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Curriculum / Phase 2 · Core Quantitative Finance

Derivatives Pricing and Computational Finance

Learn option pricing and hedging through no-arbitrage, Black–Scholes, binomial trees and Monte Carlo methods.

Why study Derivatives Pricing and Computational Finance?

An option value is a claim about replication, uncertainty and the cost of hedging. This programme connects those ideas to numerical prices so you can explain a result and investigate where the assumptions fail.

Who this is for

For learners moving into derivatives research or pricing who have calculus, probability and scientific Python foundations.

What you should be able to do

  • Connect option payoffs, replication and risk-neutral valuation.
  • Study Black–Scholes, Greeks and hedging.
  • Compare computational methods for European, American and path-dependent options.

An example of the work this prepares you for

A pricing comparison with a benchmark, a convergence check and an explanation of the position’s main hedging sensitivities.

Prerequisites and suggested preparation

You should be comfortable with the background covered in these programmes. Equivalent knowledge from university study or independent learning is also suitable.

The goal is to use the foundations in context: explain the assumptions, carry out a calculation and interpret the result. If one of those steps feels unfamiliar, review the linked preparation first.

A preview of the learning journey

The lessons build towards these kinds of reasoning and practical work.

Reason from a payoff

Connect a contract’s economics to a defensible valuation argument.

Understand a hedge

Explain how exposures change when market inputs move.

Compare pricing methods

Judge accuracy, computational cost and model assumptions.

Members work through the detailed lessons, derivations, worked examples and solutions inside the learning dashboard.

Explore lesson previews by topic

Open a topic preview to see its introduction, learning objectives and prerequisites. Previous and next links let you explore the lessons in study order. Full lessons are available in the member dashboard; selected samples are free to read in full.

Topic previewFoundations of Computational Option Pricing11 lessonsTopic previewBinomial Trees, Barrier and American Options6 lessonsTopic previewMonte Carlo Methods and Stochastic Volatility9 lessonsTopic previewPath-Dependent Exotics Beyond Barriers5 lessonsTopic previewIndex, Currency, Futures and Multi-Asset Options4 lessons

Free resources to start learning

Use these alongside the programme or to prepare independently. Start with the introductory material, work through an example, then return to the research papers when the underlying ideas are familiar.

  1. University course · Free

    Foundations of Financial Engineering

    Columbia · Martin Haugh

    Read martingale pricing and Black–Scholes notes in sequence.

  2. University course · Free

    Topics in Mathematics with Applications in Finance

    MIT OpenCourseWare · 18.S096

    Watch the stochastic-process and options lectures for a mathematical bridge.

  3. Documentation · Free

    QuantLib

    QuantLib contributors

    Compare educational implementations with an established open-source library.

  4. Research paper · Free

    Volatility is rough

    Jim Gatheral, Thibault Jaisson and Mathieu Rosenbaum

    Later reading on why a simple volatility assumption may be insufficient; also catalogued in Directory.

    View research in Directory →

Optional textbook reference

These books are paid references. Check your university or public library for access.

  1. Textbook · Paid / library

    Options, Futures, and Other Derivatives

    John C. Hull · Pearson

    Optional textbook for instrument examples, pricing methods and hedging.

Links reviewed 14 October 2026. Free refers to the linked reading, notes or videos; printed books and certificates may cost extra.

Find more papers and learning materials in the SelfMadeQuant Directory.

Where this programme fits

  • Derivatives Pricing and Model Quant · required programme
  • Risk and Model Validation Quant · required programme

Ready to study Derivatives Pricing and Computational Finance? Explore membership for access to the complete lessons.

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Phase 2Portfolio Theory and Quantitative InvestmentStudy portfolio optimisation, diversification, factor models and performance evaluation for quantitative investment.Phase 2Fixed Income and Interest-Rate ModelsStudy bond pricing, yield curves, interest-rate risk and no-arbitrage term-structure models.Phase 2Quantitative Risk ManagementStudy quantitative risk management through loss distributions, tail risk, dependence, credit risk and model validation.Phase 2Quantitative Research, Data and BacktestingLearn to design financial research with point-in-time data, time-ordered validation and economically realistic backtests.Phase 2Market Microstructure and ExecutionStudy order books, liquidity, market impact and execution analysis from market data to executed positions.Phase 2Professional Quant PracticeDevelop the reproducibility, documentation, validation and communication practices used in quantitative model work.