Think about options on futures contracts and their premiums, and specifically about intrinsic value and time value.

a$.$ How does the intrinsic value for puts and calls change as the underlying futures price changes?

b$.$ How does the intrinsic value for puts and calls change as the option contract approaches its expiration day?

c$.$ How does the time value for puts and calls change as the underlying futures price changes?

d$.$ How does the time value for puts and calls change as the option contract approaches its expiration day?

e$.$ Today a put on the soybean futures contract for January delivery with strike $$10\mathrm{.}90/$bu is trading at $$0\mathrm{.}37/$bu $($premium$).$ Knowing that the futures price for January delivery is now $$10\mathrm{.}59/$bu$,$ what should happen with the premium of this put if the underlying futures contract keeps going up until its expiration? Make sure to explain what should happen to both intrinsic and time value.

f$.$ Today a put on the corn futures contract for March delivery with strike $$4\mathrm{.}60/$bu is trading at $$0\mathrm{.}11/$bu $($premium$).$ Knowing that the futures price for March delivery is now $$4\mathrm{.}66/$bu$,$ what should happen with the premium of this put if the underlying futures contract starts going down until its expiration? Make sure to explain what should happen to both intrinsic and time value.