Environmental Engineering Reference
In-Depth Information
The convenience yield may be nonconstant, may be a deterministic function dðtÞ
or
may even be modeled as another stochastic process. 6
In the case of mean reverting model 1 (Inhomogeneous Geometric Brownian
Motion (IGBM) 7 ) the drift is:
kðS m S t ÞkS t ¼ ðr dðtÞÞS t
ð 5 Þ
so the convenience yield is variable:
kS m
S t
dðtÞ ¼ ðk þ k þ rÞ
ð 6 Þ
:
is high the convenience yield is also high. 8
In this case when the current price S t
appears can be found in the availability of
stocks and inventories of the commodity in question. Everyone who owns inventory
has the choice between consumption today and investment for the future. Rational
investors will choose the outcome that is best for themselves.
When inventories are high, this suggests an expected relatively low scarcity of
the commodity today as compared to some time in the future. Otherwise investors
would see no bene
One of the main reasons that dðtÞ
t in holding onto inventory and would therefore sell their
stocks. Hence, expected future prices should be higher than current prices. Futures
or forward prices Fðt ;
of the asset should thus be higher than the current spot
price, S t . It is known that
kS m
k þ k
Fðt ; ¼
ð 7 Þ
F ð t ;
S t
r dðtÞ ¼ ðk þ kÞ
1
ð 8 Þ
:
0.
The line of reasoning becomes interesting when inventories are low, in which
case scarcity can be expected to be greater now than in the future. Unlike the
previous case, the investor cannot buy inventory to make up for demand today. In a
sense, the investor wants to borrow inventory from the future but is unable to do so.
Therefore future prices can be expected to be lower than today
The above formula only reveals that r dðtÞ [
'
s prices and hence
Fðt ; \ S t . This implies that r dðtÞ \
0.
Consequently, the convenience yield is inversely related to inventory levels.
6
See the second model in [ 26 ].
7
The characteristics of this stochastic model are analyzed in [ 24 ].
8
For the case of S m ¼
0 with a ¼ k the IGBM becomes GBM and d is constant:
d ¼ ðk a þ rÞ .
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