This paper introduces two classes of path-dependent derivatives: options on stockprice length and options on stock-price speed. Stock-price length is defined as the sum of the absolute price changes observed over a predetermined discrete sampling grid. Stock-price speed is the corresponding length divided by the duration of the observation period. Unlike conventional options, which depend primarily on the terminal stock price, these contracts depend on the distance travelled by the price along its realized path, irrespective of direction. They are therefore sensitive to oscillation, volatility, trading activity, and market microstructure. The contracts are formulated using both arithmetic price increments and logarithmic returns. Under geometric Brownian motion, absolute log-return increments follow foldednormal distributions, which permits analytical calculation of the first two moments of realized stock length. Normal, gamma, and lognormal approximations are developed for European calls on stock length and speed, and the exact scaling relation between length and speed options is established. Stochastic volatility, hedging, market microstructure, and practical contract design are also discussed. The statistical object underlying logarithmic stock length is closely related to realized absolute variation and realized power variation. The proposed contribution is the explicit formulation of calls and puts on total discretely observed stock-price length and on its time-normalized speed.