# Greeks, American Options and Volatility

Learn about Greeks, American Options, and Volatility.

## There is one session available:

After a course session ends, it will be archived.
Estimated 3 weeks
1–2 hours per week
Self-paced

In this course, three methods are presented for pricing an option.

1. The first method is an analytical one whereby the Black Scholes formula is used to price a call or a put. The drawback of the analytical approach is that it only works for European options.
1. The second method presented is the binomial tree, which is illustrated in the pricing of an American option to facilitate early exercise.
1. The third method presented is the Monte Carlo simulation.

Then the assumption of constant volatility is challenged, due to the presence of the volatility smile, which is formally defined and shown to be empirically observed in all derivatives markets. Monte Carlo simulations are run to generate a distribution with kurtosis -- a mixture of normal distributions.

Finally, the Heston Model, which relaxes the assumption of constant volatility is presented.

• First, the Heston Model is shown to incorporate kurtosis by allowing volatility.
• Second, the Heston model includes an additional Brownian motion that allows volatility to mean-revert.
• Third, these Brownian motions are linked by a correlation.

Sample code is provided to run the Heston model. The corresponding implied volatilities are graphed and shown to replicate the volatility smile.

### At a glance

• Institution: NYIF
• Subject: Economics & Finance
• Level: Introductory
• Prerequisites:
• • Intermediate MS Excel skills (use solver, etc.)
• • Basic probability
• • Basic calculus
• • Some knowledge of equity markets
• Knowledge of fixed income basics
• Language: English
• Associated programs:

# What you'll learn

Skip What you'll learn
• Define and discuss the Greek sensitivities of the option price to underlying variables.

• Price European and American options, and compare their methods and values.

• Identify weaknesses within the assumptions of Black Sholes, particularly constant volatility.

• To implement and price the Heston model to address the limitation of constant volatility.

• To define the volatility smile, and illustrate how the output from the Heston Model can replicate it.

# Syllabus

Skip Syllabus

Module 01: Greeks

Lesson 01: Delta and Gamma

Lesson 02: Theta

Lesson 03: Vega

Lesson 04: Stock Pinning

Module 02: American Options

Lesson 01: Introduction

Lesson 02: Monte Carlo Simulation