# range of non-arbitrage futures prices

So*e^(Rf+storage costs - convenience yield)*T <=F0,T <= So*e^(Rf+storage costs)*T In this range of non-artitrage futures price, why is lease rate not a component? I would think below range looks right theoretically? Anythoughts? So*e^(Rf+storage costs - convenience yield - lease rate )*T <=F0,T <= So*e^(Rf+storage costs)*T

I think that lease rate is incoporated in convenience yield. Am I right ?

AMC Wrote: ------------------------------------------------------- > I think that lease rate is incoporated in > convenience yield. Am I right ? nope. they are different things. I’ve seen questions that give you both lease rate and convenience yield and ask you to come up with the lower range of non-arbitrage futures price.

happyking02 Wrote: ------------------------------------------------------- > So*e^(Rf+storage costs - convenience yield)*T > <=F0,T <= So*e^(Rf+storage costs)*T > > In this range of non-artitrage futures price, why > is lease rate not a component? I would think below > range looks right theoretically? Anythoughts? > > So*e^(Rf+storage costs - convenience yield - lease > rate )*T <=F0,T <= So*e^(Rf+storage costs)*T happyking02 First I don’t have the answer for not including lease rate. I think this is a very sensible question and hopefully someone can help to answer. On the other hand, regarding your theoretical formula, I think you also need to subtract lease rate from upper bound furtures price when including it in the lower bound price?

Storage cost = negative lease Convenience yield = positive lease. I.e. Storage cost and Convenience yield are both sub components of lease rate.

The above formula already incorporates the lease rate. Lease rate = convenience yield - storage costs. Hence, So*e^(Rf+storage costs - convenience yield)*T <=F0,T <= So*e^(Rf+storage costs)*T can also be written as: So*e^(Rf - lease rate)*T <=F0,T <= So*e^(Rf+storage costs)*T

sparty419 Wrote: ------------------------------------------------------- > The above formula already incorporates the lease > rate. > > Lease rate = convenience yield - storage costs. > > Hence, > > So*e^(Rf+storage costs - convenience yield)*T > <=F0,T <= So*e^(Rf+storage costs)*T > > can also be written as: > > So*e^(Rf - lease rate)*T <=F0,T <= > So*e^(Rf+storage costs)*T Good point. Thanks!

Schweser R38 p72 Q#4. Owner of the commodity decides to lend out the commodity, If the commodity has a continuously compounded yield of ‘c’, what is the lowest forward price? Answer: S * e^(Rfr+storage-c)*T. Although i understood the minimum price formula for the forward, how is lender of commodity related to forward rate? I know it something realted to cash and carry…but how does a lender of commodity creates a cash and carry?

Schweser notes also directly explains this. “The lease rate compensates for the loss of the convenience yield less storage costs, so Lease Rate = Convenience Yield – Storage Cost. Since the convenience yield and storage costs are already incorporated into the lease rate, any combination of the two symbols C and storage cost can’t appear in the exponent of the spot price as the same time with the lease rate.”