Hi, I have a problem getting my head around the following pricing problem.
I want to price equity forward. I want to take into account the possibility of lending the stock in the replication portfolio. This is not an issue in case of no dividends as i just end up with S(t) * exp(stockLendingRate*tau). Similarly, the classical case of dividends which are accrued from payment date at risk free rate is also not a problem. However, i have a problem building replication portfolio (assuming dividends and dividend timing being deterministic) which would give me a pricing formula. Has anyone encountered this problem before?
So the question for a case of single dividend at t_k would be:
Fwd = S(t) * exp (stockLendingRate*(T-t) - Div(t_k) * exp(stockLendingRate*(T-t_k)) OR
Fwd = S(t) * exp (stockLendingRate*(T-t) - Div(t_k) * exp(OIS*(T-t_k))
and why (arbitrage argument?)

Have a look at attached short article by BNP Paribas, which I think answers your question and discusses the importance of (implied) repo rates.

take a look at the paper on dividend modeling from here
https://www.voladynamics.com/research.html