Irish Calculators
Saving & investing

Binomial Option Pricing Calculator

Model an option through a binomial tree with explicit exercise style and pricing assumptions. Results depend on the step count and exclude discrete cash dividends and barrier features.

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Your numbers

%
Annual standard deviation; not a price-growth forecast.
%
Use a rate consistent with the horizon.
%
Proportional dividend yield, not a cash dividend.
Display currency only. Convert all inputs to this currency before calculation.
Your figures stay on this device.

How the calculation works

A binomial tree prices an option by breaking its lifetime into short steps with upward and downward price branches. This implementation uses a Cox–Ross–Rubinstein tree and can compare European exercise at expiry with American exercise at the modelled nodes.

CRR uses u=exp(σ√dt), d=1/u and p=[exp((r−q)dt)−d]/(u−d). Discount risk-neutral continuation values; compare intrinsic value at each American exercise node.

  1. Construct the price branches

    Volatility and step length determine the up and down factors. The risk-free rate and dividend yield determine the risk-neutral weighting used for valuation.

  2. Value expiry payoffs

    At the final nodes, calls receive positive spot-minus-strike amounts and puts receive positive strike-minus-spot amounts. Negative exercise values are set to zero.

  3. Work backwards through the tree

    Discount each weighted continuation value towards today. American mode also tests immediate exercise at each node; the larger of exercise and continuation is retained.

Worked example: Check Binomial option value

Sample inputs demonstrate the method. They are not a forecast or product offer.

The first example prices a European call with spot and strike 100, one year, 20% volatility, a 5% continuous rate and 1,000 steps. The tree gives approximately 10.448584, close to but distinct from the continuous-model value.

Underlying spot price
100
Strike price
100
Time to expiry (years)
1
Annual volatility (%)
20
Continuously compounded risk-free rate (%)
5
Continuous dividend yield (%)
0
Tree steps
1000
Exercise style
European: expiry only
Option type
Call
Currency for all amounts
Euro (EUR)

Expected result

Binomial option value
€10.448584
Worked example: Check Binomial option value

Sample inputs demonstrate the method. They are not a forecast or product offer.

Underlying spot price
100
Strike price
100
Time to expiry (years)
1
Annual volatility (%)
0
Continuously compounded risk-free rate (%)
5
Continuous dividend yield (%)
0
Tree steps
10
Exercise style
European: expiry only
Option type
Call
Currency for all amounts
Euro (EUR)

Expected result

Binomial option value
€4.877058

Understanding your result

The output is a model value per underlying unit under the selected tree. A contract multiplier, market spread or dealing fee is not automatically included.

Invalid branch probabilities are rejected rather than clipped. Zero volatility uses a deterministic path, while zero time leaves only the current exercise payoff.

Questions you might have

What does the result include?

Price a European or American option with a Cox–Ross–Rubinstein tree and explicit exercise assumptions.

Which limits should I check?

A probability outside [0,1] is rejected. Zero volatility uses a deterministic path rather than dividing by zero.

Choosing the right inputs

Tree steps
Choose the number of tree steps. More steps refine the time grid but can change rounding and convergence behaviour; a coarse grid is not an exact market price.
Exercise style
European mode considers exercise only at expiry. American mode compares immediate exercise with continuation at each tree node.
Continuous dividend yield
Enter a continuous dividend yield, not a cash distribution on a particular date. Discrete cash dividends require a different tree specification.

Common mistakes to avoid

  • Do not treat European and American as labels for trading location; they describe exercise rights.
  • Increasing the step count does not add barriers, discrete dividends or other missing contract features.

Assumptions to check

  • A probability outside [0,1] is rejected. Zero volatility uses a deterministic path rather than dividing by zero.
  • All calculations run on your device. Figures are scenarios based on your inputs, not investment recommendations.

Sources and method

Read our calculation and testing approach.