Q Fin
1.0.0
A Python library for mathematical finance.
https://pypi.org/project/QFin/
pip install qfin
QFin is being reconstructed to leverage more principals of object-oriented programming. Several modules in this version are deprecated along with the solutions to PDEs/SDEs (mainly in the options module).
QFin now contains a module called 'stochastics' which will be largely responsible for model calibration and option pricing. A Cython/C++ equivalent to QFin is also being constructed so stay tuned!
Stochastic differential equations that model underlying asset dynamics extend the 'StochasticModel' class and posses a list of model parameters and functions for pricing vanillas, calibrating to implied volatility surfaces, and Monte Carlo simulations (particularly useful after calibration for pricing path dependent options).
Below is a trivial example using ArithmeticBrownianMotion - first import the StochasticModel...
from qfin.stochastics import ArithmeticBrownianMotion
Next initialize the class object by parameterizing the model...
# abm parameterized by Bachelier vol = .3abm = ArithmeticBrownianMotion([.3])
The abm may now be used to price a vanilla call/put option (prices default to "CALL") under the given parameter set...
# F0 = 101# X = 100# T = 1abm.vanilla_pricing(101, 100, 1, "CALL")# Call Price: 1.0000336233656906
Using call-put parity put prices may also be obtained...
# F0 = 99# X = 100# T = 1abm.vanilla_pricing(99, 100, 1, "PUT")# Put Price: 1.0000336233656952
Calibration and subsequent simulation of the process is also available - do note that some processes have a static volatility and can't be calibrated to an ivol surface.
The arithmetic Brownian motion may be simulated as follows...
# F0 = 100# n (steps) = 10000# dt = 1/252# T = 1abm.simulate(100, 10000, 1/252, 1)
Results of the simulation along with the simulation characteristics are stored under the tuple 'path_characteristics' : (paths, n, dt, T).
Using the stored path characteristics we may find the price of a call just as before by averaging each discounted path payoff (assuming a stock process) with zero-rates we can avoid discounting as follows and find the option value as follows...
# list of path payoffspayoffs = []# option strike priceX = 99# iteration through terminal path values to identify payofffor path in abm.path_characteristics[0]: # appending CALL payoff payoffs.append(max((path[-1] - X), 0))# option value todaynp.average(payoffs)# Call Price: 1.0008974837343871
We can see here that the simulated price is converging to the price in close-form.
Theoretical options pricing for non-dividend paying stocks is available via the BlackScholesCall and BlackScholesPut classes.
from qfin.options import BlackScholesCallfrom 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 interesteuro_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
First-order and some second-order partial derivatives of the Black-Scholes pricing model are available.
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
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
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
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
Simulating asset paths is available using common stochastic processes.
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 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 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.
from qfin.simulations import MonteCarloCallfrom 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 volatilityput_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
from qfin.simulations import MonteCarloBinaryCallfrom 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
from qfin.simulations import MonteCarloBarrierCallfrom 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 Outbarrier_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
from qfin.simulations import MonteCarloAsianCallfrom 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
from qfin.simulations import MonteCarloExtendibleCallfrom 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 expirationextendible_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
