a. In a well-functioning market without transaction costs, the price of a 3-year forward on oil can be determined using the zero-coupon bond prices and the oil swap prices. The price of a 3-year forward on oil can be calculated by discounting the expected future spot prices back to present value using the zero-coupon bond prices.

For Year 1, the price of the oil swap is $42. For Year 2, it's $42.5, and for Year 3, it's $43. To find the present value of the oil swap prices, we would multiply each year's oil swap price by the corresponding zero-coupon bond price and then sum these discounted values:

Year 1: $42 * 0.9895 = $41.578 Year 2: $42.5 * 0.9856 = $41.86 Year 3: $43 * 0.9782 = $42.12

Adding these up, the theoretical price of the 3-year forward on oil would be $41.578 + $41.86 + $42.12 = $125.558. This is the price at which James should enter into the 3-year forward contract.

Given his belief that oil prices will be high in three years, James should go long the 3-year forward contract, expecting the price of oil to be higher than the forward contract price when it matures.

b. One year later, the market value of the forward position would be calculated using the updated market information.

Year 1: $42.2 * 0.9808 = $41.556 Year 2: $42.8 * 0.9750 = $41.64

The new market value of the forward position after one year would be $41.556 + $41.64 = $83.196. This is the current market value of James' forward position. Since he initially expected high oil prices, he might have taken a long position in the forward contract, so if the oil price is indeed increasing, his position would currently be worth more than when he first entered the contract.