## How long?

• 5 days
• in person, online

## What are the topics?

New York Institute of Finance

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## Who should attend

• desk quants
• risk analysts and financial engineers

Gain a deep understanding of derivative instruments. Learn the essential underlying mathematics in an intuitive, accessible fashion. Develop expertise in the theory and practice of derivatives valuation including the use of finite difference techniques. Understand volatility and variance products and volatility trading strategies.

Prerequisite knowledge:

• Familiarity with derivative instruments
• Intermediate to advanced MS Excel skills
• Intermediate probability and statistics
• Basic calculus, including partial differentiation and integration

CURRICULUM

Day 1

MODULE 1: REVIEW OF DERIVATIVES BASICS

• The no-arbitrage pricing principle
• Objective vs. risk-neutral probabilities
• Forwards and Futures
• Swaps
• Options
• Put-Call Parity

MODULE 2: DISCRETE PROCESSES FOR ASSET PRICES

• Discrete stochastic processes
• The Markov property
• The Martingale property
• The binomial model
• The trinomial model

MODULE 3: DISCRETE TIME AND STATE PRICING MODELS FOR DERIVATIVES

• A binomial formula for European options
• American options
• Options on assets paying dividends
• Options on stock indices, bonds, currencies, futures and commodities

Day 2

MODULE 1: CONTINUOUS PROCESSES FOR ASSET PRICES

• The Wiener process as the limit of a random walk
• Brownian motion and Ito processes
• Basic stochastic integration
• Functions of stochastic processes
• Ito's lemma
• Jump-diffusion processes

MODULE 2: CONTINUOUS TIME AND STATE PRICING MODELS FOR DERIVATIVES

• No-arbitrage in continuous time
• The Black-Scholes-Merton partial differential equation
• Black-Scholes-Merton formulas for options
• The Greeks
• American options in continuous time

MODULE 3: VOLATILITY

• Historical vs Implied Volatility
• Estimating volatility
• Implied volatility surfaces: Skews and smiles
• GARCH models
• Stochastic volatility

Day 3

MODULE 1: EXOTIC OPTIONS AND PATH DEPENDENCY

• Strong vs. weak path dependency
• Asian Options
• Barrier Options
• Exchange options
• Lookback options

MODULE 2: OVERVIEW OF NUMERICAL METHODS

• Valuation techniques for path dependent options
• Monte Carlo basics
• Finite difference methods
• Numerical Integration

MODULE 3: MONTE CARLO METHODS FOR DERIVATIVES VALUATION

• Monte Carlo methods applied to discrete models
• Monte Carlo methods applied to continuous models
• Getting to the Greeks
• Techniques for accelerating convergence
• Pros and Cons of Monte Carlo techniques

Day 4

MODULE 1: FINITE DIFFERENCE METHODS: ONE FACTOR MODELS

• The fundamental PDE and boundary conditions
• Explicit finite difference methods
• Implicit finite difference methods
• Crank-Nicolson method

MODULE 2: FINITE DIFFERENCE METHODS: TWO FACTOR MODELS

• Explicit finite difference methods
• Alternating direction implicit method
• Hopscotch method

Day 5

MODULE 1: VOLATILITY INSTRUMENTS

• Volatility swaps
• Variance swaps
• Gamma swaps
• Options on variance
• VIX futures and options

MODULE 2: VALUATION AND HEDGING

• Vanilla options: Delta hedging and P&L path dependency
• Static replication of variance swaps
• Log contract replication

• Volatility trading with vanilla options

MODULE 4: DESK READY SKILLS KNOWLEDGE CHECK

WHAT YOU'LL LEARN

• Understand the no-arbitrage principle in the context of complete markets
• Understand and use basic elements of stochastic calculus
• Learn how to measure the observed and implied volatility of asset prices
• Use binomial models to price American options and interest rate derivatives
• Learn volatility estimation techniques
• Use numerical methods to price American- and exotic options
• Understand volatility instruments and trading strategies

Advanced Derivatives Professional Certificate at New York Institute of Finance

From  \$5,395

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### Disclaimer

Coursalytics is an independent platform to find, compare, and book executive courses. Coursalytics is not endorsed by, sponsored by, or otherwise affiliated with any business school or university.

Full disclaimer.

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