"Option Volatility and Pricing", Sheldon Natenberg. This book helps readers to understand option from a trader"s perspective. Other relevant reading materials: Risk related Chapters: Gamma is a measurement of magnitude risk . Options have positive gamma. This seems to correspond to volatility. If we have a negative gamma, we want the market to remain relatively quiet. Isn"t this the same as saying we want lower volatility? Although the volatility of the underlying contract and changes in implied volatility are often correlated, this is not always the case. Because the delta depends on the volatility, but volatility is an unknown factor, calculation of the delta can pose a major problem for a trader, especially for a large option position. This is because both OTM and ITM options have very little time value. The option price as volatility change is quite similar to theta one. where: If the option is ATM, we have , and if the interest rate is negligible (r = 0), we have: The sensitivity of vega to a change in volatility (volga): So it is negative, which means it is true that "the vega of an at-the-money option declines as we raise volatility". As for the magnitude of change, the book says it is "very slight", let"s verify it with formula (if ATM): It seems negligible if the time to expire is small enough. let"s verify with an ATM option with: Its vega is 11.51, usually we use 1% change in volatility so it becomes 0.1151, which means +1% volatility change will +0.1151 to ATM option price. Its volga is 0.06, compared to 11.51 this is negligible. With less time to expiration or lower volatility, OTM and ITM options" time value will be lower because they will be less likely that a large price change will happen. Gamma will also be lower, the graph becomes "thin". More time to expiration, like higher volatility, will make OTM and ITM options behave like ATM ones. The graph becomes "fat". Scalping tries to make a market and make profit from liquidity. However, option markets are rarely sufficient liquid to support this type of trading. When market condition changes, two legs of spread will gain and lose value respectively. Many common spreading strategies are based on arbitrage relationships. Another type of spreading strategy involves buying and selling futures contracts of different maturities on the same underlying commodity. It is similar to the cash-and-carry strategy. Besides, we can also do this in different markets (intramarket spread v.s. intermarket spread). cash-and-carry strategy cancels the the directional risk, the trader does not need to tell which contract is mispriced, he only need to know if the spread is profitable. Note that the spread is not NECESSARILY a contract. We can"t guarantee the entire spread will be executed at one time. Trade has to choose the best time to execute each leg. In this procedure, the portfolio is at risk. Most traders learn that it is usually best to execute the more difficult leg first . Spreading strategies are widely employed in option markets, because: In option trading, assuming the theoretical price is correct, the immediate reward of a trade is the captured edge. Because there is no guarantee that our theoretical price will be right, the risk associated with the trade is also introduced. The risk is from multiple dimension: So basically, in option trading, we only need to worry about two things: In fact, they are both volatility risk . As we mentioned before, Gamma is related to realized volatility, and Vega is related to implied volatility. Steps to analysis risk for multiple kinds of spreads: Suppose that we find the implied volatility is higher than our theoretical value (18%). If we believe in our model, we conclude that they options are overpriced . To make a profit, trade chooses to short vega . There are multiple spreads to consider (excluding calendar spreads): Below is the greeks for each spread: Theoretical PnL of each spread when underlying price moves: Because we are shorting Gamma, large underlying price move will hurt our position . But different spreads have different exposure to the risk. Theoretical PnL of each spread when implied volatility moves: Because we are shorting Vega, increasing of volatility will also hurt the position . When deciding which spread to trade, we can analysis from 2 aspects. This can be easily seen from their payoff graphs. The interest-rate and dividend risk associated with volatility spreads is usually small compared with the volatility (gamma and vega) risk. Nonetheless, a trader ought to be aware of these risks, especially when a position is large and there is significant risk of a change in either interest rates or dividends. For example, a trader is considering two possible spreads, both with a positive gamma and negative theta. The reward coms from the Gamma and the risk is mainly from Theta. Of course the trader want the reward (Gamma) to be as large as possible compared to the risk (Theta). The efficiency is a ratio of the absolute value: We can calculate the efficiency for above 3 spreads: Because we are shorting Gamma, the reward is from Theta. So the smaller efficient is, the better. As a result, from a fast comparison, we find Spread3 is the best in risk term, which is consistent with our previous analysis of each spread. (Why the spread 2 is the worst? The book does not explain...) In cases that the Gamma and Theta are the primary risks to the position , Assuming that all strategies have approximately the same theoretical edge , the efficiency can be a reasonable method of quickly comparing strategies where all options expire at the same time . Trader needs to adjust the position to remain delta-neutral. Again, use above case as example.
