Course Outlines-Quantitative Analysis
Courses
1)
2)
3)
4)
5)
6)
7)
8)
Derivatives 101
Financial Econometrics
Monte Carlo Analysis
Options Theory
Volatility Trading
Option Trading
Market Risk measuring
Quantitative Risk Analysis
2 days
2 days
2 days
3 days
3 days
3 days
3 days
3 days
Your Trainer
PIERLUIGI CERUTTI is an experienced practitioner in the
world of derivatives and financial modelling. He obtained a
degree in Monetary and Financial Economics from Luigi Bocconi University in Milano. He joined Banca d’Italia,
Milan branch in 1991 as a supervisor on banks and financial firms. He has been consulting and teaching in the field
of quantitative finance, risk management and option trading for Banca d’Italia. He had a Master degree in
Quantitative Finance from Birckbeck College, University of London and in 1999 he joined Banca Caboto (first
Caboto Sim, now Banca IMI) as a proprietary option trader. As a market maker and a volatility trader, he became
head of covered warrants and certificates desk. He has been consulting for trading on line platform and structured
products pricing.
PIERLUIGI CERUTTI si occupa di derivati e di finanza quantitativa da diversi anni. Dopo una laurea in Economia
Monetaria e Finanziaria presso l’Università Luigi Bocconi è entrato nella filiale milanese della Banca d’Italia nel
1991 dove sì è occupato principalmente di vigilanza bancaria e sugli intermediari finanziari oltre a partecipare
come docente all’attività di formazione per i dipendenti della Banca d’Italia a livello regionale in materia di derivati e
di risk management. Ha conseguito un master in Quantitative Finance presso il Birckbeck College dell’Università di
Londra per poi passare nel 1999 all’attività di market making su prodotti retail per Caboto Sim prima e poi Banca
Caboto (ora Banca IMI) diventando responsabile del desk di negoziazione ed occupandosi del business a livello
globale. E’ stato consulente per la predisposizione di piattaforme di trading on line e di software per il pricing di
prodotti strutturati.
Course 1: Derivatives 101
Day 1-Derivatives 101
The Futures and Forwards Market





Futures and Forward Prices
Using Futures Markets.
Interest Rate Futures
Equity Futures
Foreign Exchange Futures
The Swaps Market




Economic Analysis and Pricing
Interests Rate Swaps
Asset Swaps
Currency Swaps
Day 2-Derivatives 101
The Options Market








Option Payoffs and Option Strategies.
Bounds on Option Prices.
European Option Pricing.
Option Sensitivities and Option Hedging.
American Option Pricing.
Options on Stock Indexes, Foreign Currency, and Futures.
Exotic Options.
Interest Rate Options.
Course 2: Financial Econometrics
Day 1-Financial Econometrics
Features of Financial Returns


Asset Returns
Distributional Properties of Returns
Linear Time Series Analysis and Its Applications











Stationarity
Correlation and Autocorrelation Function
White Noise and Linear Time Series
Simple AR Models
Simple MA Models
Simple ARMA Models
Unit-Root Nonstationarity
Seasonal Models
Regression Models with Time Series Errors
Consistent Covariance Matrix Estimation
Long-Memory Models
Day 2-Financial Econometrics
Conditional Heteroscedastic Models - Modelling Price Volatility












Characteristics of Volatility
Structure of a Model
Model Building
The ARCH Model
The GARCH Model
The Integrated GARCH Model
The GARCH-M Model
The Exponential GARCH Model
The Threshold GARCH Model
Stochastic Volatility Model.
Long-Memory Stochastic Volatility Model.
Application
Continuous-Time Models and Their Applications









Some Continuous-Time Stochastic Processes
Ito's Lemma
Distributions of Stock Prices and Log Returns
Derivation of Black–Scholes Differential Equation
Black–Scholes Pricing Formulas
Extension of Ito's Lemma
Stochastic Integral
Jump Diffusion Models
Estimation of Continuous-Time Models
Course 3: Monte Carlo Analysis
Day 1- Monte Carlo Analysis
Introduction to simulation and Monte Carlo



Evaluating a definite integral.
Monte Carlo is integral estimation.
An example.
Uniform random numbers






Linear congruential generators.
Theoretical tests for random numbers.
Shuffled generator.
Empirical tests.
Combinations of generators.
The seed(s) in a random number generator.
General methods for generating random variates




Inversion of the cumulative distribution function.
Envelope rejection.
Ratio of uniforms method.
Adaptive rejection sampling.
Generation of variates from standard distributions











Standard normal distribution.
Lognormal distribution.
Bivariate normal density.
Gamma distribution.
Beta distribution.
Chi-squared distribution.
Student’s t distribution.
Generalized inverse Gaussian distribution.
Poisson distribution.
Binomial distribution.
Negative binomial distribution.
Day 2-Monte Carlo Analysis
Variance reduction





Antithetic variates.
Importance sampling.
Stratified sampling.
Control variates.
Conditional Monte Carlo.
Simulation and finance






Brownian motion.
Asset price movements.
Pricing simple derivatives and options.
Asian options.
Basket options.
Stochastic volatility.
Discrete event simulation







