finance.

Installation

https://pypi.org/project/QFin/

pip install qfin

Time Value of Money

Bond Pricing

Option Pricing

Black-Scholes Pricing

Theoretical options pricing for non-dividend paying stocks is available via the BlackScholesCall and BlackScholesPut classes.

from qfin.options import BlackScholesCall
from qfin.options import BlackScholesPut
# 100 - initial underlying asset price
# .3 - asset underlying volatility
# 100 - option strike price
# 1 - time to maturity (annum)
# .01 - risk free rate of interest
euro_call = BlackScholesCall(100, .3, 100, 1, .01)
euro_put = BlackScholesPut(100, .3, 100, 1, .01)
print('Call price: ', euro_call.price)
print('Put price: ', euro_put.price)
Call price:  12.361726191532611
Put price:  11.366709566449416

Option Greeks

First-order and some second-order partial derivatives of the Black-Scholes pricing model are available.

Delta

First-order partial derivative with respect to the underlying asset price.

print('Call delta: ', euro_call.delta)
print('Put delta: ', euro_put.delta)
Call delta:  0.5596176923702425
Put delta:  -0.4403823076297575

Gamma

Second-order partial derivative with respect to the underlying asset price.

print('Call gamma: ', euro_call.gamma)
print('Put gamma: ', euro_put.gamma)
Call gamma:  0.018653923079008084
Put gamma:  0.018653923079008084

Vega

First-order partial derivative with respect to the underlying asset volatility.

print('Call vega: ', euro_call.vega)
print('Put vega: ', euro_put.vega)
Call vega:  39.447933090788894
Put vega:  39.447933090788894

Theta

First-order partial derivative with respect to the time to maturity.

print('Call theta: ', euro_call.theta)
print('Put theta: ', euro_put.theta)
Call theta:  -6.35319039407325
Put theta:  -5.363140560324083

Stochastic Processes

Simulating asset paths is available using common stochastic processes.

Geometric Brownian Motion

Standard model for implementing geometric Brownian motion.

from qfin.simulations import GeometricBrownianMotion
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .3 - underlying asset volatility
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
gbm = GeometricBrownianMotion(100, 0, .3, 1/52, 1)
print(gbm.simulated_path)
[107.0025048205179, 104.82320056538235, 102.53591127422398, 100.20213816642244, 102.04283245358256, 97.75115579923988, 95.19613943526382, 96.9876745495834, 97.46055174410736, 103.93032659279226, 107.36331603194304, 108.95104494118915, 112.42823319947456, 109.06981862825943, 109.10124426285238, 114.71465058375804, 120.00234814086286, 116.91730159923688, 118.67452601825876, 117.89233466917202, 118.93541257993591, 124.36106523035058, 121.26088015675688, 120.53641952983601, 113.73881043255554, 114.91724168548876, 112.94192281337791, 113.55773877160591, 107.49491796151044, 108.0715118831013, 113.01893111071472, 110.39204535739405, 108.63917240906524, 105.8520395233433, 116.2907247951675, 114.07340779267213, 111.06821275009212, 109.65530380775077, 105.78971667172465, 97.75385009989282, 97.84501925249452, 101.90695475825825, 106.0493833583297, 105.48266575656817, 106.62375752876223, 112.39829297429974, 111.22855058562658, 109.89796974828265, 112.78068777325248, 117.80550869036715, 118.4680557054793, 114.33258212280838]

Stochastic Variance Process

Stochastic volatility model based on Heston's paper (1993).

from qfin.simulations import StochasticVarianceModel
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .01 - risk free rate of interest
# .05 - continuous dividend
# 2 - rate in which variance reverts to the implied long run variance
# .25 - implied long run variance as time tends to infinity
# -.7 - correlation of motion generated
# .3 - Variance's volatility
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
svm = StochasticVarianceModel(100, 0, .01, .05, 2, .25, -.7, .3, .09, 1/52, 1)
print(svm.simulated_path)
[98.21311553503577, 100.4491317019877, 89.78475515902066, 89.0169762497475, 90.70468848525869, 86.00821802256675, 80.74984494892573, 89.05033807013137, 88.51410029337134, 78.69736798230346, 81.90948751054125, 83.02502248913251, 83.46375102829755, 85.39018282900138, 78.97401642238059, 78.93505221741903, 81.33268688455111, 85.12156706038515, 79.6351983987908, 84.2375291273571, 82.80206517176038, 89.63659376223292, 89.22438477640516, 89.13899271995662, 94.60123239511816, 91.200165507022, 96.0578905115345, 87.45399399599378, 97.908745925816, 97.93068975065052, 103.32091104292813, 110.58066464778392, 105.21520242908348, 99.4655106985056, 106.74882010453683, 112.0058519886151, 110.20930861932342, 105.11835510815085, 113.59852610881678, 107.13315204738092, 108.36549026977205, 113.49809943785571, 122.67910031073885, 137.70966794451425, 146.13877267735612, 132.9973784430374, 129.75750117504984, 128.7467891695649, 127.13115959080305, 130.47967713110302, 129.84273088908265, 129.6411527208744]

