DEXISION offers simple, Web-based Derivatives Analytics. This is the first post in a series that explains where the simplicity of our Web-based analytics suite stems from. We start today with the single numerical method, Monte Carlo simulation.
From the beginning on, we knew that we wanted to be able to value complex derivative instruments with, for example, multiple underlyings and path-dependent payoffs with DEXISION. Taking this a as a starting point—and nothing more—Monte Carlo simulation is almost always the only numerical method that remains to attack such problems.
But maybe one step back. You could argue that Monte Carlo simulation might be good for the problem described before but that other methods could be beneficial if you face a different problem, like plain vanilla option pricing. Granted this is of course the case. But what we had in mind for DEXISION was an analytics suite that should be as flexible as possible, giving the user (a financial engineer, quant, researcher, trader, etc.) as much flexibility in defining derivative instruments as possible.
To this end, we developed a modeling approach that rests on fundamental building blocks with which every instrument—be it vanilla or highly structured, equity or interest-sensitive—is engineered. A building block could be a base object (underlying) like an index (geometric Brownian motion). It could be a financial object with free-to-define payoff function and Bermudan exercise. In other words, for DEXISION a plain vanilla product is the same (technically) as a highly structured one and both are valued in the same fashion,s via Monte Carlo simulation.
Even if you can model and value plain vanilla options with DEXISION, our analytics suite was never targeted at this specifically. There are many other powerful analytics suites that accomplish such tasks better and faster (even in real-time for hundreds or thousands of positions).
From our point of view, sacrificing some things (like fast and accurate plain vanilla option pricing) on the one hand yields a number of substantial benefits on the other hand:
- unified modeling: all derivatives instruments are modeled in the same way
- unified valuation: they are also valued in the same way
- consistent value & risk aggregation: DEXISION produces for all base and financial objects consistent paths/ scenarios during a simulation run such that values (and risk measures) can be aggregated in a consistent fashion; something sometimes called “Global Valuation”
- unlimited modeling options: since Monte Carlo simulation is the most flexible numerical method it can handle almost anything you hand over to it
- easy enhancements: having available a generic Monte Carlo simulation engine (which takes care, for example, of all relevant dates), you can easily add new underlyings (i.e. new types of stochastic processes) as well as new structures (i.e. new types of payoff features)
- full visualization: Monte Carlo simulation lends itself perfectly well to visualizations of simulation and valuation results; no other method is comparable in this respect
All these benefits are from the viewpoint of a user of DEXISION and in that sense more of economic or financial nature. However, implementation issues also play a role. In his book “Introduction to C++ for Financial Engineers” (2006), the author Daniel Duffy compares on page 341 Monte Carlo simulation (MCS) to finite difference (FDM) and lattice methods (LAT). He comes to the following ranking (1 = best in this category, 3 = worst):
| FDM | MCS | LAT | |
| Accuracy | 2 | 1 | 3 |
| Performance | 1 | 3 | 2 |
| Applicability | 2 | 1 | 3 |
| Fault Tolerance | 3 | 1 | 2 |
| Maintainability | 2 | 1 | 3 |
| Extendability | 2 | 1 | 3 |
At least in this contest, Monte Carlo simulation seems to be the clear winner. However, for us as we are now working with it intensively since years we can fully agree with the rankings. Considering the advances in technology over the last years, the performance issue does not seem to be a real issue anymore. Just think of recent advancements with regard to Graphical Processing Units (GPU) for low cost but high performance financial computing. Or the availability of NumPy for Python which allows array manipulations with Python at the speed of C code. Not to mention the ever rising computing performance of standard processors from Intel or AMD.
What you can accomplish with simple means (i.e. Python on a notebook computer) in terms of speed of Monte Carlo simulations is analyzed in the context of American options with stochastic volatility and short rates in the paper Fast Monte Carlo Valuation.
All in all, to have only one numerical method for a derivatives analytics suite is simple in itself and reduces complexity significantly. However, the complete and consistent reliance on this method brings with it a number of benefits that will never be achievable by any other numerical method.
So Simplicity Principle No. 1 also implies that relying on only one (appropriate) numerical method can mean a major strength.
Yves Hilpisch
