Intermediate Mathematics: Understanding Stochastic Calculus
Short course
In London
Description
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Type
Short course
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Location
London
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Duration
2 Days
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Start date
Different dates available
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.
This course is also available remotely via LFS Live.
Facilities
Location
Start date
Start date
About this course
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
Delegates should have a good understanding of Elementary Probability Theory, Calculus and Linear Algebra (covered in Maths Refresher).
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The average rating is higher than 3.7
More than 50 reviews in the last 12 months
This centre has featured on Emagister for 16 years
Subjects
- Probability
- Calculus
- Financial Training
- Financial
- GCSE Mathematics
- Mathematics
- Stochastic Calculus
- Markov Chains
- Binomial
- Differential Equations
- Gamma distribution
- Exponential distribution
- Poisson Distribution
- Bernoulli
Teachers and trainers (1)
Dan Crisan
Teacher
Dan Crisan is a Professor in Mathematics at Imperial College London. His expertise is in the area of Stochastic Analysis with applications in Engineering and Finance. He has published over 30 articles in journals world-wide. His book "Fundamentals of Stochastic Filtering" was published by Springer Verlag in their prestigious series Stochastic Modelling and Applied Probability. He has also completed the editorial work on "The Oxford Handbook of Nonlinear Filtering" - an advanced monograph on the subject.
Course programme
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
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
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
Workshop: Pricing European options within the Cox Ross Rubinstein model
- Continuous time Markov chains. Generators
- Forward/backward equations. Generating functions
Exercise: Superposition of Poisson Processes. Thinning
Day Two
Stochastic Calculus
- The Wiener process. Path properties. Monte Carlo simulation
- Gaussian processes. Diffusion processes
Exercise: The Geometric Brownian Motion. Properties of its distribution (moments)
- Semi martingales. Stochastic integration
- Ito's formula. Integration by parts formula
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
Workshop: The Cox Ingersoll Ross Model. Connection with the O U process. Properties of its distribution (mean variance, covariance). Pricing zero coupon bonds
Intermediate Mathematics: Understanding Stochastic Calculus