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Replicating Options in a Binomial Tree with a Cash Dividend

Article Quant Q&A · Author: Math122
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Summary

The document addresses how a cash dividend paid during a multi-step binomial model affects a replicating strategy. Its central instruction is to reduce the stock price by the dividend amount at the payment node, then continue building the tree from the adjusted price. For example, a stock valued at 100 immediately before a dividend of 10 is modeled at 90 after payment.

The note indicates that the resulting stock-price tree, and therefore the replication, differs from a tree that omits the dividend. It offers no derivation of the hedge ratios, worked multi-period replication, or comparison with martingale valuation. The adjustment described assumes a known cash dividend and does not discuss proportional dividends, taxes, or other market frictions.

Key ideas

  • A cash dividend reduces the modeled stock price at the payment node.
  • Build subsequent branches from the post-dividend stock price.
  • The dividend changes the price tree used to construct the replicating portfolio.
  • The note does not provide a full derivation of the replication strategy.

Tags

OptionsDerivatives pricing
Full text
# Replication (binomial tree)


# Replication (binomial tree)












Hey what is the replication strategy on the binomial tree when I have for example 10 step model and dividend is paid at step 3? I have a well-written price tree but I do not know what the replication strategy looks like because the price is not the same as in the case of using the martingale valuation. How does this one dividend impact replication strategy?

## Answer by piterbarg (score 3, accepted)

https://quant.stackexchange.com/a/59554

When the dividend is paid, the stock price on your tree should drop by the same amount. Ie if the dividend is 10 and the value of stock is 100 before the dividend at a node, you should change it to 90 and then continue building the tree from there. A cursory google brings quite a few results, eg this around slide 46 seems to explain it well

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