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# Q4 2013 Volatility Monitor

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Each quarter, CME Group Research analyzes price volatility for the previous three months across key asset classes and presents it in the Volatility Monitor Update. The purpose of the update is to provide a solid understanding of volatility as one of the prime drivers of options premiums.

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### Q4 2013 Volatility Monitor

1. 1. Volatility Monitor 4th Quarter 2013 JANUARY 6, 2014 John W. Labuszewski Managing Director Research & Product Development 312-466-7469 jlab@cmegroup.com
2. 2. !"#\$" = % ) =% Historic Volatility P = Price of underlying market 10% 60% Eurodollars 80% 40% 5% 20% T-Bonds 10-Yr T-Notes Jul-13 Oct-13 0% Jan-13 0% Apr-13 Where: 15% Jul-12 /P 100% Oct-12 = ln P − 120% 20% Jul-11 1 140% Jan-11 = √252 ∙ 30-Day HVs: Interest Rates 25% Apr-11 Note that over the past month (roughly 30 calendar days), there are generally 21 trading days; 42 trading days over the past 60 calendar days, etc. An annualized historic volatility (HV) is generally calculated using the following formula, assuming that there are 252 trading days in a calendar year. !"#\$", , ', (, Unfortunately, solving a mathematical option pricing model, such as the Black formula (1976) for options on futures, results in an unsolvable polynomial. However, it is possible to utilize a computer assisted iterative methodology quickly to converge to a solution. Bonds & Notes There are many ways to measure volatility in any particular option market. “Historic volatility” is a reference to the annualized standard deviation of day-to-day price movements in the market that underlies the option of interest. This figure is generally calculated over a particular prior time period, e.g., 30 days, 60 days, 90 days, etc. , ', , (, But there may be no need to calculate the theoretical option premium when the premium may be observed in a competitively traded marketplace. An implied volatility (IV) is derived by solving the option pricing formula to find volatility as a function of market price, strike price, term and short-term rates. Jan-12 This report represents an update of volatility through the 4th quarter 2013 in a variety of what we might consider to be CME Group “flagship” products. Implied volatility (IV) may be thought of as the volatility that is implicit in the premium associated with any specific option. You can use any number of available mathematical option pricing models to derive the (theoretical) option on futures premium as a function of the current market price (P), strike price (S), volatility (V), term until option expiration (t) and short-term rates (r). Apr-12 Traders may “buy volatility” generally by buying options; or, “sell volatility” by selling options, often in concert with the placement of a hedge in the futures market structured by reference to the net delta associated with the option positions. Implied Volatility Oct-11 Volatility is one of several key inputs into mathematical option on futures pricing models along with market price, strike price, term until expiration and short-term interest rates. While market price movements exert the most obvious impact upon the option premium, volatility remains a very important factor. So much so that many traders strive to predict future levels of volatility and engage in socalled “volatility plays” as a result. Eurodollars (3rd Mth) N = Number of business days in period, generally 20 for 1 month; 40 for 2 months, etc. Mean Reversion While volatilities may vary considerably over time in the context of any given market, they do tend to hover towards a long-term mean or characteristic level. Thus, option traders often find it useful to 1 | Volatility Monitor 4th Quarter 2013 | January 6, 2014 | © CME GROUP
