How to Generate Correlated Assets and Why?

As soon as you will get into pretty complex derivatives, for example, you will need to generate correlated assets for pricing purposes. Example of such derivatives can be: Basket options Rainbox options Moutain ranges (created by Société Générale) The most complex amongst these derivatives cannot be priced using closed form formulae, Monte Carlo simulations are … Continue reading How to Generate Correlated Assets and Why?

Speed Execution Benchmark on Monte Carlo

Today I will try to benchmark the execution speed of several programming languages on a Monte Carlo example. This benchmark involves VBA, C++, C#, Python, Cython and Numpy vectorization. I will try to add progressively other programming languages so that this article will be more thorough. Execution environment All the chunks of code have been … Continue reading Speed Execution Benchmark on Monte Carlo

Barrier option pricing with Monte Carlo

In this short article, I will apply Monte Carlo to barrier option pricing. Here are the points I am going to tackle: Quicker barrier options reminder Pros and cons of Monte Carlo for pricing Steps for Monte Carlo Pricing Up-and-Out Call pricing example Conclusion and ideas for better performance Barrier options Before entering in pricing … Continue reading Barrier option pricing with Monte Carlo

Monte Carlo Simulations of an asset with Black & Scholes dynamic

Introduction This first and basic article will show how to simulate a security following the Black & Scholes dynamic : $latex \frac{dS_t}{S_t} = \mu dt + \sigma dB_t$ When solving this stochastic differential equation with Ito, you finally obtain: $latex S_T = S_0 e^{(\mu - \frac{\sigma ^2}{2})T + \sigma B_T}$ The browian motion $latex B_T$ … Continue reading Monte Carlo Simulations of an asset with Black & Scholes dynamic