Delivery in Futures Markets - Relationship between futures price and time to maturity

[Bruno]

Hi David,

I don't see the relationship between time to maturity and futures prices (page 24)


If the futures price is an increasing function of time to maturity, the short should deliver as early as possible. (And for modeling purposes, here we assume delivery at beginning of period.)

If the futures price is a decreasing function of time to maturity, the short should deliver as late as possible. (And for modeling purposes, here we assume delivery at end of period.)


Why should the short deliver as early as possible when the futures price is an increasing function of time to maturity and viceversa? Would you please elaborate a little bit more on this arguments?

Is this directly related to the cost of carry model? Is Fo an increasing function of time to maturity (T) as long as (r + u) > (q + y) ?.

kind regards,

 

[David Harper CFA FRM]

Hi Bruno,

Yes, this is merely a modeling assumption that follows directly from Hull's setup on the cost of carry. The short wants to maximize his/her profit (delivery price - any costs). The delivery price is given, so the short wants to minimize the cost of carrying the asset.

If forward curve is upward sloping (contango), then holding the asset is costly (e.g., storage costs), so, given the delivery price is fixed, the short wants to get rid of the asset ASAP as holding the asset implies more cost over time (e.g., storage fee, financing)

If forward curve is plunging (backwardation), then holding the asset is profitable (e.g., high convenience), so, given fixed delivery, short wants to hold on as long as possible as holding implies gains over time (e.g., income, convenience)

Hope that helps, David