Delta Hedging Asian Options in a Binomial Tree

Summary

The document explains how to adapt the usual one-step binomial delta hedge for an Asian option. Between averaging dates, the hedge uses the standard comparison of option value across the up and down stock-price branches, provided the average state is held fixed. The tree needs an additional state dimension to track the running average, since the option’s value depends on both the underlying price and the average accumulated so far.

At an averaging date, the hedge must account for how the newly fixed price changes that average state. This requires comparing option values across average levels as well as considering stock-price moves. The explanation is conceptual and does not provide a full pricing recursion or numerical example. The precise implementation depends on the averaging convention and frequency, which must be specified to construct the tree and calculate the hedge.

Key ideas

• An Asian option’s binomial tree must track the average as an additional state variable.
• Between averaging dates, the ordinary up-versus-down delta applies while holding the average state fixed.
• At a fixing date, the hedge must account for the change in the average caused by the new fixing.
• The averaging type and frequency must be defined before constructing the tree.

Tags

# Delta hedging of binomial Asian options


# Delta hedging of binomial Asian options












The expression of $\Delta$ hedge for a binomial European option is

$$ \Delta_t = \frac{C^u_{t+1}-C^d_{t+1}}{S^u_{t+1}-S^d_{t+1}} $$

What is the expression of the $\Delta$ hedge for a binomial Asian option?

## Answer by Andrea (score 1)

https://quant.stackexchange.com/a/81090

Basically the same.

But, you will have to define exactly the type of averaging, in particular the frequency. And the binomial tree will acquire another dimension (the average).

So, in between averaging dates, the formula is exactly the same one (staying on the same level of the 2nd dimension).

Exactly on an averaging date, it will become more sophisticated, but exactly like any other derivative with fixings. You will have a question like

"how will my delta change if the Asian fixed right now at this level"

Which requires a (delta) (i.e. difference) across values of the 2nd dimension.

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