Poisson process.
Time-dependent Poisson process.
Poisson processes in the plane.
Markov chains.
Regenerative analysis.
Simulating a G/G/1 queueing system using the three-phase method.
Simulating a hospital ward.
Course 4: Option Theory
Day 1-Option Theory
Elements of option theory

Fundamentals

Option Basics

Stock Price Distribution

Principles of Option Pricing

The Black Scholes Model

American Options
Numerical Methods

The Binomial Model

Numerical Solutions of the Black Scholes Equation

Variable Volatility

Monte Carlo
Day 2- Option Theory
Exotic Options

Simple Exotics

Two Asset Options

Currency Translated Options

Options on One Asset at Two Points in Time

Barriers: Simple European Options

Barriers: Advanced Options

Asian Options

Passport Options
Stochastic theory

Arbitrage

Discrete Time Models

Brownian Motion

Transition to Continuous Time

Stochastic Calculus

Equivalent Measures

Axiomatic Option Theory
Course 5: Volatility Trading
Day 1- Volatility Trading
What is volatility?

Practical issues concerning volatility and its measurement, past and predicted
An introduction to the concept of volatility trading

Traditional investment and view taking

Examples of buying volatility

The instruments
A review of same basic concepts

Rates of change and gradients of straight lines

Long and short

Profit, loss and price changes

The importance of using exposure to measure risk

Nonlinear pricing profiles

Measuring volatility
The price profile of derivatives before expiry

The call option

Options terminology

Probability, averages, expected payoffs and fair values

The fair value of a call option

The nonlinearity of call option prices and the averaging process

The fair value of a longer dated call option

Introducing more realistic distributional assumptions

Introducing dividends and interest rate consideration

Stock exposure of call options and the Delta

The Delta as a slope and its profile
Day 2- Volatility Trading
The simple long volatility trade

Outperforming stock portfolios with call options

The long volatility delta neutral trade

The effects of time decay- Theta

An alternative view on option fair value
Volatility and Vega

Implied volatility

The importance of curvature and Gamma

Time decay effects on Delta and Gamma

Delta contours

Three simulations

Vega effects on Delta and Gamma

Worst and best case scenarios
The short volatility trade






The short call option
Sensitivities of the short call option position
The simple short volatility trade
Time decay and Vega effects
The best and worst case scenarios
Long volatility against short volatility
Day 3- Volatility Trading
Using put options in volatility trades







The put option
Put price sensitivities prior to expiry
Time and Vega effects
The long volatility trade
The equivalence of put and call options
The short volatility trade
Net option position
Managing combinations of options










The vertical call spread
The time spread
Near dated two by one ratio put spread with far dated call
The additivity of sensitivities
Monitoring the risk of a complex options portfolio
Adjusting the risk profile of an option portfolio
Approximate direction risk assessment
Approximate volatility risk assessment
Volatility trades and market manipulation
Synthetic options from dynamic trading of stock
More complex aspects of volatility trading







Trading mispriced options
Trading permanently mispriced options- empirical Delta
Different volatilities for different strike prices
Different volatilities across time
Floating volatilities
The effects of transaction costs
Arbitrages between different options market
Course 6: Option Trading
Day 1- Option Trading
Introduction to Options




Options
Specifications for an Option Contract
Uses of Options
Market Structure
Arbitrage Bounds for Option Prices


American Options Compared to European Options
Absolute Maximum and Minimum Values
Pricing Models




General Modeling Principles
Choice of Dependent Variables
The Binomial Model
The Black-Scholes-Merton (BSM) Model
The Solution of the Black-Scholes-Merton (BSM) Equation





Delta
Gamma
Theta
Vega
Rho
Day 2- Option Trading
Option Strategies


Forecasting and Strategy Selection
The Strategies
Volatility Estimation



Defining and Measuring Volatility
Forecasting Volatility
Volatility in Context
Implied Volatility




The Implied Volatility Curve
Parameterizing and Measuring the Implied Volatility Curve
The Implied Volatility Curve as a Function of Expiration
Implied Volatility Dynamics
General Principles of Trading and Hedging




Edge
Hedging
Trade Sizing and Leverage
Scalability and Breadth
Day 3- Option Trading
Market Making Techniques



Market Structure
Market Making
Trading Based on Order-Book Information
Option Hedging









Hedging
Hedging in Practice
The P/L Distribution of Hedged Option Positions
Rho Pinning
Pin Risk
Forward Risk
Exercising the Wrong Options
Irrelevance of the Greeks
Expiring at a Sort Strike.
Risk Management









Example of Position Repair
Inventory
Delta
Gamma
Vega
Correlation
Rho
Stock Risk: Dividends and Buy-in Risk
The Early Exercise of Options
Course 7: Market Risk Measuring
Day 1 –Market Risk Measuring
Measures of Financial Risk



The Mean–Variance framework for measuring financial risk
Value at risk
Coherent risk measures
Estimating Market Risk Measures: An Introduction and Overview
 DataEstimating historical simulation VaR
 Estimating parametric VaR
 Estimating coherent risk measures
 Estimating the standard errors of risk measure estimators
Non-parametric Approaches





