Heston model for Options pricing with ESGtoolkit

By Thierry Moudiki’s blog

Hi everyone! Best wishes for 2016!

In this post, I’ll show you how to use ESGtoolkit, for the simulation of Heston stochastic volatility model for stock prices. This is probably my last post on ESGtoolkit, before I start working on the project again (yeah, I know it’s been a while since v0.1! ).

If you’re interested in seeing other examples of use of ESGtoolkit, you can read these two posts: the Hull and White short rate model and the 2-factor Hull and White short rate model (G2++).

The Heston model was introduced by Steven Heston’s A closed-form solution for options with stochastic volatility with applications to bonds an currency options, 1993. For a fixed risk-free interest rate , it’s described as:

where .

In this model, under a certain probability, the stock price’s returns on very short periods of time of length , are: the risk-free rate + a random fluctuation driven by the terms and . The ‘s can be thought of (very simply put) as the gaussian increments of a random walk, which are centered, and have a variance equal to .

On the other hand, is the stochastic variance of the stock prices. is always positive, and tends to return to a fixed level at a speed controlled by . The variance of <img src="https://s0.wp.com/latex.php?latex=v_t&bg=ffffff&%23038;fg=333333&%23038;s=0" …read more

Source:: r-bloggers.com