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Roadmaps / Pricing and derivatives

Derivatives Pricing Quant

Builds the models and code a derivatives desk uses to price and hedge, and makes the numbers defensible.

The job

A derivatives pricing quant, often called a front-office or model-development quant, builds the formulas, trees, PDE solvers and Monte Carlo engines a desk prices and hedges with, plus the Greeks that come out of them. Related roles in valuation control check that the desk’s marks are supported by market quotes. The work is making prices correct, fast and defensible. Things go wrong when numerical error is mistaken for model error, or when a model is calibrated to quotes nobody could trade.

Supports
Front-office derivatives desks and valuation control
Stages
6 to learn, then proof of work
Two routes
Free resources, or SelfMadeQuant programmes and projects

The roadmap

The same stages either way. The free route uses university courses, lectures, books and papers that are free online. The SelfMadeQuant route maps each stage to our programmes and ends in projects on real market data.

  1. Stage 01 · Foundations

    Probability and stochastic calculus

    The language every pricing model is written in.

    • Brownian motion
    • Itô’s lemma
    • Martingales
    • Risk-neutral pricing

  2. Stage 02 · Foundations

    Options and no-arbitrage

    Payoffs, bounds and the first pricing models. Every later price must respect these bounds.

    • Payoffs and put–call parity
    • Arbitrage bounds
    • Binomial model
    • Black–Scholes and Greeks

  3. Stage 03 · Core

    Trees, PDEs and Monte Carlo

    The three engines behind almost every price a desk quotes.

    • Binomial and trinomial trees
    • Finite differences
    • Monte Carlo and variance reduction
    • American and barrier options

  4. Stage 04 · Core

    Numerical analysis and calibration

    Telling numerical error from model error, and fitting a model to quotes.

    • Floating point and conditioning
    • Root finding
    • Calibration as optimisation

  5. Stage 05 · Specialist

    Smile models

    Why Black–Scholes is not enough, and the models that fit the smile.

    • Implied vol surface
    • Local volatility (Dupire)
    • Heston
    • SABR

  6. Stage 06 · Specialist

    Rates and counterparty risk

    The rest of the derivatives pathway: rate models and the cost of counterparty default.

    • Short-rate models
    • Exposure simulation
    • CVA and DVA

  7. Stage 07 · Proof of work

    Calibrate Heston to a live crypto option surface

    Pull Bitcoin option quotes from Deribit's public API, back out implied volatilities and calibrate both Black-Scholes and Heston to the surface. Answer whether Heston's fit error and parameter stability across days justify its extra complexity over a per-expiry Black-Scholes fit.

    Free data to start with

Practise the interview

Questions this role gets asked, each with a hint and a worked solution.

  1. Price a cash-or-nothing digital call under Black–Scholes, and explain why it is hard to hedge near expiry.
  2. What does Itô’s lemma say, and why does every pricing quant need it?
  3. Prove that a European call price is convex in its strike. What trade do you put on if quotes break that?

Start the SelfMadeQuant route free: a free account opens one complete topic from each primer and the interview question bank. No card needed.

Start free