Module 4: ImpliedVolatility Derivative and Financial Markets Concepts Module 4: ImpliedVolatility Objectives: To understand how implied volatility is measured, its importance, and the patterns of option value implied volatility across time and future spot prices. Structure: Implied Volatility Exercises Currency Option Pricing [OPTPRICE.XLS] Direction and Volatility Option Strategies S&P 500 Volatility History (Optional) S&P 500 option volatility"Smiles/Smirks”[OPTIMPVL.XLS] Lecture and Discussion Direction and Volatility Positioning Options 9th: Chapter 15 (1-4, 8-9, 11), optional Chapter 20 Options 8th: Chapters 14 (1-4, 8-9, 11)  Options 6th and 7th: Chapters 13 (1-4, 8-9, 11)  Options 5th: Chapters 12 (1-5, 8-9, 11), optional 16.4 Options 4th: 11.10-11.11, Chapter 17; optional Chapter 15 Jointly-developed module licensed to James Bodurtha Copyright Ó Financial Labs, Inc., 1993, 1994, 1995, 1996 all rights reserved. Confidential, Proprietary Information of Financial Labs, Inc. 1 1 1

This page is intentionally left blank.

Understanding Implied Volatility [OPTPRICE.XLW]Currency Option Pricing Derivative Concepts Understanding Implied Volatility [OPTPRICE.XLW]Currency Option Pricing Situation In 60 days, the UK budget will be released. Your feel that the market will show greater uncertainty leading up to the budget release than afterwards • Current price: $1.5000 • Exercise price: $1.5000 • Eurodollar interest rate: 3.5% • Europound rate: 6.0% Prices quoted by GlobeOne and Regent Bank for at the money European call options on the British pound: Days to Quoted Implied Implied Price at other Maturity Price: Volatility? Bank’s Implied Volatility? GlobeOne 90 $.0279 or 1.86% ? @ Regent vol = ? Regent Bank 60 $.0259 or 1.73% ? @ Globe One vol = ? Use this to introduce the exercise on implied volatility. Read through the overhead slowly. Tell them they will need to use the model in PRICE-C2 to determine what volatility was used for each quote.They will need to do this by going through manual iterations of changing volatility until they arrive at the corresponding price in $ and %. This exercise is relatively short. It leads to a discussion as follows: - They conclude that Solomon's is more expensive at 11% v.s. 10% volatility. - Make the point that option prices can be reduced to volatility quotes since that is the only unknown. - Ask if it is reasonable to assume that people quote the same volatility for different maturities. Be sure that they understand that it would not necessarily be and that volatility has a term structure and that different traders have different views on this term structure. Also mention that since OTC options are for specific dates for each contract, traders are very careful to check maturities against particular events like trade number dates, elections, or other things that might influence volatility. • Explanation - 2 2 2

Optional - Volatility Forward Curve 3

Two   Direction Views Up Down tility +C +P Vola -P -C Option Strategies: Combining Volatility and Direction with 60 day maturity at-the-money (ATM) options Volatility Strategy Direction Strategy Days 0 30 60 90 120 Combined Strategy 10

Derivative Concepts Two   Direction Views Up Down tility +C +P Vola -P -C Option Strategies: Combining Volatility and Direction with 60 day maturity at-the-money (ATM) options After having completed this, emphasize how complex it can be to combine views of direction and volitility since the sensitivities of the options values to these two dimensions are both different and constantly changing. Explain that options traders typically are "volatility" traders and try to manage down their sensitivity to directional changes. Point out that in their books they have several graphs of implied volatilities and directional changes for selected instruments such as the U.S. 30 Year Treasury, the Yen, the DM, and Eurodollar deposits. Ask them to look at these to see if they can see what strategies would have been particularly good at points in the past. - P - C Volatility Strategy - P - C +P +C +P +C +P - C +P - C Direction Strategy - P +C - P + C 0 30 60 90 120 Days Combined Strategy +2P - 2C +2C -2P 8 11 10

Bloomberg Screen Command - SSMY <Cmdty> HIVG <GO> Bloomberg Screen Command - SSMY <Cmdty> HIVG <GO> SS is symbol and SP for the S&P500 futures M is maturity and H is March, M is June, U is September and Z is December Y is the maturity year, 200Y. The SPM8 futures information is for the June 2008 S&P500 contract.

Implied (and Historical) Volatility Information

Long Option Position Value as Function of Spot Price and Maturity (Initial vlaues = 3.79787) Spot price=100, eXercise price=100, Yield=4.939%, maTurity=1.0, Rate=4.939%, Volatility=s=10%

Short Option Position Value as Function of Spot Price and Maturity (Initial vlaues = 3.79787) Spot price=100, eXercise price=100, Yield=4.939%, maTurity=1.0, Rate=4.939%, Volatility=s=10%

This page is intentionally left blank.