The percentage change in an option's price for a 1% change in the underlying; the honest measure of how much leverage a contract provides.
Lambda is delta scaled into percentage terms: delta times the underlying price divided by the option price. It answers the question traders actually mean when they say an option is leveraged.
The number is large and unstable. A far out-of-the-money call might have a lambda above 20, meaning a 1% move produces a 20% swing in the position, but that leverage collapses as the option comes into the money. Sizing on lambda rather than on contract count is the difference between leveraged and reckless.
Example: XYZ at $50, the $55 call at $0.80 with delta 0.20. Lambda is 0.20 × 50 ÷ 0.80 = 12.5. A 1% rise in XYZ moves the call about 12.5%, so a $2,000 position behaves like $25,000 of stock.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Delta across the range of prices. Delta says how much a call's price moves for a one-point move in the stock. Far below the strike it is near 0 and the option barely reacts; at the strike it is about 0.50; far above it approaches 1 and tracks the stock.Buying a call: payoff at expiry. A 105-strike call bought for 3 loses that whole 3 if the price finishes at or below 105, breaks even at 108, then gains a dollar for every dollar higher. The loss is capped at the premium; the upside is not capped.
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