HESTON MODEL – MONTERCARLO SIMULATION

HOW CAN YOU MAKE A MONTECARLO SIMULATION WITH THE HESTON MODEL? 

Normally, when stocks prices are in a downward trend, volatility spikes. On the other hand, when the market is going upwards, volatility tends to diminish. To refer to this phenomenon people say “stocks take the stairs up and the elevator down” meaning stocks go up slowly and down very fast. One can simulate this kind of behavior using some special kind of models known as stochastic volatility models. This kind of models simulate not only the evolution of the stock price or an underlying such as an exchange rate or a commodity prices, but also its volatility. The Heston model belongs to this type of models. The Heston model has become very popular, specially in the FX Options arena. The reason is that it helps you model the volatility smile very easily. There is not a way to discretize the Heston differential equation to get an exact solution. However there is an approximation using the euler method, which we share here. 

HOW DOES A MONTERCARLO SIMULATION OF THE HESTON MODEL LOOK LIKE? 

In the chart below, we show a Montecarlo Simulation for the S&P500 starting at 4250 using the Heston Model. In this model you have parameters such as the correlation between the spot price and the volatility. A negative correlation means, that when stocks go down, volatility rises.

Figure 1

Here is a link to our github site where you can get python code to run this Montecarlo Simulation for the Heston Model. The link allows you to play with the different parameters you need to model the underlying price, its volatility, the correlation of the volatily of the underlying and the volatility and so on. Please tak a look and write us if you have any doubts. We hope you find it useful!

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