Implied Volatility of Options-Volatility Analysis in Python

Volatility measures market expectations regarding how the price of an underlying asset is expected to move in the future. There are two types of volatility: historical volatility and implied volatility. In a series of previous posts, we presented methods and provided Python programs for calculating historical volatilities. In this post, we are going to discuss implied volatility and provide a concrete example of implied volatility calculation in Python.

In financial mathematics, the implied volatility (IV) of an option contract is that value of the volatility of the underlying instrument which, when input in an option pricing model (such as Black–Scholes), will return a theoretical value equal to the current market price of said option. A non-option financial instrument that has embedded optionality, such as an interest rate cap, can also have an implied volatility. Implied volatility, a forward-looking and subjective measure, differs from historical volatility because the latter is calculated from known past returns of a security. To understand where implied volatility stands in terms of the underlying, implied volatility rank is used to understand its implied volatility from a one-year high and low IV. Read more

Since there is no analytical formula for calculating the implied volatility of an option, we must use numerical root-finding techniques. While there are many techniques for finding roots, two of the most commonly used are Newton’s method and Brent’s method.  More details about these methods can be found in Reference [1].

In this post, we utilize a Python program to calculate the implied volatility of a European call option. The parameters of the option are as follows.

Valuation date: August 31, 2020

Expiry: August 31, 2021

Option type: Call

Exercise type: European

Option price: 10

Strike: 100

Underlying asset price: 100

Risk-free rate: 2%

Dividend yield: 1%

The picture below shows the implied volatility calculated by the Python program.

Implied Volatility of Options in Python

We note that the implied volatility calculated by the Python program agrees well with the result obtained by using a third-party software as shown below.

Implied Volatility of Options

References

[1] William H. Press, Saul A. Teukolsky, William T. Vetterling , Brian P. Flannery, Numerical Recipes 3rd Edition: The Art of Scientific Computing, Cambridge University Press, 3rd Edition, 2007.

Further questions

What's your question? Ask it in the discussion forum

Have an answer to the questions below? Post it here or in the forum

LATEST NEWS‘Enough pollution’ in low-income NJ area with 1 power plant
‘Enough pollution’ in low-income NJ area with 1 power plant

WOODBRIDGE, N.J. (AP) — Residents of low-income communities in New Jersey that would get a second gas-fired power plant nearby are urging the governor to halt the project, which they said flies in the face of an environmental justice law he signed with great fanfare…

Stay up-to-date with the latest news - click here
LATEST NEWSAbsolute Software to Present at Raymond James Annual Institutional Investors Conference
Absolute Software to Present at Raymond James Annual Institutional Investors Conference

VANCOUVER, British Columbia & SAN JOSE, Calif. — Absolute Software™ (NASDAQ: ABST) (TSX: ABST), the only provider of self-healing, intelligent security solutions, today announced the company will present at the Raymond James 44th Annual Institutional Investors Conference on Wednesday, March 8, 2023 at 11:35 am…

Stay up-to-date with the latest news - click here
LATEST NEWSUS pick to head World Bank, ex-Mastercard CEO Banga, starts ‘charm offensive’
US pick to head World Bank, ex-Mastercard CEO Banga, starts ‘charm offensive’

WASHINGTON, March 1 (Reuters) – U.S. President Joe Biden’s pick to head the World Bank, ex-Mastercard CEO Ajay Banga, met on Wednesday with executive directors at the bank as he launched a “charm offensive” to win the post, sources familiar with the plans said. Biden…

Stay up-to-date with the latest news - click here
LATEST NEWSSnowflake and AWS Significantly Deepen Commitment to Driving Customer-focused Innovation
Snowflake and AWS Significantly Deepen Commitment to Driving Customer-focused Innovation

Snowflake and AWS expand their successful partnership by boosting sales collaboration, industry solution alignment, and joint go-to-market strategies Over 6,000 joint customers1 including Goldman Sachs and other Fortune 500 enterprises, are using Snowflake and AWS to rapidly innovate Approximately 84% of Snowflake’s customers run their…

Stay up-to-date with the latest news - click here
LATEST NEWSNew Grain February Record Set
New Grain February Record Set

Improved grain industry collaboration leads to shipping record MONTREAL, March 01, 2023 (GLOBE NEWSWIRE) — CN (TSX: CNR) (NYSE: CNI) today announced that February 2023 was the best February ever for Western Canadian grain movement on CN’s network. The Company worked with its customers and…

Stay up-to-date with the latest news - click here

Leave a Reply