Compiling historical simulation data
Estimation of historical simulation VaR and ES
Estimating confidence intervals for historical simulation VaR and ES
Weighted historical simulation
Advantages and disadvantages of non-parametric methods
Day 2-Market Risk Measuring
Forecasting Volatilities, Covariances and Correlations



Forecasting volatilities
Forecasting covariances and correlations
Forecasting covariance matrices
Parametric Approaches






Conditional vs unconditional distributions
Normal VaR and ES
The t-distribution
The lognormal distribution
Miscellaneous parametric approaches
The multivariate normal variance–covariance approachNon-normal variance–covariance approachesHandling
multivariate return distributions with copulas
Extreme Value



Generalised extreme-value theory
The peaks-over-threshold approach: the generalised pareto distribution
Refinements to EV approaches
Monte Carlo Simulation Methods





Uses of monte carlo simulation
Monte carlo simulation with a single risk factor
Monte carlo simulation with multiple risk factors
Variance-reduction methods
Advantages and disadvantages of monte carlo simulation
Day 3-Market Risk Measuring
Estimating Options Risk Measures



Analytical and algorithmic solutions for options VaR
Simulation approaches
Delta–gamma and related approaches
Mapping Positions to Risk Factors


Selecting core instruments
Mapping positions and VaR estimation
Stress Testing



Benefits and difficulties of stress testing
Scenario analysis
Mechanical stress testing
Backtesting Market Risk Models






Preliminary data issues
Backtests based on frequency tests
Backtests based on tests of distribution equality
Comparing alternative models
Backtesting with alternative positions and data
Assessing the precision of backtest results
Model Risk




Models and model risk
Sources of model risk
Quantifying model risk
Managing model risk
Course 8: Quantitative Risk Analysis
Day 1 –Quantitative Risk Analysis
Why do a risk analysis?





Moving on from “What If” Scenarios
The Risk Analysis Process
Risk Management Options
Evaluating Risk Management Options
Inefficiencies in Transferring Risks to Others
Planning a risk analysis




Questions and Motives
Determine the Assumptions that are Acceptable or Required
Time and Timing
You’ll Need a Good Risk Analyst or Team
The quality of a risk analysis





The Reasons Why a Risk Analysis can be Terrible
Communicating the Quality of Data Used in a Risk Analysis
Level of Criticality
The Biggest Uncertainty in a Risk Analysis
Iterate
Choice of model structure





Software Tools and the Models they Build
Calculation Methods
Uncertainty and Variability
How Monte Carlo Simulation Works
Simulation Modelling
Understanding and using the results of a risk analysis




Writing a Risk Analysis Report
Explaining a Model’s Assumptions
Graphical Presentation of a Model’s Results
Statistical Methods of Analysing Results
Day 2 –Quantitative Risk Analysis
Probability mathematics and simulation




Probability Distribution Equations
The Definition of “Probability”
Probability Rules
Statistical Measures
Building and running a model




Model Design and Scope.
Building Models that are Easy to Check and Modify.
Building Models that are Efficient.
Most Common Modelling Errors.
Some basic random processes







The Binomial Process
The Poisson Process
The Hypergeometric Process
Central Limit Theorem
Renewal Processes
Mixture Distributions
Martingales

Miscellaneous Example
Data and statistics






Classical Statistics
Bayesian Inference
The Bootstrap
Maximum Entropy Principle
Which Technique Should You Use?
Adding uncertainty in Simple Linear Least-Squares Regression Analysis
Fitting distributions to data




Analysing the Properties of the Observed Data
Fitting a Non-Parametric Distribution to the Observed Data
Fitting a First-Order Parametric Distribution to Observed Data
Fitting a Second-Order Parametric Distribution to Observed Data
Sums of random variables


The Basic Problem
Aggregate Distributions
Day 3 –Quantitative Risk Analysis
Forecasting with uncertainty









The Properties of a Time Series Forecast
Common Financial Time Series Models
Autoregressive Models
Markov Chain Models
Birth and Death Models
Time Series Projection of Events Occurring Randomly in Time
Time Series Models with Leading Indicators
Comparing Forecasting Fits for Different Models
Long-Term Forecasting
Modelling correlation and dependencies





Introduction
Rank Order Correlation
Copulas
The Envelope Method
Multiple Correlation Using a Look-Up Table
Optimisation in risk analysis



Introduction
Optimisation Methods
Risk Analysis Modelling and Optimisation
Checking and validating a model



Spreadsheet Model Errors
Checking Model Behaviour
Comparing Predictions Against Reality
Discounted cashflow modelling




Useful Time Series Models of Sales and Market Size
Summing Random Variables
Summing Variable Margins on Variable Revenues
Financial Measures in Risk Analysis
Project risk analysis




Cost Risk Analysis
Schedule Risk Analysis
Portfolios of risks
Cascading Risks
Insurance and finance risk analysis modelling










Operational Risk Modelling
Credit Risk
Credit Ratings and Markov Chain Models
Other Areas of Financial Risk
Measures of Risk
Term Life Insurance
Accident Insurance
Modelling a Correlated Insurance Portfolio
Modelling Extremes
Premium Calculations