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UNLIKE AN ACTUAL BROKERAGE ACCOUNT, SIMULATED RESULTS DO NOT REPRESENT ACTUAL TRADING AND MAY NOT BE IMPACTED BY BROKERAGE AND OTHER SLIPPAGE FEES AND MAY ALSO SEE SIGNIFICANT PRICE DISCREPANCIES. ADDITIONALLY THE TRADES HAVE NOT BEEN EXECUTED WITH REAL CAPITAL, AND THE RESULTS MAY HAVE UNDER OR OVER COMPENSATED FOR THE IMPACT OF BEING PLACED IN A VIRTUAL ACCOUNT. SIMULATED TRADING ACCOUNTS IN GENERAL MAY EXPERIENCE TECHNICAL FAULTS THAT ACTUAL ACCOUNTS MAY NOT, POTENTIALLY SKEWING PERFORMANCE. NO REPRESENTATION IS BEING MADE THAT ANY OTHER ACCOUNT WILL OR IS LIKELY TO ACHIEVE GAINS OR LOSSES SIMILAR TO THOSE SHOWN IN THIS PRESENTATION OR DISPLAYED IN ANY MEDIA. Fundamental Concept Option prices don’t move in a linear way compared to their underlying stocks and this makes them complex to understand. Using the Greeks we can understand what will happen to options prices when the market changes. What are the Greeks? The Greeks are values that describe the sensitivity to change in the price of the Option relative to the factors that drive an option’s price. ??? Price factors and their Greeks Underlying price relative to the strike Delta Perceived risks to the option Implied Volatility Vega Time to expiration Theta Knowledge is Power (and other clichés) Using the Greeks we can create what-if style analysis that helps us understand the trade. By understanding the Greeks you can change the way your trade works so it better fits your needs. What are these Greeks? The main Greeks we care about are; • Delta – The change in price of the option relative to a $1 change in the underlying asset price • Vega – The change in the price of the Option relative to a 1% change in the Implied Volatility • Theta – The amount the option price will change over the next one day period as the option gets closer to the expiration date An Important Second Order Greek Gamma – The rate of change in Delta relative to the change in the underlying asset price A little more complex, but very handy for understanding trade risks The Rest of the Greeks - 1 (per Wikipedia) • Rho, measures sensitivity to the interest rate: it is the derivative of the option value with respect to the risk free interest rate (for the relevant outstanding term). • Lambda, omega, or elasticity is the percentage change in option value per percentage change in the underlying price, a measure of leverage, sometimes called gearing. • Vanna, also referred to as DvegaDspot and DdeltaDvol, is a second order derivative of the option value, once to the underlying spot price and once to volatility. It is mathematically equivalent to DdeltaDvol, the sensitivity of the option delta with respect to change in volatility; or alternatively, the partial of vega with respect to the underlying instrument's price. Vanna can be a useful sensitivity to monitor when maintaining a delta- or vega-hedged portfolio as vanna will help the trader to anticipate changes to the effectiveness of a delta-hedge as volatility changes or the effectiveness of a vega-hedge against change in the underlying spot price. • Vomma, Volga, Vega Convexity, Vega gamma or dTau/dVol measures second order sensitivity to volatility. Vomma is the second derivative of the option value with respect to the volatility, or, stated another way, vomma measures the rate of change to vega as volatility changes. With positive vomma, a position will become long vega as implied volatility increases and short vega as it decreases, which can be scalped in a way analogous to long gamma. And an initially vega-neutral, long- vomma position can be constructed from ratios of options at different strikes. Vomma is positive for options away from the money, and initially increases with distance from the money (but drops off as vega drops off). (Specifically, vomma is positive where the usual d1 and d2 terms are of the same sign, which is true when d2 < 0 or d1 > 0.) The Rest of the Greeks - 2 (per Wikipedia) • Charm or delta decay, measures the instantaneous rate of change of delta over the passage of time. Charm has also been called DdeltaDtime. Charm can be an important Greek to measure/monitor when delta-hedging a position over a weekend. Charm is a second-order derivative of the option value, once to price and once to the passage of time. It is also then the derivative of theta with respect to the underlying's price. The mathematical result of the formula for charm is expressed in delta/year. It is often useful to divide this by the number of days per year to arrive at the delta decay per day. This use is fairly accurate when the number of days remaining until option expiration is large. When an option nears expiration, charm itself may change quickly, rendering full day estimates of delta decay inaccurate. • DvegaDtime, measures the rate of change in the vega with respect to the passage of time. DvegaDtime is the second derivative of the value function; once to volatility and once to time. It is common practice to divide the mathematical result of DvegaDtime by 100 times the number of days per year to reduce the value to the percentage change in vega per one day. • Vera measures the rate of change in rho with respect to volatility. Vera is the second derivative of the value function; once to volatility and once to interest rate. Vera can be used to assess the impact of volatility change on rho-hedging. • Color, gamma decay or DgammaDtimemeasures the rate of change of gamma over the passage of time. Color is a third- order derivative of the option value, twice to underlying asset price and once to time. Color can be an important sensitivity to monitor when maintaining a gamma-hedged portfolio as it can help the trader to anticipate the effectiveness of the hedge as time passes. The mathematical result of the formula for color is expressed in gamma/year. It is often useful to divide this by the number of days per year to arrive at the change in gamma per day. This use is fairly accurate when the number of days remaining until option expiration is large. When an option nears expiration, color itself may change quickly, rendering full day estimates of gamma change inaccurate. The Rest of the Greeks - 3 (per Wikipedia) • Speed measures the rate of change in Gamma with respect to changes in the underlying price. This is also sometimes referred to as the gamma of the gamma or DgammaDspot. Speed is the third derivative of the value function with respect to the underlying spot price. Speed can be important to monitor when delta-hedging or gamma-hedging a portfolio. • Ultima measures the sensitivity of the option vomma with respect to change in volatility. Ultima has also been referred to as DvommaDvol.] Ultima is a third-order derivative of the option value to volatility. • Zomma measures the rate of change of gamma with respect to changes in volatility. Zomma has also been referred to as DgammaDvol. Zomma is the third derivative of the option value, twice to underlying asset price and once to volatility. Zomma can be a useful sensitivity to monitor when maintaining a gamma-hedged portfolio as zomma will help the trader to anticipate changes to the effectiveness of the hedge as volatility changes. Are these useful? To us, probably not All Greeks are estimates and can vary based on the estimation method used Second order Greeks are estimates based on estimates and can be very imprecise True Value - If you happen to be in certain bars in Chicago then knowing what these are may win you a free drink in a trivia contest Is Implied Volatility a Greek? Technically Implied Volatility is not a Greek, it is a measurement of risk and similar to time and underlying price. The Good Stuff • Delta, Vega and Theta – Extremely important for analyzing and constructing Trades – Should be available