Binomial Option Pricing Calculator

Estimate the theoretical price of a European Call or Put option using the Cox-Ross-Rubinstein binomial tree model. This tool provides a step-by-step valuation approach.

Understanding Binomial Option Pricing

The Binomial Option Pricing Model is a widely used method for valuing options. It uses a discrete-time approach, creating a “tree” of possible future prices for the underlying asset. By working backward from the option’s expiration date, we can determine its value at the present time.

How to Use This Calculator:

• Current Underlying Asset Price (S): The current market price of the stock or asset.
• Strike Price (K): The price at which the option holder can buy (for a call) or sell (for a put) the underlying asset.
• Time to Expiration (T): The time remaining until the option expires, expressed in years (e.g., 3 months = 0.25 years).
• Annual Risk-Free Interest Rate (r): The annualized rate of return on an investment with no risk, like a government bond. Enter as a percentage (e.g., 5 for 5%).
• Annual Volatility (σ): A measure of the expected fluctuation in the asset’s price, expressed as an annualized standard deviation. Enter as a percentage (e.g., 20 for 20%).
• Number of Steps in Tree (N): The number of discrete time steps the model will use to build the price tree. More steps generally lead to a more accurate price but increase computation time. For European options, a higher number (e.g., 50-200) is often suitable.
• Option Type: Choose whether you are pricing a Call (right to buy) or a Put (right to sell) option.

The Cox-Ross-Rubinstein (CRR) Method:

This calculator employs the CRR binomial model. The key steps are:

1. Calculate Time Step (Δt): `Δt = T / N`
2. Calculate Up and Down Factors (u, d):
   `u = e^(σ * √Δt)`
   `d = e^(-σ * √Δt)` (or `1/u`)
3. Calculate Risk-Neutral Probability (q):
   `q = (e^(r * Δt) – d) / (u – d)`
   This is the probability of an upward price movement in a risk-neutral world. The probability of a downward movement is `(1-q)`.
4. Build Asset Price Tree: Starting from `S`, project possible asset prices at each step until expiration. At step `j` and `i` up-moves, the stock price is `S * u^i * d^(j-i)`.
5. Calculate Option Values at Expiration (Step N):
   • For a Call: `max(0, StockPrice_At_Node – K)`
   • For a Put: `max(0, K – StockPrice_At_Node)`
6. Work Backward Through The Tree: For each node before expiration, the option value is the discounted expected value of the option from the next step:
   `OptionValue_Node = e^(-r * Δt) * [q * OptionValue_UpNode + (1-q) * OptionValue_DownNode]`

The option price calculated is the value at the very first node (time 0). This calculator assumes a European-style option, which can only be exercised at expiration.