3. 3. study those average levels identifying mispriced options. in the hopes of Comparing HV and IV We might compare those levels to current implied volatilities in actively traded options to get a feel for whether options are reasonably priced relative to historic averages. 30-Day HVs: Currencies 40% 35% 30% 30-Day HVs: Grains 25% 80% 20% 70% 15% 60% 10% 50% 5% 40% 30-Day HVs: Energy 10% Corn Soybean Meal Soybeans Wheat Oct-13 Jul-13 Apr-13 Jan-13 Oct-12 Jul-12 Apr-12 Oct-11 Jan-12 0% Jul-11 One popular technique is to study the average (median) volatility observed in the marketplace over the past year or past three (3) years. The tables found at the conclusion of this document provide the median, maximum and minimum levels of 30-day historic volatilities in a sampling of some of the most actively traded CME Group markets including the interest rate, stock index, currency, energy, grain, precious metals and livestock complexes. 20% Apr-11 Oct-13 Jul-13 Apr-13 Japanese Yen Swiss Franc Canadian Dollar 30% Jan-11 EuroFX British Pound Australian Dollar Jan-13 Oct-12 Jul-12 Apr-12 Jan-12 Oct-11 Jul-11 Apr-11 Jan-11 0% Soybean Oil E.g., assume that a (hypothetical) call option exercisable for corn futures had an implied volatility of 25.00%. The 1-year median observation for 30day HVs in nearby corn futures is at 23.46%. Thus, this option displays volatility that is just a bit higher than observed volatility over the past year, falling somewhere between the median and 60th percentile. 80% 70% 30-Day HVs: Precious Metals 90% 60% 80% 50% 70% 40% 60% 30% 50% We further include graphics of 30-day historic volatilities over the past several years. Generally, we examine volatility in the lead or nearby month, with the exception of Eurodollar futures where the 3rd month historically has often represented the most actively traded contract. 2 | Volatility Monitor 4th Quarter 2013 | January 6, 2014 Gold Oct-13 Jul-13 Apr-13 Jan-13 Oct-12 Jul-12 Apr-12 Jan-12 Oct-11 Jul-11 0% Apr-11 Oct-13 Jul-13 Apr-13 Oct-12 Jul-12 Apr-12 Jan-13 Natural Gas RBOB Gas 10% Jan-11 WTI Crude Oil Heating Oil Jan-12 20% Oct-11 0% Jul-11 30% Apr-11 40% 10% Jan-11 20% Silver The 3-year median observation for 30-day HVs in corn is at 28.21%. The IV of 25.00% is below the 3-year median falling between the 25th and 40th percentiles. Viewed by this metric, the IV appears to be well below average by historic standards. | © CME GROUP
4. 4. E.g., a hypothetical at-the-money call exercisable for S&P 500 futures displayed an implied volatility of 14.50%. This is above the 1-year median of 11.20% and between the 75th and 90th percentiles. It is also above the 3-year median of 13.39%, falling between the 60th and 75th percentiles. sampled over a variety of liquid CBOE S&P 500 options. While the VIX and 30-day HVs typically run up and down in parallel, the 30-day HV tends to be a bit over-reactive relative to the VIX. I.e., traders’ aggregate expectations regarding volatility in the S&P 500 tend to be a bit more stable than the 30day historic average. 