---
title: Financial Mathematics
description: Financial mathematics applies mathematical modeling and quantitative methods to financial markets. Learners will understand how to price derivative securities, manage portfolio risk, and model asset price movements using stochastic calculus and interest rate theory.
category: mathematics
subcategory: applied-mathematics
difficulty: beginner, intermediate, advanced
url: /subject/financial-mathematics
---

# Financial Mathematics

Financial mathematics applies mathematical modeling and quantitative methods to financial markets. Learners will understand how to price derivative securities, manage portfolio risk, and model asset price movements using stochastic calculus and interest rate theory.

## Available Resources

3 Books • 1 Courses • 1 Websites • 1 Papers

## Websites

### 1. 46-944 Stochastic Calculus for Finance — CMU Course Notes

**Author:** Gautam Iyer

Free lecture notes and scanned board notes from Carnegie Mellon's graduate stochastic calculus course. Covers martingales, Brownian motion, Itô integrals, Girsanov's theorem, and risk-neutral measures, with homework, exams, and full solutions. Creative Commons licensed.

**Difficulty:** Advanced | **Language:** English | **Price:** Free

**Link:** https://www.math.cmu.edu/~gautam/sj/teaching/2016-17/944-scalc-finance1/

**Tags:** stochastic-calculus, brownian-motion, ito-calculus, martingales, risk-neutral-pricing

## Papers

### 1. The Pricing of Options and Corporate Liabilities (1973)

**Author:** Fischer Black, Myron Scholes

The 1973 Journal of Political Economy paper deriving the option pricing formula from a riskless hedged portfolio argument. Scanned original, hosted by Princeton. Also shows how corporate bonds, stock, and warrants can be valued as options.

**Difficulty:** Advanced | **Language:** English | **Price:** Free

**Link:** https://www.cs.princeton.edu/courses/archive/fall08/cos323/papers/black_scholes73.pdf

**Tags:** black-scholes, option-pricing, derivatives, financial-economics, corporate-liabilities

## Books

### 1. Stochastic Calculus for Finance II: Continuous-Time Models

**Author:** Steven E. Shreve

Grew out of Carnegie Mellon's computational finance master's program. Builds measure-theoretic probability, Brownian motion, Itô integration, and risk-neutral pricing, then applies them to exotic options, term structure models, foreign exchange, and jump-diffusion processes.

**Difficulty:** Advanced | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0387401016?tag=edmonddante07-20

**Tags:** stochastic-calculus, continuous-time-finance, risk-neutral-pricing, ito-calculus, derivatives-pricing

### 2. Financial Calculus: An Introduction to Derivative Pricing

**Author:** Martin Baxter, Andrew Rennie

A compact bridge from binomial trees to continuous-time martingale pricing. Develops change of measure, the Girsanov theorem, and the Heath-Jarrow-Morton interest rate framework without heavy measure-theoretic machinery, favoring financial intuition over formal proof. Fills the level gap that otherwise kills people: Hull is too light on theory, Shreve demands measure theory.

**Difficulty:** Intermediate | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/0521552893?tag=edmonddante07-20

**Tags:** derivatives-pricing, martingales, girsanov-theorem, interest-rate-models, financial-mathematics

### 3. Options, Futures, and Other Derivatives (11th Edition)

**Author:** John C. Hull

The standard derivatives reference across trading desks and MFE programs. Covers forwards, futures, swaps, option pricing, the Greeks, volatility smiles, interest rate derivatives, and credit risk, using minimal stochastic calculus before introducing the Black-Scholes-Merton framework. The prerequisite layer for everything else in this topic: you cannot price a derivative with stochastic calculus until you know what the instruments are.

**Difficulty:** Beginner | **Language:** English | **Price:** Paid

**Link:** https://www.amazon.com/dp/013693997X?tag=edmonddante07-20

**Tags:** derivatives, options, futures, swaps, black-scholes, risk-management

## Courses

### 1. Topics in Mathematics with Applications in Finance (MIT 18.S096)

**Author:** Peter Kempthorne, Choongbum Lee, Vasily Strela et al.

Pairs mathematics lectures by MIT faculty with lectures from industry practitioners: linear algebra, probability, time series, volatility modeling, portfolio theory, stochastic calculus and Black-Scholes pricing. Includes 24 lecture videos, lecture slides and problem sets, showing how these quantitative tools are used in finance.

**Difficulty:** Intermediate | **Language:** English | **Price:** Free

**Link:** https://ocw.mit.edu/courses/18-s096-topics-in-mathematics-with-applications-in-finance-fall-2013/

**Tags:** financial-mathematics, stochastic-calculus, time-series, portfolio-theory, quantitative-finance

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