Binary options offer a fixed amount payout structure – either $100 or $0. This unique payoff allows binary options to be used for hedging and risk mitigation for various other securities. This article uses a working example to show how a long call option position can be hedged using binary put options. (For more info on call options and binary options, see:* Options Basics: What Are Options?*, Call Option Basics – Video and Information and Advice on Binary Option.)

Long call options provide profit when the underlying stock’s price moves above the strike price and leads to losses on the downward price move. Binary put options provide profits on the downside and loss on the upside. Combining the two in an appropriate proportion offers the required hedging for a long call option position. (See related: Hedging Basics: What Is A Hedge?)

Assume Paul, a trader, holds a long position with three lots (= 300 contracts) on call options of ABC, Inc., which have a strike price of $55. They cost him $2 per contract (the option premium). Binary put options with a strike price of $55 are available at an option premium of $0.2 per contract. How many binary put options would Paul need to hedge his long call position?

Arriving at the number of binary puts needed involves multiple steps: calculating an initial number of binary options, then the number of binary options required to pay for hedging, and finally the number of binary options needed for total cost adjustment (if required). The sum of all three will yield the total number of binary put options needed for hedging.

Here are the calculations:

- Total cost of long call position = $2 * 300 contracts = $600.
- Initial number of binary put options = total cost of long call / 100 = 600/100 = 6 lots.
- Cost of initial number of binary put options =$0.28 * 6 lots * 100 contracts = $168.
- Number of binary options required to pay for hedging = (cost of initial number of binary put options / 100) = (168/100) = 1.68, rounded to 2.
- Total number of binary put options needed = initial number + number required to pay for hedging = 6 + 2 = 8.
- Cost of binary put options = $0.28 * 8 lots * 100 contracts = $224.
- Maximum payout from 8 binary put options = 8* $100 = $800 (Each binary put can give maximum payoff of $100).
- Total Cost of Trade = cost of long calls + cost of binary puts = $600 + $224 = $824.

Since the total cost of trade ($824) is more than the maximum payout ($800), more binary put options are needed for hedging. Increasing the binary put options from eight to nine leads to:

- Cost of binary put options = $0.28 * 9 lots * 100 contracts = $252.
- Maximum payout from nine binary put options = 9* $100 = $900.
- Total Cost of Trade = cost of long calls + cost of binary puts = $600 + $252 = $852.

With nine binary put options, the total cost of trade is now less than the maximum payout. It indicates a sufficient number for hedging. As a general rule, the number of binary options should be increased incrementally until the total cost of trade becomes lower than the binary options payout.

Here is the scenario analysis of how this hedged combination will perform on the expiry date, according to the different price levels of the underlying:

Underlying Price at Expiry |
Profit/Loss from Long Call Option |
Binary Put Payout |
Binary Put Net Payout |
Net Profit/ Loss |

(a) |
(b) = ((a - strike price) * quantity) - buy price |
(c ) |
(d) = (c ) - binary option premium |
(e ) = (b) + (d) |

35.00 |
-600.00 |
900.00 |
648.00 |
48.00 |

40.00 |
-600.00 |
900.00 |
648.00 |
48.00 |

45.00 |
-600.00 |
900.00 |
648.00 |
48.00 |

50.00 |
-600.00 |
900.00 |
648.00 |
48.00 |

54.99 |
-600.00 |
900.00 |
648.00 |
48.00 |

55.00 |
-600.00 |
0.00 |
-252.00 |
-852.00 |

56.00 |
-300.00 |
0.00 |
-252.00 |
-552.00 |

57.84 |
252.00 |
0.00 |
-252.00 |
0.00 |

60.00 |
900.00 |
0.00 |
-252.00 |
648.00 |

65.00 |
2,400.00 |
0.00 |
-252.00 |
2,148.00 |

70.00 |
3,900.00 |
0.00 |
-252.00 |
3,648.00 |

75.00 |
5,400.00 |
0.00 |
-252.00 |
5,148.00 |

where,

Call Strike = Binary Put Option Strike = |
55.00 |

Call Buy Price = |
$2 |

Call Option Quantity = |
300 |

Call Cost = |
$600 |

Binary Put Option Premium = |
$0.28 |

Without the hedge from the binary put option, the maximum loss incurred by Paul would be $600. It equals the total cost of call option premium and is indicated in column (b). This loss will be incurred if the underlying settlement price ends below the strike price of $55.

Adding the hedge using binary put options converts the loss of $600 to a profit of $48, if the underlying settlement price ends below the strike price of $55. By spending $252 towards hedging from nine lots of binary put options, the loss transformed into profit.

However, combining the linear payoff structure of call option and the flat payoff structure of the binary put option leads to a small-range high-loss area around the strike price.

Maximum loss occurs at the strike price of $55, as there will be no payout from the long call option, and no payout from the binary put option either. Paul will lose a total of $852 on both option positions, if the settlement price ends at the strike price of $55 on the expiry date. This is the maximum loss.

The breakeven point for this combination occurs at the settlement price of $57.84, where there is no profit and no loss from this hedged position (as indicated with $0 in column (e)). Theoretically, it is computed by adding the long call strike price, long call premium and the factor (binary put cost/ long call quantity).

Breakeven point = $55 + $2 + ($252/300) = $57.84.

Between the strike price and breakeven point ($55 to $57.84), the trader has a loss that goes down linearly and converts to profit once the underlying goes above the breakeven point of $57.84.

Above the breakeven point, the position becomes profitable. The net profit of hedged position remains lower due to hedging costs, as against the naked call position. This is indicated by higher values in column (b) compared to those in column (e) when underlying settlement value of above $57.84. However, the purpose of hedging is served.

**The Bottom Line**

With the availability of multiple asset categories with unique payout structures, it is easy to hedge different kinds of positions. Using binary options is an effective method for hedging call options, as demonstrated above. Since the process is calculation-intensive, traders should perform due diligence in making calculations. The final results should be double-checked to avoid any costly mistakes. One can also try other variations with slightly different strike prices of plain vanilla call options and binary put options, and select the one which best suits their trading needs.