Early Exercise Decisions for Dividend-Paying American Options

Summary

The document presents an early-exercise question for American call and put options on a dividend-paying stock. It specifies a nine-month term, two scheduled dividends, a strike, a continuously compounded risk-free rate, a current stock price, and quoted option prices. It then states that the call should be exercised at the second dividend and that the put should not be exercised before the first dividend payment, and asks how to derive those conclusions.

The case raises the key issue that dividends can make early exercise of an American call worth considering, while puts involve a trade-off between receiving intrinsic value sooner and retaining the option’s time value. However, no derivation, valuation method, or comparison of continuation and exercise values is included. The stated recommendations therefore cannot be checked from the document alone; a proper decision would require evaluating exercise at relevant dates and accounting for dividend timing, rates, and option value.

Key ideas

• Dividend timing can affect whether early exercise of an American call is optimal.
• The example asks readers to assess both call and put exercise decisions over the option’s life.
• The document states exercise recommendations but supplies no supporting calculation.
• A defensible answer requires comparing immediate exercise value with the value of continuing to hold the option.

Tags

# What is the optimal time for exercising American call and put option?


# What is the optimal time for exercising American call and put option?












A `9 month` American option (underlying) is known to pay dividend of `USD 1 and USD 0.75` at the end of the `3rd and the 07th` month respectively. The `strike price` considered is `USD 45`. The `Risk Free Rate` is continuously compounded and is fixed at `6%` over the tenure. The `stock` is currently trading at `42`. The `put` options are trading at `USD 7.5` and the `call` options at `USD 4.0`. What would be the optimum time to exercise the call and put option based on the information given above?

The answers for the above questions are :-

a) The American call option should be bought and exercised at the second dividend.

b) The American Put option should be bought, but should not be exercised before the first dividend payoff.

How to arrive at this solution?

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