Advanced Mathematics: Financial Tools and Applications

Advanced Mathematical Models in Finance

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: Probability and Stochastic Processes)
Course Programme*
Day One

Complete-incomplete markets. Non-arbitrage Pricing
Black-Scholes Formula, Pricing Equation, Risk-Neutral Valuation

Workshop: Excel Implementation Black-Scholes formula; Calculation of Implied Volatility

Market price of Risk
Quanto Options

Workshop: Pricing Quanto Call option

Chooser Options; Forward Start Options

Workshop: Structuring and Pricing cliquet reverse cliquet
Day Two

Asian Options
Analytical and Monte Carlo Pricing

Workshop: Monte Carlo Option Pricing and Applications to Risk Management

Jump-diffusion pricing: Merton Model
Rating transition matrix: Markov chain calculations

Workshop: Derivation of default probabilities from a rating agency default matrix

Swap Pricing; CDS swap Pricing
Bootstrapping default probabilities from CDS curves
Value at Risk calculation; Quantile Calculation


* Subject to change. Please contact course provider for more details.

This program is eligible for 16 Continuing Education credit hours from the CFA Institute. If you are a CFA Institute member, CE credit for your participation in this program will be automatically recorded in your CE Diary.