Probability of profit (PoP)

How BOSS computes it

A strategy's payoff at expiry is a function of the settlement price. Its breakevens split the price axis into intervals where it either makes or loses money. Probability of profit (PoP) is the probability that the price lands in one of the profitable intervals. BOSS computes it the same way for every strategy:

• after costs: each leg is priced at execution, the ask when buying, the bid when selling, with its trading fee included, so the breakevens are the ones you actually face;
• lognormal around the forward: the settlement price follows a lognormal distribution whose mean is the expiry's forward, the same risk-neutral distribution the Black-76 model uses;
• at one volatility: the expiry's at-the-money implied volatility, flat across strikes.

It is therefore the probability the options market implies, not a forecast. A flat volatility ignores the skew: when out-of-the-money puts trade at higher IV, the market sees more downside than this PoP assumes.

A worked example

A 30-day short strangle on BTC, with the forward at $100,000 and IV at 50%: sell the $110,000 call for $2,275 and the $90,000 put for $1,828.

• At mid, the credit is $4,103 and the breakevens are $85,897 and $114,103. The lognormal probability of settling between them is 67.8%.
• At execution, selling at the bids (say $40 under the mid on each leg) and paying about $30 of fees per leg, the credit falls to $3,963 and PoP to 67.3%.

Two trades in three win. But the loss in the remaining third has no cap, so the result summary shows no reward-to-risk ratio for it.

Add wings to cap it, a short iron condor: also buy the $115,000 call for $1,341 and the $85,000 put for $847. The credit drops to $1,915, the maximum loss is $5,000 − $1,915 = $3,085, and PoP at mid falls to 59.6%. The reward-to-risk is $1,915 / $3,085 ≈ 0.62: win less than two times in three, make $1 for every $1.61 you can lose.

High PoP, poor reward-to-risk

Probability and payoff trade off against each other. A strategy that wins often wins small: short options far out of the money keep their premium most of the time and occasionally lose many times that premium. A long call far out of the money is the opposite: a low PoP and a large potential gain. Neither number alone says whether a trade is good. BOSS shows PoP next to maximum profit, maximum loss and reward-to-risk so the trade-off stays visible, and flags as lopsided a structure whose capped loss is many times what it can realistically make.

PoP is not expected value

Expected value weighs every outcome by its probability and size. Under the market's own distribution, an option priced at fair value has an expected value of about zero: for the strangle above at mid, the 67.8% of small gains and the 32.2% of larger losses cancel out. After costs the expected value is negative, about −$140 here, the spreads and fees paid. A positive edge needs a view that the market's distribution is wrong, for example that realized volatility will stay below implied, not a high PoP.