Simulation Pricing

Exotic Options

Simulation pricing for exotic options is available under the assumptions associated with the respective stochastic processes. Geometric Brownian motion is the base underlying stochastic process used in each Monte Carlo simulation. However, should additional parameters be provided, the appropriate stochastic process will be used to generate each sample path.

Vanilla Options

from qfin.simulations import MonteCarloCall
from qfin.simulations import MonteCarloPut
# 100 - strike price
# 1000 - number of simulated price paths
# .01 - risk free rate of interest
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .3 - underlying asset volatility
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
call_option = MonteCarloCall(100, 1000, .01, 100, 0, .3, 1/52, 1)
# These additional parameters will generate a Monte Carlo price based on a stochastic volatility process
# 2 - rate in which variance reverts to the implied long run variance
# .25 - implied long run variance as time tends to infinity
# -.5 - correlation of motion generated
# .02 - continuous dividend
# .3 - Variance's volatility
put_option = MonteCarloPut(100, 1000, .01, 100, 0, .3, 1/52, 1, 2, .25, -.5, .02, .3)
print(call_option.price)
print(put_option.price)
12.73812121792851
23.195814963576286

Binary Options

from qfin.simulations import MonteCarloBinaryCall
from qfin.simulations import MonteCarloBinaryPut
# 100 - strike price
# 50 - binary option payout
# 1000 - number of simulated price paths
# .01 - risk free rate of interest
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .3 - underlying asset volatility 
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
binary_call = MonteCarloBinaryCall(100, 50, 1000, .01, 100, 0, .3, 1/52, 1)
binary_put = MonteCarloBinaryPut(100, 50, 1000, .01, 100, 0, .3, 1/52, 1)
print(binary_call.price)
print(binary_put.price)
22.42462873441866
27.869902820039087

Barrier Options

from qfin.simulations import MonteCarloBarrierCall
from qfin.simulations import MonteCarloBarrierPut
# 100 - strike price
# 50 - binary option payout
# 1000 - number of simulated price paths
# .01 - risk free rate of interest
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .3 - underlying asset volatility
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
# True/False - Barrier is Up or Down
# True/False - Barrier is In or Out
barrier_call = MonteCarloBarrierCall(100, 1000, 150, .01, 100, 0, .3, 1/52, 1, up=True, out=True)
barrier_put = MonteCarloBarrierCall(100, 1000, 95, .01, 100, 0, .3, 1/52, 1, up=False, out=False)
print(binary_call.price)
print(binary_put.price)
4.895841997908933
5.565856754630819

Asian Options

from qfin.simulations import MonteCarloAsianCall
from qfin.simulations import MonteCarloAsianPut
# 100 - strike price
# 1000 - number of simulated price paths
# .01 - risk free rate of interest
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .3 - underlying asset volatility
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
asian_call = MonteCarloAsianCall(100, 1000, .01, 100, 0, .3, 1/52, 1)
asian_put = MonteCarloAsianPut(100, 1000, .01, 100, 0, .3, 1/52, 1)
print(asian_call.price)
print(asian_put.price)
6.688201154529573
7.123274528125894

Extendible Options

from qfin.simulations import MonteCarloExtendibleCall
from qfin.simulations import MontecarloExtendiblePut
# 100 - strike price
# 1000 - number of simulated price paths
# .01 - risk free rate of interest
# 100 - initial underlying asset price
# 0 - underlying asset drift (mu)
# .3 - underlying asset volatility
# 1/52 - time steps (dt)
# 1 - time to maturity (annum)
# .5 - extension if out of the money at expiration
extendible_call = MonteCarloExtendibleCall(100, 1000, .01, 100, 0, .3, 1/52, 1, .5)
extendible_put = MonteCarloExtendiblePut(100, 1000, .01, 100, 0, .3, 1/52, 1, .5)
print(extendible_call.price)
print(extendible_put.price)
13.60274931789973
13.20330578685724

Futures Pricing