API Documentation

Timewave Engine

engine.Engine	This class implements Monte Carlo engine
engine.State	simulation state
engine.Producer	abstract class implementing simple producer for a model between grid dates
engine.Consumer	base class for simulation consumers

module containing simulation method related classes incl. multiprocessing support

class engine.Consumer(func=None)

Bases: object

base class for simulation consumers

initiatlizes consumer by providing a function :param func: consumer function with exact 1 argument which will consume the producer state. Default will return state.value

consume(state)

consume new producer state

finalize()

finalize simulation for consumer

finalize_path(path_num=None)

finalize last path for consumer

finalize_worker(process_num=None)

finalize process for consumer

get(queue_get)

to get states from multiprocessing.queue

initialize(grid=None, num_of_paths=None, seed=None)

initialize consumer for simulation :param num_of_paths: number of path :type num_of_paths: int :param grid: list of grid point :type grid: list(date) :param seed: simulation seed :type seed: hashable

initialize_path(path_num=None)

initialize consumer for next path

initialize_worker(process_num=None)

reinitialize consumer for process in multiprocesing

put()

to put state into multiprocessing.queue

class engine.Engine(producer=None, consumer=None)

Bases: object

This class implements Monte Carlo engine

run(grid=None, num_of_paths=2000, seed=0, num_of_workers=4, profiling=False)

implements simulation

Parameters:

• grid (list(date)) – list of Monte Carlo grid dates
• num_of_paths (int) – number of Monte Carlo paths
• seed (hashable) – seed used for rnds initialisation (additional adjustment in place)
• or None num_of_workers (int) – number of parallel workers (default: cpu_count()), if None no parallel processing is used
• profiling (bool) – signal whether to use profiling, True means used, else not

Return object:

final consumer state

It returns a list of lists. The list contains per path a list produced by consumer at observation dates

class engine.Producer(func=None, initial_state=None)

Bases: object

abstract class implementing simple producer for a model between grid dates

evolve(new_date)

evolve to the new process state at the next date, i.e. do one step in the simulation

Parameters:new_date (date) – date of the new state Return State:

initialize(grid, num_of_paths, seed)

inits producer for a simulation run

initialize_path(path_num=None)

inits producer for next path, i.e. sets current state to initial state

initialize_worker(process_num=None)

inits producer for a simulation run on a single process

class engine.State(value=0.0)

Bases: object

simulation state

Timewave Producer

producers.DeterministicProducer
producers.StringReaderProducer
producers.MultiProducer	initializer

module containing brownian motion model related classes

class producers.DeterministicProducer(sample_list, func=None, initial_state=None)

Bases: engine.Producer

evolve(new_date)

class producers.MultiProducer(*producers)

Bases: engine.Producer

initializer

Parameters:or produces (list(Producer)) – list of producers to be used one after another

evolve(new_date)

evolve to the new process state at the next date, i.e. do one step in the simulation

Parameters:new_date (date) – date of the new state Return State:

initialize(grid, num_of_paths, seed)

inits producer for a simulation run

initialize_path(path_num=None)

inits producer for next path, i.e. sets current state to initial state

initialize_worker(process_num=None)

inits producer for a simulation run on a single process

producers = None

list(Producer) – list of consumers to be used one after another

class producers.StringReaderProducer(data_str, str_decoder=None)

Bases: producers.DeterministicProducer

Timewave Consumer

consumers.QuietConsumer	QuietConsumer returns nothing, since QuietConsumer does simply not populate result in finalize_path()
consumers.StringWriterConsumer
consumers.StackedConsumer	stacked version of consumer, i.e. a following consumer is populated with out state of the preceding one
consumers.ConsumerConsumer	class implementing the consumer interface
consumers.MultiConsumer	initializer
consumers.ResetConsumer	FunctionConsumer that admits a reset function for each path
consumers.TransposedConsumer	TransposedConsumer returns sample distribution per grid point not per sample path

class consumers.ConsumerConsumer(*consumers)

Bases: engine.Consumer

class implementing the consumer interface several consumers can be saved and are executed one after another only the result of the last consumer is returned (see finalize_worker)

initializer

Parameters:list(Consumer) –

consume(state)

returns pair containing the result of consumption and consumer state the returned state is equal to the state.get_short_rate() the returned consume state is None

Parameters:state (State) – specific process state Return object:the new consumer state

finalize()

finalize for ConsumerConsumer

finalize_path(path_num=None)

finalize path and populate result for ConsumerConsumer

get(queue_get)

get to given consumer states. This function is used for merging of results of parallelized MC. The first state is used for merging in place. The states must be disjoint.

