Forward Start Options

A normal option is like buying a house at a price fixed in a contract signed today. A forward start option is more like signing a contract today that says "in six months, we'll agree the price will be whatever the house is worth then, and you get to buy it at that price with a further option to walk away, exercisable a year after that." The strike isn't a number yet — it's a rule for setting a number later, based on wherever the underlying happens to be at a future date. Employee stock option grants and multi-year bonus structures often work this way in disguise: the strike gets set on the grant date, which itself lies in the future relative to when the deal was agreed.

The payoff and why moneyness resets

A forward start call struck at $\alpha$ times the underlying's price on a future date $t_1$, expiring at $T$, pays:

$$\text{Payoff} = \max\!\big(S_T - \alpha S_{t_1},\ 0\big).$$

In words: $S_{t_1}$ is the underlying's price on the future "strike-setting" date $t_1$; $\alpha$ (typically 1.0, meaning at-the-money) scales that price into the actual strike; $S_T$ is the underlying's price at final expiry $T$. Because the strike is set as a multiple of wherever the underlying happens to be on $t_1$, the option is guaranteed to start out exactly at-the-money (if $\alpha=1$) at that date, no matter how far the underlying has already moved between today and $t_1$. What you're really buying today is a slice of future at-the-money optionality, insulated from where the underlying drifts in the meantime.

Worked example 1 — setting the strike

An index trades at 4,000 today. A forward start call is written with $\alpha = 1.0$ and a strike-setting date $t_1$ six months out, expiring at $T$ = 18 months. Suppose the index rallies to 4,600 by month six. The strike is set at $1.0 \times 4{,}600 = 4{,}600$ — not 4,000. The option is now a fresh at-the-money call on the index, with 12 months left to run, regardless of the 15% rally that already happened. If the index had instead fallen to 3,400 by month six, the strike would be set at 3,400: the option always resets at-the-money at $t_1$, which is exactly the point.

Worked example 2 — pricing off forward volatility

Because the strike-setting date and the moneyness are both fixed relative to $S_{t_1}$, the pre-$t_1$ Black-Scholes value of the option collapses to a formula driven almost entirely by the forward implied volatility between $t_1$ and $T$, not by the underlying's level today. Suppose one-year implied vol is 20% and the six-month implied vol is 16%, both flat rates, no dividends. Using variance additivity, the forward variance from month 6 to month 12 satisfies $0.20^2 \times 1 = 0.16^2 \times 0.5 + \sigma_{fwd}^2 \times 0.5$, so $0.04 = 0.0128 + 0.5\,\sigma_{fwd}^2$, giving $\sigma_{fwd}^2 = 0.0544$ and $\sigma_{fwd} = \sqrt{0.0544} \approx 23.3\%$. That 23.3% forward vol, not today's spot 20% vol, is what feeds into pricing the six-to-twelve-month leg of the option — the near-term implied vol is "used up" getting to $t_1$ and only the remainder is priced into the option itself.

Think of the curve above as standing in for the variance term structure: total variance to $T$ minus total variance to $t_1$ leaves the forward variance that actually prices the option — drag the parameters and notice how a steep near-term curve versus a flat far one changes how much variance is "left over" for the forward leg.

What this means in practice

Forward start options are the building block behind cliquets and ratchet notes, which chain several forward start options together, each period's strike reset off the last (see cliquets and ratchet options). They're also embedded, often unnoticed, in multi-year employee compensation plans and some structured note series. Desks price and hedge them off the forward volatility surface, not the spot surface, which is why a flattening or steepening term structure of implied vol matters more here than the current spot level does.