Module 1 - Building Blocks of Quantitative Finance

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This module covers the foundational math essential to success in the CQF program, and as a quant. You will be introduced to the rules of applied Itô calculus as a modelling framework. You will build tools in both stochastic calculus and martingale theory and look at simple stochastic differential equations and their associated Fokker-Planck and Kolmogorov equations. 

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Sections

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The Random Behavior of Assets

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  • 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

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PDEs and Transition Density Functions

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  • 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

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Applied Stochastic Calculus 1

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  • 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

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Applied Stochastic Calculus 2

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

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Binomial Model

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

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Martingales

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  • 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

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

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Quantitative Risk & Return