30-Day HVs: Livestock 70% S&P 500 Volatility 50% 60% 45% 50% 40% 40% 35% 30% 30% 25% 20% 20% 15% 10% 10% 5% 30-Day Historic Volatility Oct-13 Jul-13 Apr-13 Jan-13 Oct-12 Jul-12 Apr-12 Jan-12 Oct-11 Jul-11 Apr-11 Oct-13 Jul-13 Apr-13 Oct-12 Jan-13 Lean Hogs 0% Jan-11 Live Cattle Jul-12 Apr-12 Jan-12 Oct-11 Jul-11 Apr-11 Jan-11 0% VIX Index Implied Volatility Index Conclusion Traders often reference the IV associated with at- or near-the-money calls or puts as standard reference for where traders (implicitly) believe volatility will be between the current point in time and option expiration. As such, IVs are “forward-looking” while HVs may be regarded as “backwards-looking.” But the IV for any particular option may be a bit different than the IV for another option even where the two options are based upon the same underlying instrument with the same expiration date. That may be explained by the fact that traders may impute more or less value to options that are in- or out-ofthe-money. Finally, please be aware that volatilities associated with Eurodollar futures are calculated based on the implied yield of the instrument where yield = 100 less the quoted price. Because yields have fallen to historical lows, the base of the volatility calculation becomes very low and tends to inflate the calculated volatility. We do not, of course, purport to offer specific trading advice. Rather, our purpose here is to provide an enhanced understanding of volatility as one of the prime drivers of option premiums and to illustrate a simple but popular way of regarding volatility. The CBOE S&P 500 VIX Index is a popular measure referencing IVs. It represents an average IV 3 | Volatility Monitor 4th Quarter 2013 | January 6, 2014 | © CME GROUP
5. 5. 30-Day Historical Volatilities over 1-Year Window (1/1/13 to 12/31/13) Percentiles 60% Median Max INTEREST RATES Eurodollar (3rd Month) T-Bonds 10-Yr T-Notes STOCK INDEXES S&P 500 Nasdaq-100 CURRENCIES EuroFX Japanese Yen British Pound Swiss Franc Australian \$ Canadian \$ ENERGY WTI Crude Oil Natural Gas Heating Oil RBOB Gas GRAINS Corn Soybeans Soybean Oil Soybean Meal Wheat PRECIOUS METALS Gold Silver LIVESTOCK Live Cattle Lean Hogs 4 90% 75% 40% 25% 10% Min 86.48% 73.30% 54.07% 47.58% 45.64% 43.33% 36.98% 27.18% 21.41% 12.42% 7.87% 11.17% 7.39% 10.05% 6.17% 9.23% 5.44% 8.63% 4.72% 8.06% 3.99% 7.30% 3.67% 6.74% 3.39% 6.16% 2.61% 16.24% 17.76% 15.08% 16.31% 13.95% 14.44% 12.37% 13.25% 11.20% 12.72% 10.87% 11.86% 9.83% 10.68% 8.49% 9.72% 6.54% 8.83% 10.31% 16.74% 12.44% 13.28% 15.63% 9.38% 9.33% 15.83% 11.22% 12.05% 14.43% 7.98% 8.89% 12.98% 8.13% 10.71% 12.07% 7.30% 8.15% 12.06% 7.59% 8.66% 9.85% 5.76% 7.98% 11.57% 7.49% 8.27% 8.87% 5.57% 7.61% 10.66% 7.30% 7.91% 8.46% 5.38% 6.51% 8.77% 6.76% 7.46% 7.60% 5.02% 5.90% 7.71% 6.09% 6.87% 6.72% 4.70% 5.20% 6.29% 4.48% 5.75% 5.97% 3.91% 30.21% 40.22% 21.39% 39.96% 26.48% 38.60% 20.14% 34.31% 21.05% 36.41% 19.09% 28.74% 19.96% 33.41% 17.89% 25.99% 18.75% 31.92% 17.19% 24.41% 17.34% 29.71% 16.74% 23.76% 16.07% 27.74% 15.62% 20.39% 14.88% 25.90% 14.28% 18.51% 11.59% 24.05% 11.82% 15.90% 78.13% 49.02% 22.32% 60.92% 34.55% 76.58% 43.78% 20.55% 49.24% 32.27% 35.33% 27.70% 18.24% 38.59% 21.94% 33.20% 20.55% 16.38% 29.34% 19.72% 23.46% 19.27% 15.94% 26.45% 18.87% 18.25% 18.43% 15.42% 24.51% 18.03% 16.71% 17.72% 14.41% 23.42% 15.83% 15.28% 16.67% 12.31% 21.26% 13.25% 13.11% 14.80% 11.02% 19.61% 9.86% 37.74% 48.69% 34.29% 45.53% 26.89% 41.66% 21.55% 34.26% 19.91% 31.60% 18.21% 29.41% 13.40% 25.60% 12.18% 22.50% 11.11% 16.04% 18.88% 52.65% 17.21% 50.11% 15.14% 21.19% 12.37% 18.39% 11.75% 17.52% 10.55% 16.67% 9.01% 15.72% 7.48% 12.25% 5.07% 10.09% | Volatility Monitor 4th Quarter 2013 | January 6, 2014 | © CME GROUP