Buying Low Delta Call Options

Traders generally understand the delta of an option in one or both of the below two ways:

1.   As the percentage of a cent the option moves in price when the underlying stock moves by one full cent in a given direction, or

2.   As the implied probability that a given option will finish in the money, that is, with a non-zero (though not necessarily a profitable) payoff.

For example, with a 2.5% interest rate and 20% implied volatility, a 3-month 115 strike call on a stock currently trading at 100 with no expected dividends would have a delta of 10%, and cost 45 cents per share. In an efficient market, we would expect this type of option to expire worthless 90% of the time, with the relatively large payouts over the other 10% of scenarios making up for those 90% of losing cases and averaging out to that 45 cent price. In this article, we consider a trading strategy based on your view that certain stocks may have a higher-than-delta probability of paying out, and the risk/reward potential of this type of “long tail” strategy.

Step #1: Identifying Stocks “More Likely” To Rise Significantly

When we look back at the 5 European stocks that rose by more than 60% over the 12 month period ending 10 October 2024, that is, the top performers by price return, there seems to be no obvious common theme or driver. Below the stellar rise in the share price of aircraft engine maker Rolls Royce, the next strongest advancers over this past year were payment platform Adyen, enterprise software provider SAP, heath tech company Philips, and shopping mall owner Unibail-Rodamco-Westfield. These five companies are in very different businesses, have very different looking historical charts, and don’t seem to have been driven up by any common catalyst, though at least two of them might be described as recoveredfrom oversold levels. That at first may sound complicating, but it actually means there are more chances to be “right” about big movers than just trying to find the next Nvidia. Ultimately, the strategy of buying low-delta call options is a numbers game, and adds up to buying calls on stocks with lower deltas than your estimated probability of that stock finishing above the strike price.

Step #2: Choosing option tenor

As with any option strategy, the next important decision along with choosing the stock and strike price is choosing the expiry date or time horizon, and time horizon is especially important when options have a low delta. A quote often attributed to Bill Gates is that “people overestimate what they can do in one year and underestimate what they can do in ten years”, and the same can be said for what we expect of stocks over one month vs one year time frames. That said, it is worth repeating that buying these low-delta options is a numbers game, and the main factor a professional trader would use in choosing a time frame is the likelihood of a significant catalyst occurring over that time frame. For example, a one month option spanning an earnings announcement may make more sense at times than a two month option spanning no earnings announcements.

Sample math on this strategy

Suppose we have ten hypothetical stocks, each with a single letter ticker A, B, C, etc all the way to J, and each of them happen to be trading at €100 per share. We then look at 3-month, 10 delta call options, which as we saw earlier assuming a 2.5% interest rate, no dividend, and 20% volatility would be 115 strike. More volatile stocks would mean a higher strike price and a higher premium for the 10-delta call, for example, 30% volatility with all other parameters held the same would imply a strike price of 123 and a call premium of 69 cents, instead of 45 cents per share. Given the second interpretation of delta as the probability of the option finishing in the money, we would expect that on average, nine of these ten call options would expire worthless, and the one that doesn’t would have a payoff that makes up for the premium lost on the other nine. Our goal is then to put on this trade when we either expect that more than one of these stocks will break out above the strike price, or that the payout on one winning option exceeds the premium on all ten options combined, or preferably both.

Assuming all ten of these hypothetical stocks and corresponding options are identical, so that we buy one 115 strike, 10-delta, 3-month call on each of stocks A-J for a total premium of €450 (€0.45/share x 100 shares/contract x 10 contracts). That means the simplest way for this trade to be profitable is if any one of these stocks finishes the three month period above 119.50, even if the other nine all finish below 115 (and it doesn’t matter how much below 115). Obviously, a larger move would mean a bigger payout, as would having additional stocks finish above at least 115, but this is the basic framework for calculating the risk/reward of this kind of trade.

Conclusions

Low delta options are sometimes referred to as “lottery tickets”, as their very pricing implies the low probability of their value expiring with a value greater than zero, meaning a very high probability of losing 100% of the premium paid on such options. That said, there are scenarios where professional traders may find buying a low-delta call option, or a portfolio of such options, to be a limited downside way of capturing some participation to large upside surprises. 

Learn more

Visit Cboe’s Options Institute to explore the basics of options trading.

Cboe Europe offers trading in shares from across Europe and, through Cboe Europe Derivatives (CEDX), options are also available on shares on over 300 leading European companies. Learn more about CEDX here.

Disclaimers

·The above is the product of external market analysis commissioned on behalf of Cboe Europe B.V. The views expressed herein are those of the author and do not necessarily reflect the views of Cboe Europe B.V., Cboe Global Markets, Inc. or any of its affiliates (‘Cboe’). For more information on how this research was conducted and/or the author please contact [email protected]

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·Hypothetical scenarios are provided for illustrative purposes only. The actual performance of financial products can differ significantly from the performance of a hypothetical scenario due to execution timing, market disruptions, lack of liquidity, brokerage expenses, transaction costs, tax consequences, and other considerations that may not be applicable to the hypothetical scenario.

·Trading in options and options strategies can be complex and recommended for sophisticated investors with the appropriate level of knowledge and expertise in these transactions

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