What do Future price and Forward price represent

Question

In Shreve's Finance and Stochastic calculus, definitions are:

Forward Price: The $T$-forward price $For_S(t,T)$ of this asset at time $t$, where $0\leq t\leq T$, is the value of $K$ that makes the forward contract have no-arbitrage price zero at time $t$. ($K$ is the striking price)

Futures price: The futures price of an asset whose value at time $T$ is $S(T)$ is \begin{align*} Fut_S(t,T)=E(S(T)|\mathcal{F}(t)) \end{align*}

They seem to be different from the price of an asset derivative, which satisfy the formula: \begin{align*} V(t)= \frac{1}{D(t)}E(D(T)V(T)|\mathcal{F}(t)) \end{align*} where $V(T)$ is the pay-off. (Where $D(t)$ is the discount process)

So my question is: What do these two concepts really mean? Does anyone have any comments?

Thanks in advance!

Answer 1

Is there any particular reason you are looking at Shreve? Euan Sinclair for example mentions in all his books that "Traders really do not need to know stochastic calculus or to be able to rigorously derive a pricing model." I am not trying to discourage you from looking at stochastic calculus. However, I think getting the basics in finance right is more important than anything else.

Forwards are agreements to buy/sell an asset at a certain time in the future for a certain price. Main difference to futures is that forwards are OTC, and futures exchange traded. As long as the maturities are the same, forward and future prices will be very close. You can find a very basic and good introduction in Hull.