Question

You are examining the corn market on July 1. The spot price is $3.80 per bushel and the September futures price is $4.55 per bushel. Delivery on the corn futures contract begins on September 1. You have access to a corn storage facility and you can store corn at a cost of $0.25 per bushel per month (payable at the beginning of each month). The one-month LIBOR rate is 2.50% and the two-month LIBOR rate is 2.6% (continuous compounding, expressed as annual rate). Is there an arbitrage opportunity? What are the cash flows generated by the arbitrage strategy?

Answer 1

Answer ) Spot Price (S) = $ 3.80 at 1 July and future contract till September i.e for 3 months

Future price(F) , is based on the concept of cost and carry model. with cost of storage(C) paid at start of month and interest rate is continuous compounding.

here, value of Interest rate (r) 2.50% for first month and 2.60% for next two months

r1 = 2.50%/12 , t1= 1 month

r2 = 2.60%/12 , t2= 2 month

F = (3.80+0.25)* e ^ ( 0.0021+0.0043)

F = 4.05 * 1.00645 = $ 4.0761 ---------(1)

Calculated F in Eq(1) is less than actual Future price $ 4.55

Support existence of arbitrage,

Cash flow from arbitrage = $ 4.0761 - $4.55 = ($ 0.474)