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?

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