股票遠期價格計算
在約翰赫爾的書中，支付股息股票的股票遠期價格公式為：
$$ F_0 = (S_0 - I)e^{rT} $$ where [Math Processing Error] $ r $ is the risk free rate and [Math Processing Error] $ I $ is present value of the stream of dividend payments over the life of the forward. In practice, what is the risk-free rate used for forward contracts? Would the correct rate to use be the repo rate or OIS rate? Furthermore, are dividends discounted using the same rate?
There is no real “risk-free” rate.
Now to answer your question, [Math Processing Error] $ r $ is time-dependent and should correspond to the repo rate corresponding to the maturity of your forward. In [Math Processing Error] $ I $ , dividends should be “discounted” using the same time-dependent repo rate. Contrary to what others have suggested here, the use of an OIS rate or some other rate is not appropriate, otherwise arbitrage is possible.
Each dividend may not be discounted at the same rate, but the discounting will correspond to an interpolation of the equity repo rates.
As @ilovevolatility mentioned, the logic behind what I describe above is proved in Piterbarg paper Funding Beyond Discounting published in Risk Magazine, really a must read paper on the subject.
Finally, the price of an equity forward is an ambiguous terminology. What Hull refers to is the forward price. In reality, the NPV for an equity forward will include a strike price and an additional discounting, typically using OIS rate [Math Processing Error] $ r_c $ :
[Math Processing Error] $ NPV = e^{-r_c (T-t)}\left(e^{r (T-t)}(S(t)-I) - K \right) $