Digital Option Payoff Height and Its Meaning

Summary

A digital option pays a fixed amount if it finishes in the money and nothing otherwise. The note explains that the payoff diagram’s height is this fixed payment, often denoted by δ. The underlying price determines whether the payment is triggered, while the payment amount sets the height of the payoff above the strike threshold.

The explanation is qualitative and does not cover valuation, probability of exercise, or how the payoff behaves near expiry. It refers to an accompanying diagram, but the text alone gives the core interpretation: the digital payoff is a step, with its nonzero level equal to the contract’s stated payout.

Key ideas

• A digital option pays a fixed amount when it finishes in the money.
• The payoff height is equal to the fixed payment amount.
• The strike determines the threshold for receiving the payment.

Tags

# Digital height of an option


# Digital height of an option












Could someone please help me explain the concept of Digital Height clearly in the options world? Thank you

## Answer by Jan Stuller (score 3, accepted)

https://quant.stackexchange.com/a/54735

Digital option pays the amount $\delta$ if it ends up in the money otherwise it pays zero. Therefore, the pay-off diagram (pay-off on the y-axis, underlying price on the x-axis) looks like a straight line that starts at $S_T = K$ and the y-axis value of this straight line is equal to $y=\delta$. In other words, the "height" of the pay-off is equal to the digital option pay-off.

In the diagram below, $\delta = C$ and therefore the "height" of the digital option pay-off is $C$.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.