Computational cost in Monte Carlo simulation using vectorization

Introduction

This repo contains an implementation of pricing financial derivatives using Monte Calo simulation with vectorization calculation. Generally speaking, computer program spend most of the time in loop process. Especially, Monte Carlo simulation(MCS) in finance is mainly composed of for-loop or while-loop.

The main purpose of this repo is to introduce the method for increasing performance of MCS using vectorization calculation. The program is performed by Python.

Methods

As I mentioned in Introduction, loop is the main reason for increasing cpu time. It means that the more the number of loop and nested-loop, the more programs spend more time. In most programs with numerical methods, one of role of loop is to handle vector or matrix type data. To improve the performance of vector and matrix operation, several libraries has been developed such as Eigen-C++, Boost-C++, and Numpy-Python.

Environment

• CPU : Intel(R) Core(TM) i5-6400 @ 2.7GHZ
• RAM : DDR3L 16GB PC3-12800
• Python 2.7, numpy 1.10.4

Parameters

• Test case : European vanilla call option

	Stock	Strike	Maturity	Riskless interest rate	Volatility	Number of simulations
Parameters	100.0	100.0	1.0	0.03	0.3	105, 106, 107

Result

• In this repo, I compare the cpu time(seconds) of three version for MCS using Numpy-Python. The parameters can be modified freely.
• version 0 : Call random number function every time
• version 1 : Call random number function at a time such as (# of simulations × # of time steps)
• version 2 : Vectorized path generation and call random number function at a time such as (# of simulations × # of time steps)

cpu time(sec)	105simuls	106simuls	107simuls
version 0	0.1176	1.2223	11.6426
version 1	0.1354	1.3635	13.1086
version 2	0.0059	0.0726	0.7396

** Exact value of European call option: 13.28331

Note

• If you're interested in my works, please email me.