Advanced Mathematics Financial Tools and Applications
Training
Provided by London Financial Studies
Course Outline
The scope of this course is to revise some of the theories and principles used for calculating the price of financial derivatives. The Black-Scholes model is used as the starting point but gradually the level of complexity is increased to discuss the jump-diffusion models, stochastic volatility models as well as discussions of pricing various exotic pay-offs that will be the new vanilla products tomorrow.
Who The Course is For
Quantitative analysts, risk managers, product controllers, financial engineers, researchers. Past participants have included: Chief investment officers, Asset Managers, Strategists, Private Banks, Relationship Managers.
Prior Knowledge:
Differential calculus, yield curves, duration, convexity, covariance matrix, Riemann integral, ODE (covered in Maths Refresher)
Random variable, expectation and moments, conditional expectation, Central Limit Theorem, Random walk, Markov chain, Wiener process, Geometric Brownian motion, Ito formula, Girsanov transform (covered in Intermediate Mathematics: Understanding Stochastic Calculus)
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Advanced Mathematics Financial Tools and Applications
Day One
* Introduction and Course Outline
* Complete-incomplete markets. Non-arbitrage Pricing. Arrow Debreu prices
* Black-Scholes Formulas:
o time dependent coefficients;
o jumps;
o dividend yield;
o Margrabe formula;
o convergence of binomial tree to Black-Scholes.
Workshop: Pricing freight derivatives
* Options pricing when asset prices are predictable:
o trended O-U process;
o impact of drift estimation on volatility estimation;
o autocorrelation.
Workshop: Pricing real estate derivatives, forward contracts and total return swaps.
* Risk-neutral density recovering models:
o Studying the market stability;
o Options pricing with Weibull, generalized gamma, GB2 and g-and-h distribution;
Workshop: Testing for market stability in stock and interest rate markets. Was there any impact of London bombings in July 2005 on the interest markets?
Day Two
* Deterministic methods for multi-asset option pricing and other financial calculus:
o Theory based on weak convergence of probability measures and local limit theorems;
o One-dimensional formulas;
o Multi-dimensional formulas.
* Application of deterministic algorithms to pricing:
o Asian;
o basket;
o rainbow options.
Workshop: Numerical examples of deterministic algorithms and comparison with Monte Carlo Option Pricing.
* Probability distortion operators for option pricing:
o A unified approach to pricing in financial markets and insurance markets;
o Determination of market price of risk;
o No-arbitrage violations.
Workshop: Pricing options with normal and student distortion operators.
* Mathematical bounds for options prices; distribution free bounds. A new paradigm in risk management and algorithmic trading.
Workshop: Structuring and Pricing cliquet reverse cliquet. When is a principal guaranteed product really protected?
* Introduction and Course Outline
* Complete-incomplete markets. Non-arbitrage Pricing. Arrow Debreu prices
* Black-Scholes Formulas:
o time dependent coefficients;
o jumps;
o dividend yield;
o Margrabe formula;
o convergence of binomial tree to Black-Scholes.
Workshop: Pricing freight derivatives
* Options pricing when asset prices are predictable:
o trended O-U process;
o impact of drift estimation on volatility estimation;
o autocorrelation.
Workshop: Pricing real estate derivatives, forward contracts and total return swaps.
* Risk-neutral density recovering models:
o Studying the market stability;
o Options pricing with Weibull, generalized gamma, GB2 and g-and-h distribution;
Workshop: Testing for market stability in stock and interest rate markets. Was there any impact of London bombings in July 2005 on the interest markets?
Day Two
* Deterministic methods for multi-asset option pricing and other financial calculus:
o Theory based on weak convergence of probability measures and local limit theorems;
o One-dimensional formulas;
o Multi-dimensional formulas.
* Application of deterministic algorithms to pricing:
o Asian;
o basket;
o rainbow options.
Workshop: Numerical examples of deterministic algorithms and comparison with Monte Carlo Option Pricing.
* Probability distortion operators for option pricing:
o A unified approach to pricing in financial markets and insurance markets;
o Determination of market price of risk;
o No-arbitrage violations.
Workshop: Pricing options with normal and student distortion operators.
* Mathematical bounds for options prices; distribution free bounds. A new paradigm in risk management and algorithmic trading.
Workshop: Structuring and Pricing cliquet reverse cliquet. When is a principal guaranteed product really protected?
About The Training Provider: London Financial Studies
London Financial Studies - London Financial Studies is a specialist teaching resource that concentrates exclusively on capital markets. We offer individuals, teams and companies expert teaching that combines theoretical understanding with practical experience.
Our business is driven by a distinct philosophy and clear values:
* Practical Application
* Intellectual Clarity
* Personal Approach
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