# Stochastic Data¶

Generating Price Data using Stocastic Processes

• Geometric Brownian Motion (GBM)
• Fractional Brownian Motion (FBM)
• Heston Stochastic Volatility Model
• Cox Ingersoll Ross (CIR)
• Ornstein Uhlebneck stochastic process

Model Parameters

The model parameters class contains all of the parameters used by the following stochastic processes. The parameters have been prefixed with the name of the stochastic process they are used in. Calibration of the stochastic processes would involve looking for the parameter values which best fit some historical data.

• all_s0 This is the starting asset value
• all_time This is the amount of time to simulate for
• all_delta This is the delta, the rate of time e.g. 1/252 = daily, 1/12 = monthly
• all_sigma This is the volatility of the stochastic processes
• gbm_mu This is the annual drift factor for geometric brownian motion
• jumps_lamda This is the probability of a jump happening at each point in time
• jumps_sigma This is the volatility of the jump size
• jumps_mu This is the average jump size
• cir_a This is the rate of mean reversion for Cox Ingersoll Ross
• cir_mu This is the long run average interest rate for Cox Ingersoll Ross
• all_r0 This is the starting interest rate value
• cir_rho This is the correlation between the wiener processes of the Heston model
• ou_a This is the rate of mean reversion for Ornstein Uhlenbeck
• ou_mu This is the long run average interest rate for Ornstein Uhlenbeck
• sheston_a This is the rate of mean reversion for volatility in the Heston model
• heston_mu This is the long run average volatility for the Heston model
• heston_vol0 This is the starting volatility value for the Heston model
import random

%matplotlib inline


Geometric Brownian Motion

data = sp.gbm(
base_price=100,
base_volume=5,
start_date="2010-01-01",
times_to_generate=1000,
time_frame='1H'
)

data.close.plot()


png

Heston Stochastic Volatility Model

data = sp.heston(
base_price=100,
base_volume=5,
start_date="2010-01-01",
times_to_generate=1000,
time_frame='1H'
)

data.close.plot()


png

Fractional Brownian Motion

data = sp.fbm(
base_price=100,
base_volume=5,
start_date="2010-01-01",
times_to_generate=1000,
time_frame='1H'
)

data.close.plot()


png

Cox Ingersoll Ross (CIR)

data = sp.cox(
base_price=100,
base_volume=5,
start_date="2010-01-01",
times_to_generate=1000,
time_frame='1H'
)

data.close.plot()


png

Ornstein Uhlenbeck Process

data = sp.ornstein(
base_price=100,
base_volume=5,
start_date="2010-01-01",
times_to_generate=1000,
time_frame='1H'
)

data.close.plot()


png