[金融市場與衍生性商品] Lecture5 Determination of Commodity Forward and Futures Prices

Forward prices = Net cost of carry + Spot prices - Convenience yield

Convenience yield 便利殖利率

Some holders of a commodity's receive benefits from physical ownership (e.g., a commercial user).

The convenience yield creates different returns to ownership for different investors, and may or may not be reflected in the forward price.

The convenience yield is always positive or zero.

Ex. 假設一個蛋糕店的老闆，蛋的價值就相對家庭主婦來得高，為了未來蛋的來源穩定，會提供比較高的價格購買，這多出來的價值就是convenience yield。

Commodity Futures Price and the Current Spot Price

Let S be the current price of the asset.

U is the present value of the storage costs.

Y is the present value of the convenience yield.

F(0, T) = (S0+U-Y)*exp(rT)

Let S be the current price of the asset.

u is the storage cost per unit time as a percent of the asset value.

y is the convenience yield per unit on the consumption asset.

F(0, T) = S0*exp[(r+u-y)T]

The cost of carry, c, is (1) the physical storage cost u plus (2) the interest rate r

F(0, T) = S0*exp[(c-y)T]

The convenience yield on the consumption asset, y, is defined so that

F(0, T) = S0*exp[(c-y)T].

Futures Prices & Expected Future Spot Prices

Synthetic Commodities

1. Long forward

2. Lend out

Hence, F(0, T)*exp(-rT)=S_0

Suppose k is the expected return required by investors on an asset and S_T is the value of a unit of the commodity at time T.

E_0(S_T)=S_0*exp(kT)

=> F(0, T)=E_0(S_T)*exp[(r-k)T]

And k>r, since k is risky rate.