Forward Pricing for a Dividend-Paying ETF Without Short Selling

Summary

The document raises a forward-pricing problem for options on an ETF that cannot be shorted and pays a single annual dividend. The author is fitting an implied-volatility curve and finds that the nearby future trades below spot, while the options imply a forward above spot. An attempt to infer dividend yield from the implied forward produces unstable intraday values, including both positive and negative estimates. The question asks how to handle a discrete dividend and the no-borrow constraint so call and put implied volatilities align more closely.

It gives a pricing relation based on the risk-free rate, the spot-to-forward ratio, and time to maturity, along with example market prices for the future, ETF, and option-implied forward. However, it contains no answer or derivation that resolves the mismatch. It does not specify the dividend amount or timing, financing inputs, or the precise futures and option maturities beyond their relative dates. Those missing inputs limit what can be concluded about the correct forward price.

Key ideas

• The question concerns options on an ETF with a discrete annual dividend and a ban on short selling.
• The nearby future is below spot, while the option-implied forward is above spot.
• Inferring dividend yield from the forward appears unstable during the trading day.
• The document supplies a pricing relation and example prices but no solution to the forward-pricing problem.
• Dividend timing and amount, financing assumptions, and maturity details are needed to assess the discrepancy.

Tags

# Forward spot calculation for a dividend paying no-short sell ETF


# Forward spot calculation for a dividend paying no-short sell ETF












I am trying to fit an implied volatility curve for options on the SSE 50 etf that has no borrow (no short selling allowed) and pays a single annual dividend. I originally thought I could use the future price (maturity is 5 days before the option with the same etf underlying) but the curve does not fit since the futures are in backwardation and the implied forward price from the options is higher than the etf spot. I do not know what the expected dividend yield is which is why I tried to calculate them from the forward- intraday it seems to vary a lot (positive and negative) based on the option implied forward.

future px = 2.5903

etf spot = 2.6329

option implied forward = 2.6574

I'm using the following equation:

d = r - ln(F/S) / tau

How should I be calculating the forward spot for a discrete dividend no borrow stock so that my put and call vol are somewhat aligned?

Thank you.

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