Using Scenario Search to Optimize a Hedged Bull Call Spread
Summary
The document considers how to reduce the worst losses of a bullish call spread by adding a bearish option position in a later expiry. It discusses balancing hedge size, the hedge’s cost, and the different rates of time decay across expiries. The proposed hedge uses calls on an inverse leveraged ETF, though the author’s main interest is the shape of the combined payoff rather than the specific symbols.
The answer recommends evaluating candidate combinations across a grid of underlying price scenarios, calculating option values for each, and using an optimizer to search over strikes and quantities. A chosen objective, such as peak profit, can be maximized subject to a loss constraint. The method turns a visual payoff problem into a constrained search. It depends on the pricing formulas and scenarios chosen, and it cannot guarantee outcomes outside them. The answer also notes that some desired combinations, such as eliminating downside while retaining upside across all market scenarios, are not feasible.
Key ideas
- Model the combined positions over a grid of underlying price scenarios.
- Search across hedge strikes and quantities with an explicit objective function.
- A maximum-loss constraint can be included in the optimization.
- Hedge size, cost, and differing time decay affect the payoff profile.
- Scenario optimization cannot make every desirable payoff constraint feasible.
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Full text
# How to hedge a bull call spread # How to hedge a bull call spread I am trying to make a theoretical hedge to a bull call spread. (buy out the money call, sell further out the money call) What I have now is almost effective but there is one possible 80% loss (amongst consistent 70% gains in an equally likely scenario, and 300% gains in an extreme scenario) Best case scenario: 70% gain Worst case scenario: 80% loss Black swan bearish scenario: 300+% gain (this is a factor of the hedge) What I would like my hedge to do is mitigate the worst case scenario. Here is the rationale: QQQ Bull Call Spread in near term, this is bullish (qqq represents the nasdaq composite) FAZ long calls in back month (to mitigate theta), this is bearish as FAZ is a 3x leveraged ETF (albiet on the finance sector). FAZ will increase in value 3x for every 1 point move down QQQ makes. Calls will get intrinsic value very quickly. For this site's sake, I'm not caring too much about the symbols. I am interested trying to find a cheap hedge that increases 3x faster if the other side of the trade fails. Right now I almost have that, but not yet. The key variables to manipulate are: Balance: How much of the hedge is held in proportion to the main trade. This simulation shows 10 bull call spreads, hedged by 1 long call in an inverse ETF Theta: The front month expires faster than the back month. The back month hedge can be closed before the effects of theta become apparent. But the further out you go for the back month, the most expensive it gets Expense: the hedge ideally should not be more expensive than the potential profit of the main trade, but it is expected to cut into the theoretical max profit of the main trade. The key is to get the shape of the risk profile to have a smaller dip into the negative at any point on the graph. ## Answer by Brian B (score 2) https://quant.stackexchange.com/a/2658 I suggest searching all the possibilities using Excel. Code the option pricing formulas into VBA functions (if you have not done so already) with cell to hold option strikes and quantities, and then set up your price scenarios for a grid of 1% moves in the underlying. You have now reproduced the information contained in your Bloomberg plots pictured above. Excel Solver will let you do a search on the outcomes, and even set constraints such as never losing more than 40% (as opposed to the 80% you now have). You will want to define a particular "utility function" cell for it to maximize, perhaps the peak profit or whatever else fits your personal desiderata. Start the solver with the best scenario you have established so far, and let it improve your utility function within whatever constraints you have set. Obviously some hypothetical constraints will be impossible to satisfy, e.g. 0% downside and >0% upside in all market scenarios.
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