Modeling American Calls with Moving-Average Lookback Features

Summary

The document describes a proposed tree-based approach for valuing an American call with two possible exercise references: a fixed strike and a floating strike tied to a 10-day moving average. The proposed model tracks both the underlying price and the moving average, then uses backward induction to compare the available exercise payoff with continuation value at each node. The author reports that the resulting deep-in-the-money deltas seem unexpectedly low and asks how to model the contract correctly.

No answer or valuation evidence is included, so the proposed method is not validated and the source of the unusual deltas remains unresolved. A key modeling challenge is that the moving average depends on the path of past prices; tracking only the current stock price and a single average may not preserve enough information to update the average correctly, depending on the precise averaging convention and tree construction. The document also leaves the exercise payoff definition and contract terms open to interpretation, so its suggested maximum-payoff rule should not be treated as an established model.

Key ideas

• The proposed valuation tracks the underlying price and a moving average in a tree model.
• Backward induction compares immediate exercise value with continuation value at each node.
• A moving-average feature depends on price history, which can complicate the state representation.
• The reported low deep-in-the-money delta is unexplained because the document contains no response or validation.

Tags

# Exotic options with lookback features


# Exotic options with lookback features












I am trying to value an american call option with a lookback feature. So the holder can choose to exercise either based on a fixed strike (K) or a floating strike equal to 10-day moving average (MA). I tried to build a tree model but results look weird and I couldn't figure out where the problem is. What I did is to construct trees for stock price (S) and 10-day moving average price, and then using backward induction to compare the exercise value vs. the continuation value at each node (ie. max(max(0, S-K, MA-K), continuation value)). It sounds pretty intuitive but I keep getting really low delta (like 0.6) for deep in the money options. Anyone came cross the same instruments and happen to have a good idea how to model it?

Thanks!

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