Modern Computational Finance

CHAPTER 12Differentiation of the Simulation Library

12.1 ACTIVE CODE

In this chapter, we apply the AAD library from the previous chapter to differentiate our simulation library from Part II. More precisely, we apply AAD to compute the differentials of prices to model parameters. In the next chapter, we discuss differentials of prices to market variables, also called market risks or hedge coefficients.

What will clearly appear is that an efficient AAD library is certainly necessary, but absolutely not sufficient for the efficient differentiation of complex valuation code. It takes work, art, and skill to correctly instrument calculation code. An efficient AAD library provides all the necessary pieces, but to articulate them together in an efficient instrumentation requires an intimate knowledge of the instrumented algorithms (known as domain-specific knowledge) and a comprehensive understanding of the inner mechanics of the AAD library. The notion that one can template calculation code, link to an efficient AAD library, and obtain differentials with AAD speed is a myth. Instrumentation takes at least as much skill and effort as the production of the AAD library itself. A naive instrumentation does produce differentials in constant time, but it may be a very long constant time, often slower than finite differences. While the notion of an efficient instrumentation depends on the differentiated code, this chapter provides general advice and battle-tested methodologies while instrumenting ...