The vision behind DEXISION has always been to build a tool that implements “global valuation”. Global valuation is to be understood in the sense of a general market model according to the elegant valuation approach of Harrison and Pliska (1981). Large parts of this vision are available by now.
Back in 1998, in the midst of my Ph.D. work in financial economics, I sat in the library at Adelphi University, Long Island (NY), and studied the seminal articles of Harrison and Kreps (1979) as well as Harrison and Pliska (1981) about what is called today risk-neutral valuation and the Fundamental Theorem of Asset Pricing. There you find the description of a general market model as follows (pp. 224-225):
The probability space (Ω,F,P) is specified and fixed. The sample space Ω has a finite number of elements … Also specified is a time horizon T … Securities are traded at time t = 0,1,…,T … Taken as primitive in our model is a K+1 dimensional stochastic process S … We define a process β … and call it the discount process.
I was fascinated by the beauty of their mathematical approach and in particular its generality—to me it almost seemed that the problem of valuing financial derivatives has been solved (apart from maybe some technical issues) once and for all in full generality … I wondered if there could be one day a technological solution fully exploiting their insights. Something like a huge computer where you define your K+1 stochastic processes, model your contingent claims and get arbitrage-free values for everything of interest—and this in a market-consistent manner.
However, back then it was the time when computing power was still relatively low and expensive, financial engineering concentrated on single products and numerical methods, like Monte Carlo, were not yet fully developed. For example, a satisfactory approach to value American options by Monte Carlo simulation was still missing. Trigeorgis comments on Monte Carlo simulation in his book “Real Options” of 1996 on page 306:
As a forward-moving technique, however, it is not as useful for American-type options involving early exercise or other types of intermediate (flexible) decisions or in determining optimal policies.
During a consulting engagement 2002 in Vienna, I first encountered the scripting language Python which was mainly used for rapid prototyping back then. I also learned about Software-as-a-Service business models. At that time, Internet technology was evolving at a fast pace and computing power increased steadily and became more and more affordable.
During the years 2001 to 2004, important results to apply Monte Carlo simulation to more complex products (with American or Bermudan exercise and/or with multiple underlyings) were published. Due to its general flexibility and these recent results, Monte Carlo suddenly emerged as a promising path to the general risk-neutral valuation engine I somehow envisioned years earlier.
In 2004, I left my old company and moved back home to marry the love of my life. I took the chance to found a new company at the beginning of 2005 – Visixion – and started looking for someone capable of making my vision of a general valuation tool implementing the Harrison/Kreps/Pliska approach real.
In 2006, I found with Michael Schwed someone with both the mathematical and technical skills – and also the drive – to implement the general valuation engine. Since then, we have progressed a lot and are now able to offer with DEXISION Derivatives Analytics On Demand in quite a general fashion—coming already close to our original ambitions.
In hindsight, the key ingredients to accomplish our goals—gathered step by step on our way—have been:
- wonderful economic insights of Harrison/Kreps/Pliska embodied in the Fundamental Theorem of Asset Pricing
- vision and strong belief in the feasibility of a general valuation engine
- new Monte Carlo methods like the LSM approach of Longstaff and Schwartz (2001)
- Python as a highly efficient language for Derivatives Analytics (with Numpy for calculations at C speed)
- Open Source technology (Linux, Apache, AJAX, mySQL) for our On Demand, but desktop-like, software delivery model
- small team sharing the vision and having endurance (it wasn’t always that easy theoretically, practically, technically, …)
Finally, we got there and can now offer a Derivatives Analytics suite based on a global Monte Carlo valuation approach …
Only recently, there has been initiatives from other sides to accomplish global valuation. For example, Claudio Albanese is one of its proponents and writes:
The quantitative finance equivalent to the grand unified theory in physics is global valuation, where a single model can be used to price all instruments, but does such a model exist?
According to the Fundamental Theory of Finance, prices obtained by consistently using a single model are guaranteed to be arbitrage free, and conversely, given a set of arbitrage free prices, there must be a single model that can reproduce them (otherwise, by definition the prices will allow for arbitrage).
So we are confident that our approach will succeed in replacing one day other approaches to Derivatives Analytics that are mainly product-centric. However, we are aware that there is still a lot to do. But we are also ready to take on the challenge.
Yves Hilpisch
