The answer to the question mentions "using stochastic or Monte Carlo techniques" I read it as pointing out two distinct methods for carrying out stress test or scenario testing.... For me stochastic or Monte Carlo are the same techniques, both based on running simulations. What are the distinct differences between stochastic and Monte Carlo techniques that the answer is implying?
Monte Carlo techniques are based on sampling but there are stochastic techniques (think Black-Scholes) which don't require sampling.
Monte Carlo is pseudo - random, you assume a probability distribution. With any stochastic simulation you don't need to use a probability distribution... ...for example simulating using an Economic Scenario Generator. Shillington, Black - Scholes is not simulation, it is a closed form solution.
Thanks Edwin. I am familiar with stochastic simulations and ESGs. How can you use Monte Carlo in practice for performing stress testing and scenario testing?
Adapt a probability distribution via the inverse transform method and use Monte Carlo to produce 2000 balance sheets, the pdf here may be underlying the assets returns and hence market values in your balance sheet. Stress testing means you now assume the assets (or equity component of the assets) in all the 2000 balance sheets are 20% down. Scenario testing means you assume equity component and interest rates and inflation say. Then you tell management if I stress test the equity returns by 20%, the effect on our ROE is X%. This X% is the average of 2000 ROEs
I wasn't saying that it was a simulation based method. I was saying that it's a stochastic method which isn't simulation based...
Hi Shillington I would argue that the Black-Scholes option pricing formula does not rely on sampling and is not stochastic. Even though it does involve a probability distribution, given a set of inputs the result will always be the same. This is because d_1 and d_2 are essentially deterministic. However, my understanding of what constitutes "stochastic" may be wrong... Thanks Alastair
I agree that the output (i.e. price) you get from Black-Scholes is not stochastic, it is a number. In much the same way that the output you get from a simulation based technique when you use a VaR is also a number. The underlying mechanics of how you got that number are still stochastic though, as you say there are distributional assumptions. Do you agree with Edwin's posts giving examples of the distinction between a "stochastic" model and a monte-carlo model?
Shillington, I was actually trying to consider the differences between Stochastic Simulation and Monte Carlo. Thanks, ddnt know it was actually just stochastic vs Monte Carlo
