Stochastic Calculus Roadmap for Quants

Watch the video for the sequence of study! https://youtu.be/whdFQLP4kO4?si=VLKfAicKKsv1p1z3

This covers the following topics:

- Topic 0: Foundations — measures P vs Q, numéraire, Greeks, price vs value function

- Topic 1: Brownian motion, filtrations, martingales

- Topic 2: Itô calculus — Itô integral, Itô’s lemma, local time

- Topic 3: SDEs and canonical diffusions — GBM, OU, CIR, CEV, local vol

- Topic 4: Measure change and risk‑neutral pricing — Girsanov, forward measures

- Topic 5: Generators, Feynman–Kac, Kolmogorov link to PDEs

- Topic 6: Greeks, replication, hedging

- Topic 7: Jumps and Lévy models

- Topic 8: Stochastic vol, local vol, and hybrids — Heston, SABR, SLV

- Topic 9: Rough volatility (optional depth)

- Topic 10: Optimal stopping and Americans

- Topic 11: Control, HJB, BSDEs, FBSDEs

- Topic 12: Term structure — short‑rate, HJM, LMM

- Topic 13: Filtering and latent‑state inference

- Topic 14: Numerics and engines — SDE, PDE, MC, Fourier

- Topic 15: Calibration, identifiability, model risk

- Topic 16: Risk, exposures, xVA