Parameters:queue_get (object) – second consumer state

initial_state = None

list(Consumer) – list of consumers to be used one after another

initialize(grid=None, num_of_paths=None, seed=None)

initialize ConsumerConsumer

initialize_path(path_num=None)

make the consumer_state ready for the next MC path

Parameters:path_num (int) –

class consumers.MultiConsumer(*consumers)

Bases: consumers.ConsumerConsumer

initializer

Parameters:list(Consumer) –

consume(state)

class consumers.QuietConsumer(func=None)

Bases: engine.Consumer

QuietConsumer returns nothing, since QuietConsumer does simply not populate result in finalize_path()

initiatlizes consumer by providing a function :param func: consumer function with exact 1 argument which will consume the producer state. Default will return state.value

finalize()

finalize_path(path_num=None)

QuietConsumer does simply not populate result in finalize_path()

class consumers.ResetConsumer(fixing_func=None, reset_func=None)

Bases: engine.Consumer

FunctionConsumer that admits a reset function for each path

finalize()

initialize_path(path_num=None)

class consumers.StackedConsumer(*consumers)

Bases: engine.Consumer

stacked version of consumer, i.e. a following consumer is populated with out state of the preceding one

consume(state)

finalize()

finalize for ConsumerConsumer

finalize_path(path_num=None)

finalize path and populate result for ConsumerConsumer

get(queue_get)

initialize(num_of_paths=None, grid=None, seed=None)

initialize StackedConsumer

initialize_path(path_num=None)

make the consumer_state ready for the next MC path

Parameters:path_num (int) –

put()

class consumers.StringWriterConsumer(str_decoder=None)

Bases: engine.Consumer

finalize()

finalize simulation for consumer

class consumers.TransposedConsumer(func=None)

Bases: engine.Consumer

TransposedConsumer returns sample distribution per grid point not per sample path

initiatlizes consumer by providing a function :param func: consumer function with exact 1 argument which will consume the producer state. Default will return state.value

finalize()

finalize for PathConsumer

Stochastic Process

module containing brownian motion model related classes

class stochasticprocess.GeometricBrownianMotion(mu=0.0, sigma=1.0, start=1.0)

Bases: stochasticprocess.WienerProcess

class implementing general Gauss process between grid dates

evolve(x, s, e, q)

mean(t)

variance(t)

class stochasticprocess.MultiGauss(mu=[0.0], covar=[[1.0]], start=[0.0])

Bases: stochasticprocess.MultivariateStochasticProcess

class implementing multi dimensional brownian motion

evolve(x, s, e, q)

mean(t)

variance(t)

class stochasticprocess.MultivariateStochasticProcess(start)

Bases: stochasticprocess.StochasticProcess

class stochasticprocess.OrnsteinUhlenbeckProcess(theta=0.1, mu=0.1, sigma=0.1, start=0.0)

Bases: stochasticprocess.StochasticProcess

class implementing Ornstein Uhlenbeck process

Parameters:

• theta (flaot) – mean reversion speed
• mu (float) – drift
• sigma (float) – diffusion
• start (float) – initial value

$$dx_t = \theta ( \mu - x_t) dt + \sigma dW_t, x_0 = a$$

evolve(x, s, e, q)

mean(t)

variance(t)

class stochasticprocess.SABR(alpha=0.1, beta=0.2, nu=0.3, rho=-0.2, start=0.05)

