Python for Finance, 3rd Edition

Chapter 29. Derivatives Valuation

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Simulating risk-factor paths is only the first half of the story. Once you have scenarios, you still need to turn them into option values and risk measures in a way that is reproducible, testable, and easy to extend. This chapter implements the “valuation layer” of dxlib and uses it to price a European option and, as the main focus, an American put option via the Longstaff-Schwartz least-squares Monte Carlo (LSM) algorithm.

This chapter extends dxlib from “model simulation” to “derivatives valuation”. You implement terminal payoff classes, deterministic discounting for year-fraction time grids, a small European Monte Carlo pricer, and an LSM pricer for an American put option on an equity index. The chapter also adds diagnostic visualizations that help you reason about Monte Carlo noise and early-exercise behavior. The examples assume numpy, Matplotlib, and the simulation layer from Chapter 28.

From Paths to Values

The risk-neutral pricing relationship introduced ...