From martingales to option pricing
4 readings
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.
- Who this is for
- Readers with calculus and probability who want to understand derivative pricing papers.
- What you will work towards
- Explain risk-neutral pricing and check a Monte Carlo price against a known analytic result.
Before you start
Use these SMQ lessons to check the ideas the readings assume. Lesson pages show the outline and how to access the full lesson.
- Expectation, Mean, and Variance
Read expected payoffs and risk estimates in the same mathematical language.
- Stochastic Processes, Brownian Motion and Itô's Lemma
Connect random price paths to the extra term in Itô’s formula.
Read in this order
Stochastic Calculus for Finance I
Use the binomial model to see replication and risk-neutral probabilities without stochastic calculus.
Stochastic Calculus for Finance II: Continuous-Time Models
Extend the discrete-time ideas to continuous price paths.
The Pricing of Options and Corporate Liabilities
Read the paper after its modelling ingredients are familiar.
Monte Carlo Methods in Financial Engineering
Turn the pricing expectation into a numerical experiment.
Continue your study on SMQ
- The Black-Scholes PDE, Formula and Implied Volatility
Connect replication, the pricing equation, and the volatility quoted by a market.
- Monte Carlo Option Pricing
Translate a risk-neutral expectation into a simulation with a standard error.
Follow the connected lessons, worked examples, and exercises in the app. Full lesson access depends on the topic and your membership.
Continue with options pricing