What are the key Greek features of lookback options?

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AcadiFi · Accepted Answer

A floating-strike lookback call pays max(S_T - S_min, 0), locking in the lowest price observed during the life of the contract. Because the payoff always captures the best entry, lookbacks are pathwise monotonic and have materially higher prices than vanilla calls — often 1.5-2x the vanilla premium for at-the-money cases.

Greek features: Delta for a floating-strike lookback call is lower than a comparable vanilla call at inception but rises as spot approaches the running minimum. Gamma is generally positive but smaller than a vanilla, because the option isn't kinked at a single strike. Vega is large and positive: higher volatility increases the expected range, widening the spread between S_T and S_min. Theta decays slowly early in life because a new minimum can reset the strike, preserving optionality.

Example: Tremayne Mining floating-strike lookback call, S = $40, σ = 35%, T = 1 year. Monte Carlo price ≈ $7.80 versus a vanilla ATM call at $4.90. Vega might be 0.24 per vol point, nearly 1.5x vanilla vega. Delta-hedging requires daily updates to the running minimum, creating path-dependent rebalancing that introduces hedging slippage.

Firms like Windhaven Structured Solutions price lookbacks using closed-form formulas from Goldman-Sosin-Gatto or numerical PDEs. FRM candidates should remember that fixed-strike lookbacks have different Greek profiles — they behave more like vanilla options but with enhanced vega. Also, extreme-value theory supports lookback pricing: the distribution of extremes has heavier tails than normal returns.

What are the key Greek features of lookback options?

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