a) Assuming a short position in a forward contract, provide a mathematical proof of why the value of a forward contract is zero at initiation, given that the forward price at initiation is simply the natural time value growth of the spot price from initiation till the contract's life?

b) Consider the information below and answer the question that follows:

K = $5 per unit

F0 shortly before maturity = $7 per unit

ST = $5 per unit

Contract size = 1,000 units

As a speculator with a profit motive, what strategy will you follow?

Why is this situation untenable?

c) Why is it optional for an option holder to exercise an option while it is obligatory for an option writer to honor the contract? Why holders of futures contract do not get an option to exercise?

d) What is the relationship between the value of an options contract and the time remaining to maturity? Explain