One of the major cultural changes, and at the same time technical changes, the task force should address is the company’s need to learn how to live with mod- els. Several engineering companies have done so since the 1930s. The models at the time were water basins, where harbour projects and hydroelectric dams were studied. There were also wind tunnels for aerodynamic aircraft design studies.
Physical models are still around, but after World War II they started giving way to digital differential analysers. In 1951, when I served my apprenticeship at
Electricité de France, through an EDF scholarship, I was studying powergrids with them and found it to be a rewarding experience. Simulation provides both:
● Insight, and
● Foresight.
Digital differential analysers were a hybrid, half physical and half mathematical, engine. As simulators they were a precursor to digital simulation done by means of mathematical models and digital computers. Simulation has been the gateway of mathematical analysis into finance.
All simulations are based on analogies.3 These analogies are made of a number of working assumptions reflected into algorithms and heuristics. Algorithms may not be capable of duplicating actual life, but they are approximating it.
Therefore, results obtained through modelling have inherent limitations. For instance, in finance, unlike a real life performance record, simulated returns do not represent actual trading. Still they can be very useful for:
● Prognostication
● Experimentation, and
● Management control reasons.
The first lesson in learning to live with models is that when analogous systems are found to exist, or are constructed to map into them some other system’s behaviour, then studies done in one of them – the simulator– can help in mak- ing inferences about the other.
● The benefit is better vision, and
● The cost is a lower accuracy than observation made in real life.
For instance, since the trades have not actually been executed, the results obtained through modelling may have over- or under-compensated for the impact of market factors. When this happens, it is mainly due to the hypotheses we have made, scarce data we have available, or plain algorithmic insufficiency.
This leads to model riskand it constitutes the second lesson in learning to live in a financial world populated with models. All domains, from engineering and physics to finance, are exposed to varying degrees of model risk. Financial mar- ket factors we often study through simulation are:
● Changes in volatility
● Liquidity constraints
● Product pricing
● Extreme market events
● Changes in exposure
● Capital at risk
● Fee schedules
● Transaction costs, and more.
Many people think of the Monte Carlo method as being the only simulator.
(‘Monte Carlo’ is the name Dr John von Neumann gave to Lord Raleigh’s random walks – a stochastic process developed in the late 19th century.) The method makes possible studying the behaviour of patterns as diverse as the:
● Decay of atomic particles, and
● Prepayment of a pool of securitized mortgages, which is also a process of decay over time.
Modelling and simulation does not really need to be awfully complex, neither should one shy away from learning how to develop and use models. For instance, actuarialmodels are today second nature in the insurance industry, so much so that really nobody thinks of them as being mathematical artifacts. This is the third important lesson, in connection to learning to live with models.
When it is used for the purpose of discounting cash flow from a financial instru- ment inventoried in the bank’s portfolio, an actuarial model provides a good example of fair value computation requested by IAS 39. However, let us take good note of the fact that:
● The actuary makes no claim as to any special ability to predict interest rates.
● What he or she does is to compute compound interest, by knowing how to apply mathematics to practical problems.
Actuaries make wide use of present value, in which future money flows are dis- counted. This means they are valued in a current time frame by taking into explicit account the time value of money. The basic formula for present value of a dollar in future years is:
(1 ⫹i)t where:
t the number of years hence
i the effective annual rate of interest
Present value calculations can also involve discounts for other factors, but invariably the time value of money is present. Many investors, too, have learned to differentiate between discounted and not-discounted cash flows, gross and net interest, before tax and after tax, nominal, effective, and real rates of interest, as well as internal rates of return. A more sophisticated study on present value will account for yield curves, as well as for
● Relationships between interest rates for different maturity periods
● Effect of exchange rates on interest rate of return of debt instruments, and other factors.
The hypotheses we make should recognize that any specific interest rate has a basic component for time preference. There are also additional components of which we did not speak at this point; but which should be accounted for in a detailed study on risk and return. For instance, inflation expectations, and pos- sibility of default.
The reader will appreciate that we are still in the early days of rocket science in the world of finance. If we look back a few centuries, we will see that in the 17th century, physics entered into a new era, thanks to the use of mathematics. In a manner, toward the end of the 20th century finance took a similar giant step through contributions of certain brilliant individuals.4 This has been preceded by the use of mathematics in economics, which started at the end of the 19th century.
While one might suggest that IFRS and simulation are two distinct and unrelated subjects, such a suggestion would rest on very shaky ground. First and foremost, as we saw in Chapters 1 and 2, Fra Luca Paciolo who expressed the rules of accounting, which he developed as a system, in his 1494 book Summa da Arithmetica Geometria Proportioni e Proportionalita, was a mathematician.
But there is much more to the connection an IFRS project should have to mod- els and simulation, and this is for two reasons. One is a priori and the other a posteriori of IFRS. As we have already seen on several occasions in Part One:
● Fair value estimates are done partly by marking to market and partly by marking to model.
Ifthe task force leaves the concept and practice of modelling and simulation out of the sphere of its basic activities, then its work will be half-baked. The com- pany will not be able to satisfy fundamental IFRS, and most particularly IAS 39,
requirements in an able manner. It needs no explaining that this should notbe the case.
● Since IFRS provides a modern, dynamic, and fairly accurate accounting infrastructure, it would really be a pity not to use its produce to the fullest possible extent.
The example on possible benefits offered by section 6 is on personal productiv- ity. As we will see in this example, doing away with trivia and time-consuming administrative duties requires accurate accounting and statistics, a good deal of modelling, as well as the use of knowledge engineering artifacts like expert sys- tems and mobile agents. The task force should include such deliverables among its priorities.