Why American Option Values Require Early-Exercise Models

Summary

The document addresses how to value American options on SPY when dividends are present. It challenges the proposed shortcut of taking the maximum of two European option values, one tied to the ex-dividend date and one to final expiry. An American option can be exercised at other times as well, and early exercise may be optimal when the value of receiving the underlying sooner outweighs the remaining option value under the relevant rates and dividends.

The response says the shortcut may provide a lower bound, but is not a general valuation method. It identifies numerical approaches such as the binomial method as typical tools for valuing American options, and notes that European options with complicated dividend streams can also require numerical methods. The post does not specify the commercial calculator’s model or provide a recipe for calculating its Greeks, so it offers a conceptual correction rather than a replication procedure.

Key ideas

• An American option may be exercised at multiple times before expiry, not only at an ex-dividend date.
• Taking the maximum of two European option values is not a general American option valuation method.
• Early exercise can be optimal when interest rates, dividends, and remaining time value make it worthwhile.
• Numerical methods such as binomial trees are commonly used for American option valuation.

Tags

# SPY American option Greeks and Premium


# SPY American option Greeks and Premium












I am trying to replicate Ivolatility.com's option calculator for a client. Here's the example

Using standard Black Scholes model, I can replicate the exact calculations if there is no dividend. With dividend, I understand I need to subtract PV of div from current underlying price to get the adjusted underlying price to be used in standard B-S model. My questions are

1) does everything else in calculating d1, greeks and premium remain the same? or do we still need the dividend yield (even after calculating adjusted underlying price) for calculating the above parameters?

2) I understand the price of an American option is max of two european options calculated for different maturities, i.e ex dividend date and actual maturity. Can you please clarify?

Also, is it possible to know which model Ivolatility is using?

## Answer by BEZ (score 2)

https://quant.stackexchange.com/a/34452

From what authority do you understand that the value of an American option is the max of two Europeans? I believe this is a false assumption (but it might give you a lower bound value). E.g. a deep-in-the-money American option might be optimally exercisable before the ex-div date, to capture the time value of money for some interest rates vs. dividends. American option values are typically solved by numerical techniques (such as the binomial method). Ditto European options having complex dividend streams. --BEZ

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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