Mixed Dividends

Dividends are one of the most influential — and most frequently misunderstood — inputs in equity option pricing. They affect intrinsic value, forward price, and the early-exercise premium for American options. Because actual dividends arrive as discrete cash events rather than smooth cash flows, building an accurate model is essential for precise valuations.

Fixed + Proportional: How the Market Really Prices Dividends

For near-term maturities, markets overwhelmingly treat dividends as fixed cash amounts, reflecting the high confidence around upcoming payouts. But the farther out you go, the more the market shifts toward a mixed structure: part fixed, part proportional to the underlying price. This makes intuitive and economic sense — distant dividends depend on corporate performance, business cycles, and long-term growth trends.

A modern dividend model must be able to represent this transition smoothly. Ours does exactly that.

• Fixed dividends: Known dollar amounts on known dates.
• Proportional dividends: A stable percentage of the underlying, widely used in ETF options and long-dated options pricing.
• Mixed dividends: A combination of fixed and proportional.

A Real-World Example

The chart below demonstrates the practical impact of dividend assumptions. On September 7, 2025, we priced SPY call options expiring January 21, 2028. If all future dividends are treated as fixed cash versus all proportional, the theoretical value can differ by as much as $1.60 — even after calibrating proportional dividends so that both models have identical forward prices. In comparison, the bid–ask spread for the at-the-money SPY call of the same maturity is only about $0.60.

Neither “pure fixed” nor “pure proportional” is correct. The market reality sits between them, and the pricing difference is large enough to demand a mixed-dividend approach.

How Much Does It Really Matter?

A pricer that cannot model mixed dividends will systematically misprice calls and puts across the strikes — and the resulting bias is non-uniform, especially for longer-dated American options. In practice, this means it becomes impossible to align call and put volatilities at every strike when using a model that only supports pure fixed or pure proportional dividends. Our pricer solves this by integrating both fixed and proportional dividends into a single, coherent schedule, producing valuations that align with how the market actually trades.

See the difference for yourself using our option calculator here.