Forward-Start Options: Payoff Units, Fixing, Forward Volatility, and Model Risk

Audit a forward-start option's payoff units, fixing rules, forward variance, future-smile assumptions, Greeks, execution, credit, and settlement.

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

A forward-start option is committed and valued at trade date t0, but its strike or normalized return threshold is fixed from an underlying observation at a later date T1; the option then expires at T2. The confirmation must state the payoff unit. A share-based European call may pay q x M x max(S2 - alpha x S1, 0), while a fixed return-notional call may pay N x max(S2 / S1 - alpha, 0). These are different claims with different cash scaling, hedges, and settlement.

For the share-based put, the corresponding payoff is q x M x max(alpha x S1 - S2, 0). Here S1 and S2 are contract-defined observations, alpha is the strike percentage in decimal form, q is quantity, M is the deliverable or cash multiplier, and N is a currency notional. The name alone does not determine which formula applies.

Build the exact claim and lifecycle

Lock the legal payoff, call or put direction, share-based or return-notional units, alpha, quantity, multiplier, currency, and every trade, premium-payment, fixing, exercise, expiration, notice, and settlement date.
Define the T1 observation source, time zone, single price or averaging window, valid observations, holiday calendar, market-disruption fallback, correction policy, rounding, dividends, and corporate-action adjustments.
Record synchronized spot, forwards, discount curves, dividends, borrow, FX and quanto terms, and executable vanilla bid, ask, size, and surface data at comparable strikes or forward-moneyness coordinates for both horizons.
Compute total and interval forward variance with a consistent day count. If w(T) = sigma_imp(T)^2 x T, then v_fwd = [w(T2) - w(T1)] / (T2 - T1) is an annualized interval variance, not the future smile or a unique forward-start price.
Select and version the pricing model and future-smile or joint-law assumptions. Reprice pre-fixing exposure, the fixing transition, and the post-fixing vanilla claim under volatility, skew, jump, rates, dividends, correlation, and observation shocks.
Prewrite hedge, limit-order, partial-fill, unwind, collateral, counterparty, clearing, disruption, and funding branches. A theoretical value or robust bound is not an executable exit quote.
At T1 and T2, reconcile the actual observation, fixed strike, exercise decision, official settlement, cash or shares, fees, tax, collateral, and residual positions against the confirmation and model version.

When alpha = 1, the strike equals the contract’s T1 reference, so the claim is spot-ATM at fixing under that definition. It is not necessarily forward-ATM, Delta-neutral, free of carry, or free of pre-start risk. Under a scale-invariant Black-Scholes-style model, a share-based claim can be homogeneous in current spot, but discrete cash dividends, fixed cash features, barriers, quanto terms, caps, floors, and other nonhomogeneous provisions can break that shortcut.

Vanilla surfaces at T1 and T2 constrain marginal distributions but do not uniquely determine the joint law of S1 and S2, spot-volatility dependence, or the smile prevailing at T1. Stochastic-volatility, jump, local-volatility, and robust-bound approaches can therefore produce materially different values and hedges while matching today’s vanilla data.

Four worked examples

Payoff units: At t0, three share-based calls cost p = $7.50/share, with q = 3 and M = 100. At fixing, S1 = $80 and alpha = 1.05, so K = $84. At expiration, S2 = $110; gross payoff is 3 x 100 x ($110 - $84) = $7,800, initial cash is -$2,250, and pre-fee result is +$5,550. A separate normalized contract with N = $10,000 pays $10,000 x max($110 / $80 - 1.05, 0) = $3,250; it is not the same claim.
Controlled Black-Scholes case: Assume a share-based European claim with S0 = $100, T1 = 1, T2 = 2, tau = 1, alpha = 1, r = 4%, q_div = 1%, and sigma = 25%. Then d1 = 0.245, d2 = -0.005, call value is $11.1237619281/share, and put value is $8.2268370475/share. Homogeneity gives pre-start Delta0 = 0.1112376193 per share, while immediately after fixing the call’s vanilla Delta is 0.5908338059. That scheduled hedge change is model-specific, not a permanent hedge ratio.
Forward-variance diagnostic: At a matched coordinate, let T1 = 0.5, sigma1 = 20%, T2 = 1.5, and sigma2 = 30%. Then W1 = 0.0200000000, W2 = 0.1350000000, v_fwd = 0.1150000000, and sigma_fwd = sqrt(0.115) = 33.9116499156%. This describes the full one-year interval under the stated variance convention; it is not 30% - 20%, a future smile, or a unique contract value.
Observation and settlement: Three valid fixing observations are 98, 102, and 100, so their arithmetic average is S1 = 100. With alpha = 0.95, K = $95. At T2, official SET = $92; five long puts with M = 100 produce cash +$1,500 and 0 shares. A physically settled version instead produces -500 shares and +$47,500, the same $1,500 intrinsic value against a $46,000 stock mark. Using only 102 would set K = $96.90, produce $2,450, and create a $950 error.

Contract and model failure modes

Trade, premium, fixing, exercise, expiration, notice, or settlement dates are ordered or interpreted incorrectly.
Time zone, holiday, business-day convention, or payment timing is wrong.
The observation source, timestamp, valid-price rule, or averaging window is misread.
A market disruption, stale observation, correction, or fallback is omitted.
alpha is entered as a percentage rather than a decimal, or rounding is applied at the wrong stage.
Share-based and return-notional payoffs or their units are interchanged.
Call versus put, long versus short, quantity, multiplier, currency, or deliverable has the wrong sign or scale.
Dividends, corporate actions, special distributions, or adjustments around fixing are handled incorrectly.
Spot-ATM at fixing is mistaken for forward-ATM, zero Delta, or zero carry.
American exercise, European exercise, physical delivery, cash settlement, FX, or quanto terms are conflated.
Vanilla quotes, forwards, curves, dividends, borrow, or FX inputs are stale, asynchronous, or non-executable.
Midpoints, model marks, robust bounds, or displayed size are treated as executable entry or unwind prices.
Annualized IVs are subtracted directly instead of using total variance and a consistent day count.
Strikes, deltas, or forward-moneyness coordinates differ across the two surfaces.
Today’s marginal surfaces are assumed to identify the future smile or the joint law of S1 and S2.
Stochastic volatility, jumps, leverage, rates, correlation, or model calibration uncertainty is ignored.
A local Greek approximation is carried through the fixing transition, a jump, or a large surface move.
Gaps, closed markets, discrete hedging, partial fills, transaction costs, or scarce unwind liquidity break the hedge.
Bilateral OTC, issuer note, exchange FLEX, OCC clearing, counterparty credit, and collateral protections are confused.
Fees, funding, tax, observation records, exercise, cash, shares, collateral, and model governance are not reconciled.

Common misconceptions

“The option is purchased at T1.” The commitment and premium may occur at t0; fixing and activation occur later.
“An unknown future strike cannot be valued today.” It can be modeled today, but future-smile and joint-distribution assumptions create material model risk.
“alpha = 1 or a pre-fixing price decline removes risk.” The strike resets with the reference, while pre-start value and hedge exposures remain.
“Forward volatility is the difference between two IVs and uniquely determines price.” Total variance is required, and one interval scalar does not identify the future smile or joint law.
“It is the same as buying a vanilla at T1, and every reset product is a cliquet.” Future premium and execution are not locked by waiting; a cliquet usually aggregates multiple separately governed reset payoffs.