Swing Options

A gas utility doesn't consume a fixed amount of gas every day — demand swings with the weather, colder days mean more heating, and the utility needs a supply contract flexible enough to match that. A swing option is built for exactly this: instead of one fixed exercise decision like a normal option, the holder exercises repeatedly over the contract's life, choosing how much to take each time (within daily min/max limits) as well as when, subject to an overall limit on total volume across the whole contract. It "swings" between different daily volumes as conditions change, which is where the name comes from.

The structure

A swing option holder chooses a daily exercise quantity $q_t$ on each day $t$, subject to:

$$q_{\min} \le q_t \le q_{\max}, \qquad \sum_{t=1}^{T} q_t \le Q_{\text{total}},$$

paying strike price $K$ per unit exercised, so each day's decision earns $(S_t - K) \times q_t$ if $S_t > K$. In words: $q_{\min}$ and $q_{\max}$ bound the amount allowed on any single day, and $Q_{\text{total}}$ caps how much can be taken in total — the holder must plan with an eye on how much allowance is left, since taking the maximum every day, if favorable prices persist, might exhaust the limit before the contract ends.

Worked example 1 — a simple two-day swing

A swing call lets the holder buy between 0 and 100 units per day, strike $40, total cap across two days of 120 units. Day 1 price $55, Day 2 price $30. Day 1 is profitable ($55>40$), so the holder takes the daily max, 100 units, earning $(55-40)\times100=$ $1,500, leaving only 20 units of allowance for Day 2. Day 2 is below strike, so the holder exercises zero, banking the leftover 20 units unused. Total payoff: $1,500. Compare a rigid contract forcing a flat 60 units per day: Day 1 earns $(55-40)\times60=$ $900, and Day 2, forced to buy 60 units at $30 below the $40 strike, loses $(30-40)\times60=$ -$600, netting only $300. The swing structure's freedom to take more on the good day and nothing on the bad one is worth $1,200 more than the rigid version.

Worked example 2 — why the total cap creates path dependence

Same setup, now three days, total cap still 120, daily max 100. Day 1 $55 (take 100, using 100 of 120), Day 2 $60 (want 100, but only 20 remain — take 20, earning $(60-40)\times20=$ $400), Day 3 $70 (allowance exhausted — take 0, even though $70 is the best price of the three). Total payoff: $1{,}500+400+0=$ $1,900. Had the holder taken only 60 units on Day 1, saving allowance for the later, better days, they could have captured more of Day 3's price — exactly why swing options resist simple day-by-day pricing: today's optimal decision depends on what might happen on every remaining day.

Picture the curve as one day's exercise payoff against price — a swing option chains many such days under a shared budget, so the optimal strategy weighs today's payoff against the value of saving allowance for a possibly better day ahead.

What this means in practice

Swing options are the standard structure in natural gas and power supply contracts, because real buyers genuinely have day-to-day volumetric flexibility needs, not just a single all-or-nothing exercise decision. Because the optimal daily decision depends on the entire remaining path and the remaining allowance, closed-form pricing formulas don't exist for realistic cases; desks price and hedge swing options using Least-Squares Monte Carlo (the same Longstaff-Schwartz-style backward induction used for Bermudan options), extended to track remaining volume allowance as an extra state variable alongside price.