Break-even price (or break-even point or just break-even) is the underlying price at which total outcome of an option or option strategy turns from loss to profit (or vice-versa). In other words, break-even is the price where payoff diagram (chart of P/L as function of underlying price at expiration) crosses the zero line.
What Option Break-Even Price Depends On
For every option, break-even price depends on only two things:
- Initial option price (what you paid for the option when you bought it)
- Gain from exercising the option at expiration
Break-even is the price where these two things are equal – what you gain from exercising the option at expiration equals what you paid for the option, so your total P/L is exactly zero.
How to Calculate Option Break-Even Price
Calculating the break-even price of a single option is very simple.
Usually you know very well what you paid for the option, so the only thing left is finding the underlying price at which the gain from option exercise equals that.
Gain from exercise is the same thing as the option's intrinsic value, or the difference between underlying price and strike price.
So we can say that an option's break-even is the underlying price at which the option's intrinsic value equals initial option price (premium paid).
Call Option Break-Even Price Formula
For a call option, intrinsic value equals underlying price minus strike price if underlying price is above the strike and the option is in the money. It equals zero when underlying price is below the strike, but we don't need to consider that scenario, because break-even can't be reached if the option is out of the money, as it won't be exercised and we have no way to offset initial cost of the option.
Therefore, call option break-even is the underlying price where:
Call intrinsic value = initial call price
Underlying price – call strike = initial call price
Call B/E = call strike + initial call price
Call option break-even is above the strike, by the amount equal to initial option price (premium paid).
Put Option Break-Even Price Formula
Intrinsic value of put options follows the same logic, only in the other direction. A put option is in the money when underlying price is below the strike.
Put intrinsic value = put strike – underlying price
Therefore, put option break-even is the underlying price where:
Put intrinsic value = initial put price
Put strike – underlying price = initial put price
Put B/E = put strike – initial put price
Put option break-even is below the strike, by the amount equal to initial option price (premium paid).
Break-Even Price of Short Option Positions
So far we have discussed break-even price from the position of an option's holder – the trader who is long the option. The one who buys the option in the beginning, pays a price for it, and breaks even when the gain from exercise covers his initial cost.
But in fact, the break-even price is exactly the same for the corresponding short option position.
Long call B/E = short call B/E
Long put B/E = short put B/E
Why? Every option trade has two sides (buyer and seller) and can be considered a zero-sum game (one must lose what the other gains). Therefore, both sides break even at the same point. Only difference is that one side is profitable above the break-even price (e.g. long call or short put), while the other is profitable below it (short call or long put). The above break-even price formulas are the same whether you are long or short the option.
The only thing that can complicate things a bit is commissions, which both parties pay, so an option trade is not exactly a zero-sum game. But if we understand "initial price" in the above formulas as "initial price after commissions", the formulas hold for both sides.
Break-Even Prices of Option Strategies
It is also possible to calculate break-even prices of option strategies (combination of multiple long and/or short call and/or put options). It is more complicated than for single options, but the inputs needed for the calculation are the same: initial cash-flow from entering the position and strike prices of all the options involved. Some option strategies (such as straddles, strangles, butterflies, or condors) have two break-even points, and more complex option positions can have more break-evens.
Some option strategies have relatively simple break-even price formulas.
For example, a bull call spread break-even is:
Bull call spread B/E = lower strike + net initial price of the spread
Bear call spread, which is the inverse (the other side) of bull call spread has exactly the same B/E formula:
Bear call spread B/E = lower strike + net initial price of the spread
Remember the break-even is the same for both sides of the trade. The only difference is that one side is profitable above the break-even (bull call spread in this case), while the other side is profitable below it (bear call spread).
Similarly both the long straddle and the short straddle positions have the same break-even prices:
Straddle B/E #1 = strike + initial price of the straddle
Straddle B/E #2 = strike – initial price of the straddle
Long straddle is profitable outside the break-evens (above B/E #1 and below B/E #2), while short straddle is profitable inside, around the strike.
It is possible to implement a more general calculation of P/L and break-even points for different option strategies in Excel. That is covered in the Option Payoff Excel Tutorial (or you can get it ready-made in the Option Strategy Payoff Calculator).
Break-Even Prices before Expiration
All the above assumes we always hold the position until expiration – this assumption makes break-even calculations relatively simple, because the relationship between underlying price and P/L is linear.
It is possible to also calculate break-even prices before expiration, but for that we need a way to estimate P/L under different conditions. We need an option pricing model (such as Black-Scholes) and we need to make assumptions about the other factors which affect option prices and P/L, such as volatility and interest rates.