# Constructing Volatility Surfaces in EXCEL

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Volatility surface plots are a construct of the latter across moneyness (strike prices) and maturity (time to expiry). Unlike implied volatilities which are determined by backing out volatility from the Black Scholes option price equation applied to at the money options, local volatilities use implied volatilities and a one factor Black Scholes model to drive local volatility values across the surface. Calibrating volatility surfaces is one of the tweaks market practitioners use to side step the constant volatility assumption present in the Black Scholes equation for pricing European options.

This course begins by explaining the difference and pros and cons of various volatility estimates, from trailing volatilities, to implied volatilities to local volatilities. It then looks at the benefits of purchasing deep out of the money options, and how a change in volatility impacts the value of these options. The next lesson delves deeper into the differences between implied and local volatilities. The course illustrates step-by-step, how volatility surfaces for local volatilities using Dupire’s formula may be built in EXCEL. Finally, the course derives forward implied volatilities using the methodology described by Taleb.

The course consists of:

• A 40 page PDF guide that shows how to build a volatility surface step by step in EXCEL using Dupire's formula.
• An EXCEL spreadsheet that is used as a simple teaching template by the PDF tutorial above. The Excel sheet shows the implementation of Dupire's formula as well as the resultant volatility surface. The sheet also shows Taleb's implementation of implied forward volatility using term structure of volatility concepts. #### Learning Objectives

After taking this course you will be able to:

• Distinguish between trailing, implied and local volatilities
• Calculate implied volatility
• Calculate local volatility using Dupire’s formula
• Understand the advantages of purchasing a deep out of the money option
• Construct a volatility surface of implied volatilities in EXCEL
• Construct a volatility surface of local volatilities in EXCEL
• Calculate a term structure of forward implied volatilities in EXCEL

#### Prerequisites

Familiarity with the Black Scholes equation, derivative products and pricing models for pricing European options and EXCEL.

#### Target Audience

This advanced practitioner course is aimed at professionals who deal with pricing, valuation and risk issues related to derivative transactions.

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