Module 1 - Building Blocks of Quantitative Finance

In module one, we will introduce you to the rules of applied Itô calculus as a modeling framework. You will build tools using both stochastic calculus and martingale theory and learn how to use simple stochastic differential equations and their associated Fokker- Planck and Kolmogorov equations.

Sections

The Random Behavior of Assets

Accordion Content

• Different types of financial analysis
• Examining time-series data to model returns
• Random nature of prices
• The need for probabilistic models
• The Wiener process, a mathematical model of randomness
• The lognormal random walk- The most important model for equities, currencies, commodities and indices

Binomial Model

Accordion Content

• A simple model for an asset price random walk
• Delta hedging
• No arbitrage
• The basics of the binomial method for valuing options
• Risk neutrality

PDEs and Transition Density Functions

Accordion Content

• Taylor series
• A trinomial random walk
• Transition density functions
• Our first stochastic differential equation
• Similarity reduction to solve partial differential equations
• Fokker-Planck and Kolmogorov equations

Applied Stochastic Calculus 1

Accordion Content

• Moment Generating Function
• Construction of Brownian Motion/Wiener Process
• Functions of a stochastic variable and Itô’s Lemma
• Applied Itô calculus
• Stochastic Integration
• The Itô Integral
• Examples of popular Stochastic Differential Equations

Applied Stochastic Calculus 2

Accordion Content

• Extensions of Itô’s Lemma
• Important Cases - Equities and Interest rates
• Producing standardised Normal random variables

Martingales

Accordion Content

• Binomial Model extended
• The Probabilistic System: sample space, filtration, measures
• Conditional and unconditional expectation
• Change of measure and Radon-Nikodym derivative
• Martingales and Itô calculus
• A detour to explore some further Ito calculus
• Exponential martingales, Girsanov and change of measure

Message Text

Lecture order and content may occasionally change due to circumstances beyond our control. However, this will never affect the quality of the program.

Quantitative Risk & Return