Bases: stochasticprocess.MultivariateStochasticProcess

class implementing the Hagan et al SABR model

evolve(x, s, e, q)

mean(t)

variance(t)

class stochasticprocess.StochasticProcess(start)

Bases: object

diffusion_driver

diffusion driver are the underlying dW of each process X in a SDE like dX = m dt + s dW :return list(StochasticProcess):

evolve(x, s, e, q)

Parameters:

• x (float) – current state value, i.e. value before evolution step
• s (float) – current point in time, i.e. start point of next evolution step
• e (float) – next point in time, i.e. end point of evolution step
• q (float) – standard normal random number to do step

Return float:

next state value, i.e. value after evolution step

evolves process state x from s to e in time depending of standard normal random variable q

class stochasticprocess.WienerProcess(mu=0.0, sigma=1.0, start=0.0)

Bases: stochasticprocess.StochasticProcess

class implementing general Gauss process between grid dates

evolve(x, s, e, q)

mean(t)

variance(t)

Stochastic Process Simulation

module containing stochastic process model producer

class stochasticproducer.CorrelatedGaussEvolutionProducer(producers, correlation=None, diffusion_driver=None)

Bases: producers.MultiProducer

class implementing general correlated Gauss process between grid dates

Parameters:

• producers (list(GaussEvolutionProducer)) – list of producers to evolve
• or dict((StochasticProcess, StochasticProcess) (list(list(float))) – float) or None correlation: correlation matrix of underlying multivariate Gauss process of diffusion drivers. If dict keys must be pairs of diffusion drivers, diagonal and zero entries can be omitted. If not give, all drives are evolve independently.
• or None diffusion_driver (list(StochasticProcess)) – list of diffusion drivers indexing the correlation matrix. If not given and correlation is not an IndexMatrix, e.g. comes already with list of drivers, it is assumed that each process producer has different drivers and the correlation is order in the same way.

evolve(new_date)

evolve to the new process state at the next date

Parameters:new_date (date) – date or point in time of the new state Return State:

class stochasticproducer.GaussEvolutionFunctionProducer(func=None, initial_state=None, length=None)

Bases: engine.Producer

class implementing general Gauss process between grid dates

Parameters:

• func (callable) – evolve function, e.g. lambda x, s, e, q: x + sqrt(e - s) * q by default with x current state value, s current point in time, i.e. start point of next evolution step, e next point in time, i.e. end point of evolution step, q standard normal random number to do step
• initial_state – initial state (value) of evolution,
• or None length (int) – length of q as a list of Gauss random numbers, if None or 0 the evolution function func will be invoked with q not as a list but a float random number.

class implementing general Gauss process between grid dates and provides state to any evolve style function foo(x, s, e, q) with x last state, s last state time, e current point in time and q current Gauss process state

evolve(new_date)

evolve to the new process state at the next date

Parameters:new_date (date) – date or point in time of the new state Return State:

class stochasticproducer.GaussEvolutionProducer(process)

Bases: stochasticproducer.GaussEvolutionFunctionProducer

producer to bring diffusion process to life

Parameters:process (StochasticProcess) – diffusion process to evolve

class stochasticproducer.MultiGaussEvolutionProducer(process_list, correlation=None, diffusion_driver=None)

Bases: stochasticproducer.CorrelatedGaussEvolutionProducer

class implementing multi variant GaussEvolutionProducer

class stochasticconsumer.StatisticsConsumer(func=None, statistics=None)

Bases: consumers.TransposedConsumer

run basic statistics on storage consumer result per time slice

finalize()

finalize for StatisticsConsumer

class stochasticconsumer.StochasticProcessStatisticsConsumer(func=None, statistics=None)

Bases: stochasticconsumer.StatisticsConsumer

run basic statistics on storage consumer result as a stochastic process

finalize()

finalize for StochasticProcessStatisticsConsumer

class stochasticconsumer.TimeWaveConsumer(func=None)

Bases: consumers.TransposedConsumer

initiatlizes consumer by providing a function :param func: consumer function with exact 1 argument which will consume the producer state. Default will return state.value

finalize()