Two-Step Binomial Trees for Pricing Vanilla Options
Summary
This document explains a binomial tree for estimating European and American vanilla call or put values. It projects the underlying up or down over two time steps using a volatility estimate, combines possible terminal payoffs with risk-neutral probabilities, and works backward to the current value. For American options, it compares continuation value with immediate exercise value at intermediate and current nodes.
The indicator accepts the strike, rates, dividend or foreign rate, asset class, option style, option type, time to expiry, and chart timeframe. The document explains how to set those inputs for stocks, foreign exchange, and futures, and relates the approach to the greater flexibility of tree models compared with Black–Scholes. Its main limitation is the fixed two-step tree: the author says the current version may not work for stocks priced above $100 and would need more steps. The source offers an implementation, but provides no pricing validation or performance evidence.
Key ideas
- A binomial tree represents possible underlying prices through successive up and down moves.
- Terminal option payoffs are valued first, then discounted expected values are calculated backward through the tree.
- American exercise is modeled by comparing continuation value with intrinsic value at each decision node.
- The script uses only two steps, which the author identifies as a limitation for higher-priced stocks.
- Inputs for dividends and rates vary with whether the underlying is a stock, currency pair, or futures contract.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.