Pricing of forward contracts - Arbitrage-free pricing Exercise 1 An investor may
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Pricing of forward contracts - Arbitrage-free pricing Exercise 1 An investor may buy a bushel of corn for $500 today or may engage in a respective forward contract with a maturity of 3 months (1/4 year). Assume that the risk-free interest rate is at 5%. Further assume that costs of carry are at 2% and the convenience yield is (A) at 3% and (B) at 990. - Calculate the forward-price for each of the two scenarios (A) and (B) and interpret the different results! . Scenario A: F(T) S e Scenario B: F(T) = S * e(r+c-y)-T .Explanation / Answer
(A) Current Spot Price = $ 500, Risk-Free Rate = r = 5 %, Cost of Carry = c = 2 % and Convenience Yield = y = 3 %, Time to maturity = 3 months or 0.25 years
F(T) = 500 x EXP[0.05 + 0.02 - 0.03] x 0.25 = $ 505.025
(B) Current Spot Price = $ 500, Risk-Free Rate = r = 5 %, Cost of Carry = c = 2 % and Convenience Yield = y = 9 %, Time to maturity = 3 months or 0.25 years
F(T) = 500 x EXP[0.05 + 0.02 - 0.09] x 0.25 = $ 497.506
Convenience Yield is the premium or value of benefit associated with possessing an asset rather than the derivatives on the asset. The forward contract pricing for the same asset needs to account for the convenience yield. The price of the forward contract is paid to the seller of the contract who also holds the asset, thereby enjoying convenience yield. Hence, the forward contract seller's receipt of the forward price will need to be adjusted downward by an amount equal to the convenience yield. In case (A) the convenience yield is less than the opportunity cost of the risk-free rate and the cost of carrying because of which the forward price is greater than the current spot price. The opposite is true in case (B) because of which the forward price is less than the current spot price.
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