Spot, Forward, Futures, and Prepaid Forward Prices on a Stock
Summary
The document distinguishes three ways of pricing stock exposure: buying the stock now, agreeing to pay later through a forward or futures contract, and paying now for delivery of the stock at a future date through a prepaid forward. Under the stated assumptions, the deferred-payment contract price reflects financing and dividends, while the prepaid amount discounts that contract price back to today. This makes the prepaid forward’s value equal to the spot price in the simplified setup.
The explanation is intended to clear up ambiguous wording in an actuarial finance problem, especially the use of “prepaid forward price.” It provides the standard cost-of-carry relationship with a continuous interest rate and dividend yield, but does not discuss contract-specific details such as margining, daily futures settlement, discrete dividends, or other market frictions. Its conclusion therefore applies to the model assumptions presented, rather than establishing that every real futures and forward contract has identical pricing.
Key ideas
- Buying a stock outright requires paying its spot price immediately.
- A forward or futures contract defers payment to delivery and its price reflects financing and dividends.
- A prepaid forward requires payment now for stock delivered later.
- Under the stated continuous-rate and dividend-yield assumptions, the prepaid forward price equals spot.
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Full text
# How does this statement about the price of a prepaid forward on a stock follow?
# How does this statement about the price of a prepaid forward on a stock follow?
I am self-studying for an actuarial exam on financial economics. This statement in the following problem/solution seems to imply that the prepaid forward price on a stock is the same as the prepaid forward price on a futures contract for the stock, or $F_{0, T}^P(S) = F_{0, T}^P(\text{Future}(S))$. (Not sure if this is correct notation).
So why does the second statement underlined in red follow from the first statement?
## Answer by nbbo2 (score 3, accepted)
https://quant.stackexchange.com/a/27820
It is a very badly worded question in my humble opinion.
There are three "prices" to contend with.
(1) If you want to buy a stock and pay for it now, you pay the current stock price S.
(2) If you want to buy a stock and not have to pay for it until a future delivery date T, then you enter into a "forward" or (in the United States) a "futures contract" which specifies a price F, with $F=S e^{(r-d)T}$. No money is due when you enter into this contract.
(3) There is also an odd thing called a "prepaid forward" which is not much used except to get around tax and other regulations, in which you pay now the sum P in order to get the the stock later. This is priced at $P=F e^{-(r-d)T}$. Perhaps not surprisingly we have $P=S$ since you have to pay now, just like when buying the stock outright.
So there are only two prices for a stock: one if you want to pay now, and a slightly higher one (due to the time value of money) if you want to pay later.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.