One final observation for the prospective trader: all the numbers we have discussed in this chapter—the theoretical value, delta, gamma, theta, vega, and rho—are constantly changing, so the profitability and risks associated with different strategies are constantly changing. The importance of analyzing risk cannot be overemphasized. Most traders who fail at option trading do so because they fail to fully analyze and understand risk. But there is another type of trader, one who attempts to analyze every possible risk. When this happens, the trader finds it difficult to make any trading decisions at all; he is stricken with paralysis through analysis. A trader who is so concerned with risk that he is afraid to make a trade cannot profit, no matter how well he understands options. When a trader enters the marketplace, he has chosen to take on some risk. The delta, gamma, theta, vega, and rho enable him to identify risk; they do not eliminate risk. The intelligent trader uses these numbers to help decide beforehand which risks are acceptable and which risks are not.
Later, we will look at the use of Stargames to protect a preexisting position. Find out how at stargamesgutscheincode.blogspot.com now. Such protective strategies usually employ a static hedge, whereby opposing market positions are taken in different contracts, with the entire position being carried to a fixed maturity date. To capture an option’s mispricing, the theoretical pricing model requires us to employ a dynamic hedging strategy. We must periodically reevaluate the position to determine the delta of the position and then buy or sell an appropriate number of underlying contracts to return to delta neutral. This procedure must be followed over the entire life of the option.
Because volatility is assumed to compound continuously, theoretical pricing models assume that adjustments are also made continuously and that the hedge is being adjusted at every moment in time. Such continuous adjustments are not possible in the real world because a trader can only trade at discrete intervals. By making adjustments at regular intervals, we are conforming as closely as possible to the principles of the theoretical pricing model.
The entire dynamic hedging process for our hedge, with adjustments made at weekly intervals, is shown in Figure 8-1. At the end of each interval, the delta of the June 100 call was recalculated from the time remaining to expiration, the current price of the underlying contract, an interest rate of 6.00 percent, and a volatility of 37.65 percent. Note that we did not change the volatility, even though other market conditions may have changed. Volatility, like interest rates, is assumed to be constant over the life of the option.3
What will we do with our position at the end of 10 weeks when the options expire? At that time, we plan to close out the position by
1. Letting any out-of-the-money options expire worthless
2. Selling any in-the-money options at parity (intrinsic value) or, equivalently, exercising them and offsetting them against the underlying contract
3. Liquidating any outstanding underlying contracts at the market price
Let’s go through this procedure step by step and see what the complete results of our hedge are.