Chapter 37: Swaps
Commodity swaps: fixed price of swap is weighted average of corresponding forward prices.
n
P 0,tiF 0it
F i1
n
P 0,t i
i1
n
Q t 0,t Fi 0,t
i1 i i
With varying quantities: F n
Q P 0,t
i1 i i
For summer and winter varying:
F s P 0,t Q F w P 0,t Q P 0,t Q F P 0,t Q F
isummer i i iwint er i ti isummer i ti 0,tiiwint er i ti 0,ti
Because fixed swap payment equal, while the futures prices vary, the mismatch creates a
borrowing/lending component.
rT
F 0,T S 0
Synthetic commodity: long forward plus zero coupon bond w/ face value equal to forward price
Link b/w expected commodity price and forward price: F E S e rT
0,T 0 T
Nonstorability: Electricity:
different prices in summer and winter and in night and day
Commodity Lease Rate:
1
l r T ln F0,T S
Cash and carry arbitrage: borrow cash, buy commodity, lend commodity and short
forward
Reverse cash and carry arbitrage: short commodity, lend cash, long forward
Contango occurs when lease rate is less than risk-free rate;
Backwardation occurs when lease rate is greater than risk-free rate
Carry: storage
Forward price with storage costs (like negative dividend; applies only when storage
rT
occurs): F 0,T S0e
rcT
Forward price factoring in convenience yield: F0,T S 0 o Those who earn convenience yield likely already hold optimal amount of
commodity; there may be no way for you to earn convenience yield when
per

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