Quality Seal Emagister EMAGISTER CUM LAUDE

Intermediate Mathematics: Understanding Stochastic Calculus

London Financial Studies
En London (Inglaterra), New York (Estados Unidos)

1001-2000

Información importante

Descripción

The use of probability theory in financial modelling can be traced back to the work on Bachelier at the beginning of last century with advanced probabilistic methods being introduced for the first time by Black, Scholes and Merton in the seventies.

Modern financial quantitative analysts make use of sophisticated mathematical concepts, such as martingales and stochastic integration, in order to describe the behaviour of the markets or to derive computing methods.

This course bridges the gap between mathematical theory and financial practice by providing a hands on approach to probability theory, Markov chains and stochastic calculus. Participants will practice all relevant concepts through a batch of Excel based exercises and workshops.

Información importante
¿Qué objetivos tiene esta formación?

¿Esta formación es para mí?

- Quantitative analysts
- Financial engineers
- Researchers
- Risk managers
- Structurers
- Market analysts and product controllers

Past participants have included: Chief investment officers, Asset Managers, Strategists, Private Banks, Relationship Managers

Requisitos: Delegates should have a good understanding of Elementary Probability Theory, Calculus and Linear Algebra (covered in Maths Refresher).

Instalaciones y fechas

Dónde se imparte y en qué fechas

Inicio Ubicación
15 junio 2017
London
34 Curlew Street, se12nd, London, Inglaterra
Ver mapa
A elegir
New York
New York, Estados Unidos
Ver mapa

¿Qué aprendes en este curso?

Mathematics
Calculus
Financial
Financial Training
GCSE Mathematics
Probability
Poisson Distribution
Differential Equations
Mathematics
Stochastic Calculus
Markov Chains
Binomial
Gamma distribution
Exponential distribution
Bernoulli

Temario

Day One

Probability Theory
  • Random variables, independence and conditional independence. Discrete random variables: mass density, expectation and moments calculation
  • Conditional discrete distributions, sums of discrete random variables
  • Continuous random variables; Probability density function, cumulative probability density function; Expectation and moments calculation; Conditional distributions and conditional expectation; Functions of random variables
Examples: Normal distribution, gamma distribution, exponential distribution, Poisson distribution

Exercise: Properties of the gamma distribution and the log normal distribution

Workshop: Multivariate normal distributions. Linear transformations. Counter example
  • Generating functions. Moment generating functions. Characteristic functions
  • Convergence theorems: the strong law of large numbers, the central limit theorem
Examples: Characteristic functions of Bernoulli, binomial, exponential distributions

Exercise: Moment generating functions and characteristic functions of Poisson, normal and multivariate normal distributions

Markov Chains
  • Discrete time Markov chains, the Chapman Kolmogorov equation
  • Recurrence and transience. Invariance
  • Discrete martingales. Martingale representation theorem. Convergence theorems
Examples: Random walks: simple, reflected, absorbed

Workshop: Pricing European options within the Cox Ross Rubinstein model
  • Continuous time Markov chains. Generators
  • Forward/backward equations. Generating functions
Example: The Poisson process

Exercise: Superposition of Poisson Processes. Thinning

Day Two

Stochastic Calculus
  • The Wiener process. Path properties. Monte Carlo simulation
  • Gaussian processes. Diffusion processes
Examples: The Wiener process with drift. The Brownian Bridge

Exercise: The Geometric Brownian Motion. Properties of its distribution (moments)
  • Semi martingales. Stochastic integration
  • Ito's formula. Integration by parts formula
Workshop: Multivariate normal distributions. Linear transformations. Counter example

Examples: Characteristic functions of Bernoulli, binomial, exponential distributions

Exercises: Moment generating functions and characteristic functions of Poisson, normal and multivariate normal distributions

Stochastic Differential Equations
  • Stochastic differential equations. Existence and uniqueness of solutions. Equations with explicit solutions
  • The Markov property. Girsanov's theorem
Exercise: The Vasicek model. Connection with the O U process. Mean. Variance. Covariance. Pricing zero coupon bonds

Workshop: The Cox Ingersoll Ross Model. Connection with the O U process. Properties of its distribution (mean variance, covariance). Pricing zero coupon bonds