Estimating Implied Dividends from Futures and Options

# Implied dividend estimation


# Implied dividend estimation












I am looking at two different ways of estimating the expected / implied dividends from market data.

#### 1. Dividend futures

I know that this asset class is not very liquid and might not be representative enough. However, assuming that I have prices which are good enough, how could I estimate the implied divided from the contract price?

For instance, if I have an exchange traded contract whose settlement is the sum of actual dividends paid during 2013, could I just take the current contract price and capitalize it up to the settlement date in order to obtain the implied dividend for 2013?

EDIT: Example added for illustration purposes:

On 05 july 2013, the quoted prices for Santander Dividend Futures are:

- 2013 contract; Maturity 20 Dec 2013; Price: 0.58

- 2014 contract; Maturity 19 Dec 2014; Price: 0.41

- 2015 contract; Maturity 18 Dec 2015; Price: 0.32

For simplicity assume that:

- Each contract is linked to the sum of all dividends paid during the corresponding calendar year.

- Appropriate risk free rates for each contract are: 0,1%; 0,3%; 0,5%.

If I want to estimate the total amount of implied dividends for each year, could these figures be obtained as:

$$ D_{2013}=0.58e^{(0,001*0.46)}=0.5802 $$ $$ D_{2014}=0.41e^{(0,003*1.46)}=0.4118 $$ $$ D_{2015}=0.32e^{(0,005*2.45)}=0.3240 $$ Or am I missing something?

#### 2. Index / single-stock futures

Alternatively, if I wanted to estimate the dividend yield for a stock, what are the limitations of calculating the implied yield directly from the market prices as:

$$ F=S_0e^{(r-q)T} \; \; \; \; \; \Rightarrow \; \; \; \; \; q = \frac{rT-\ln{\frac{F}{S_0}}}{T} $$

I guess there must be certain shortcomings with this aprroach, since usually the synthetic forward is obtained through the put-call parity instead of using the futures prices.

Thanks in advance!

## Answer by Eli (score 8)

https://quant.stackexchange.com/a/7843

You could compute index dividend yield from ATM options using linearized put-call parity (assuming index options are European.)

The present value of the dividend payment is: $PV(div) = P - C + (S - K) + K(e^{rT} - 1)$

where $r$ is interest rate to the option expiration and $T$ is time to maturity in years. Then the implied dividend is:

$d = \frac{PV(div)}{T*S}$

I realize it's not a complete answer, but it's a starting point. Note: whether using futures or options, the implied dividend value would represent the portion paid until the contract expiry.