# Dividend price with respect to American Call Option and European Call Option

#### arupsarkar

Hi:

For a non-dividend paying stock the American Call option is equal to the European call option. For a dividend paying stock depending on the value of the dividend at times T or t, the price of the option is greater of the european or american call option.

My question is how to identify the price of the dividend so that the American call option will be less than or equal to Europen call option?

Thanks

#### Muting

Hi:

For a non-dividend paying stock the American Call option is equal to the European call option. For a dividend paying stock depending on the value of the dividend at times T or t, the price of the option is greater of the european or american call option.

My question is how to identify the price of the dividend so that the American call option will be less than or equal to Europen call option?

Thanks

Hi,

The value of American call option cannot be less than european option. When there is dividend, as long as it is worth early excercise(There is a formula in Hull identifying the situation), the american option has more value than european because it can excercise immediately before ex-dividend date.

#### pardasani

on a related but different topic: there seems very little literature on "dividend risk": to price a future (or an option) the future dividend payouts must be known which may not be the case (specially in a market like this one, where big firms are facing trouble with their dividend policy)

For e.g. the price of an index futures (say 1 yr S&P 500 futures) depends on what dividends would the securities (500 stock names in this case) pay out in the coming 1 yr. If the dividends that were actually paid out differ from what we assume: we would lose/gain money... Moreover the PnL would be almost linear with respect to the error in dividend estimation. For eg a 10 bps error in estimating ~2% dividend yield (approximately 5% error) can lead to a 10 bps loss (which may be huge since you need to multiply it with the notiona: a typical equity swap for eg would have atleast a 10mil\$ notional).

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