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Topics in Mathematics with Applications in Finance (MIT 18.S096, Fall 2013)
Course
by MIT OpenCourseWare
Tags
financemathematical financeportfolio theorystochastic calculus
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Build the foundations
Suggested foundations for stochastic processes and pricing and options and derivatives pricing. Specialist prerequisites vary by resource.
Before you read
- Conditional Expectation
Understand what it means to condition on current information.
- Stochastic Processes, Brownian Motion and Itô's Lemma
Follow Brownian dynamics and the second-order term in Itô calculus.
- The Binomial Model
Build replication and risk-neutral probabilities in a tractable model.
- Market Model and Risk-Neutral Valuation
Distinguish pricing probabilities from physical forecasts.
Go further
- Simulating SDEs
Translate continuous dynamics into a numerical experiment.
- The Black-Scholes PDE, Formula and Implied Volatility
Connect the pricing equation, closed-form value and implied volatility.
Explore a related reading path
- From martingales to option pricing
Start in discrete time, move to Brownian motion, then read the original pricing argument and simulate it.