Position Greeks

Adding Greeks across legs

Each Greek of a single option is a sensitivity per contract: delta per $1 of the underlying, gamma as the change in delta per $1 of the underlying, vega per point of implied volatility, theta per day, rho per point of interest rate. A strategy is a list of legs, each with a side and a ratio, so its Greeks are a weighted sum:

net Greek = Σ (sign × ratio × leg Greek), with sign +1 for a leg you buy and −1 for a leg you sell.

A leg on the underlying itself (the coin in a covered call, or a future) contributes a delta of 1 per unit and nothing else. The sum works because each Greek is a derivative, and derivatives add. It is also why one formula covers every structure in BOSS, from a single call to a four-leg condor, with no special case for any shape.

A worked example: a short iron condor

BTC at $100,000, 30 days to expiry, every leg at 50% implied volatility (flat, to keep the numbers clean). Buy the $85,000 put, sell the $90,000 put, sell the $110,000 call, buy the $115,000 call. The short iron condor collects a net credit of about $1,916. With each leg's sign already applied:

Read the net row as one position: a delta near zero means a small move barely changes its value; theta of +$39 a day means it earns from time passing; negative gamma and vega mean it loses from large moves and from implied volatility rising.

Delta-neutral is not risk-neutral

The condor's short strikes are closer to the money than its long wings, so the options it sells carry more gamma and vega than the ones it buys. Net, it is short both, even with a delta of almost exactly zero.

That shows as soon as the price moves. Repriced at the same 50% IV, at $105,000 the condor is about $121 down and its delta has turned to −0.049; at $95,000 it is about $160 down with a delta of +0.061. Either way, delta now points against the move, which is what negative gamma means. With BTC unchanged, a five-point rise in IV costs about $222. Those are losses on the mark before expiry; at expiry, anywhere between $90,000 and $110,000 keeps the whole credit, and the most it can lose is $5,000 − $1,916 = $3,084.

The same arithmetic explains other shapes. A covered call is the coin's delta of 1 plus a short call's −0.53: about 0.47, with the short call's negative gamma and vega. A long straddle adds a call's and a put's positive gamma and vega, with deltas that nearly cancel.

Venue Greeks and BOSS's curves

On a strategy page, the structure's metrics show its net Greeks from each venue's own reported Greeks, summed with sign and ratio as above. Those are only valid at the current price: no venue reports what delta would be at another one.

The Greek curves across a range of prices are BOSS's own: Black-Scholes at a zero rate, each leg at its current implied volatility and time to expiry, summed the same way. Vega is per volatility point and theta per calendar day, the venues' convention. At today's price the two can differ slightly, since the venues use their own models and forwards. Away from it, the curves hold every leg's IV fixed, while in a real sell-off put IV usually rises, so a short condor would lose more than the curve suggests.