# Derivative Mathematics

• 2 days
• in person

## What are the topics?

New York Institute of Finance

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## Who should attend

• desk quants
• risk analysts and financial engineers

Learn the essential mathematics used in the valuation and risk management of derivatives in an intuitive, accessible fashion. Develop deep insights into concepts such as complete markets, stochastic processes, Ito's lemma and the replication principle.

This course is a component of the Advanced Derivatives Professional Certificate.

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

WHAT YOU'LL LEARN

• Understand the no-arbitrage principle in the context of complete markets
• Understand and use basic elements of stochastic calculus including Ito's lemma
• Learn how to measure the observed and implied volatility of asset prices
• Use binomial models to price options
• Learn volatility estimation techniques

Derivative Mathematics at New York Institute of Finance

From  \$2,156

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