Additional Considerations

In addition to what has been discussed, there are a few other pertinent observations a hedger should be concerned about when running this kind of analysis. For instance:

One can extend the discussion of the delta/vega-hedging strategy to include the hedging of rho risks. To do this, the hedger needs to use at- market interest rate swaps to manage the rho risks. More precisely, like the vega risks, it is customary to monitor the short-, mid-, and long-term risks and then hedge these risks respectively, using swaps of the appropriate maturity.

I discussed two strategies to help hedge the risks underlying the sale of a 10-year put option. One was a delta-hedging strategy (in which the delta risks are managed for the entire 10-year period). The second was a delta/vega strategy (in which the delta/vega risks are managed for one year after which the strategy rolls into a 9-year option that perfectly mimicked the option sold). These strategies are by no means exhaustive; other strategies a hedger might want to test are a delta/rho-based strategy (which, with an at-market swap rate matching the maturity of the sold option, is rolled over every time the net portfolio rho risk is neutralized), a delta/vega strategy (in which short-dated options are used), and so on.

To test a collection of strategies, it is imperative for the hedger to ensure that a unique set of trading limits and the frequency of trading limit monitoring (whenever applicable) is used. Once these are identified, the strategies can be put through a series of real-world scenarios and simulated scenarios (as was done in Tables 7.13, 7.14, and 7.16) to obtain the mean and standard and whatever statistics (or metrics) the hedger wants to use to rank the strategies from the best to the worst.

When the 10-year option was sold, the predominant risks happened to be the volatility and interest-rate risks. When options are short-dated or path-dependent in nature, other types of risks tend to be more predominant (e.g., gamma risks). As such, it is imperative for the hedger to not try to naively apply what was an effective hedge strategy for one type of option to another option.

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