Compound interest is the greatest mathematical discovery of all time.
— Albert Einstein
This chapter provides the framework for the development of the
DX library by introducing the most fundamental concepts needed for such an undertaking. It briefly reviews the Fundamental Theorem of Asset Pricing, which provides the theoretical background for the simulation and valuation. It then proceeds by addressing the fundamental concepts of date handling and risk-neutral discounting. We take only the simplest case of constant short rates for the discounting, but more complex and realistic models can be added to the library quite easily. This chapter also introduces the concept of a _market environment_—i.e., a collection of constants, lists, and curves needed for the instantiation of almost any other class to come in subsequent chapters.
The Fundamental Theorem of Asset Pricing is one of the cornerstones and success stories of modern financial theory and mathematics. The central notion underlying the Fundamental Theorem of Asset Pricing is the concept of a martingale measure; i.e., a probability measure that removes the drift from a discounted risk factor (stochastic process). In other words, under a martingale measure, all risk factors drift with the risk-free short rate—and not with any other market rate involving some kind of risk premium over the risk-free short rate.
Consider a simple economy at the ...