问题如下：
Donald Troubadour is a derivatives trader for Southern Shores Investments. The firm seeks arbitrage opportunities in the forward and futures markets using the carry arbitrage model.
Troubadour identifies an arbitrage opportunity relating to a fixed-income futures contract and its underlying bond. Current data on the futures contract and underlying bond are presented in Exhibit 1. The current annual compounded risk-free rate is 0.30%.
Exhibit 1 Current Data for Futures and Underlying Bond
contract
Troubadour next gathers information on three existing positions.
Position 1 (Nikkei 225 Futures Contract):
Troubadour holds a long position in a Nikkei 225 futures contract that has a remaining maturity of three months. The continuously compounded dividend yield on the Nikkei 225 Stock Index is 1.1%, and the current stock index level is 16,080. The continuously compounded annual interest rate is 0.2996%.
Position 2 (Euro-JGB Forward Contract):
One month ago, Troubadour took long position in Euro-Japanese government bond （JGB）forward contracts with three months to expiration at a quoted price of 100.20 (quoted as a percentage of par). The contract notional amount is ¥100,000,000. The current forward price is 100.05.and the current annualized risk-free rate is 0.3%.
Position 3 (JPY/USD Currency Forward Contract):
Troubadour holds a short position in a yen/US dollar forward contract with a notional value of $1,000,000. At contract initiation, the forward rate was ¥112.10 per $1. The forward contract expires in three months. The current spot exchange rate is ¥112.00 per $1, and the annually compounded risk free rates are -0.20% for the yen and 0.30% for the US dollar. The current quoted price of the forward contract is equal to the no-arbitrage price.
Troubadour next considers an equity forward contract for Texas Steel, Inc. (TSI). Information regarding TSI common shares and a TSI equity forward contract is presented in Exhibit 2.
Exhibit 2 Selected Information for TSI
The price per share of TSI’s common shares is $250.
The forward price per share for a nine-month TSI equity forward contract is $250.562289.
Assume annual compounding.
Troubadour takes a short position in the TSI equity forward contract. His supervisor asks, "Under which scenario would our position experience a loss?"
Three months after contract initiation, Troubadour gathers information on TSI and the risk-free rate, which is presented in Exhibit 3.
Exhibit 3 Selected Data on TSI and the Risk-Free Rate
The price per share of TSI’s common shares is $245.
The risk-free rate is 0.325% (quoted on an annual compounding basis).
TSI recently announced its regular semiannual dividend of $1.50 per share that will be paid exactly three months before contract expiration.
The market price of the TSI equity forward contract is equal to the no-arbitrage forward price.
4. The value of Position 3 is closest to:
选项：
A.-¥40,020.
B.¥139,913.
C.¥239,963.
解释：
C is correct.
The current no-arbitrage price of the forward contract is
Ft(¥/$,T) = St(¥/$)FV¥,t,T(1)/FV$,t,T(1)
Ft(¥/$,T) = ¥112.00(1 - 0.002)0.25/(1 + 0.003)0.25 = ¥111.8602
Therefore, the value of Troubadour’s position in the ¥/$ forward contract, on a per dollar basis, is
Vt(T) = PV¥,t,T[F0(¥/$,T) - Ft(¥/$,T)]
=(112.10 - 111.8602)/(1 - 0.002)025 = ¥0.239963 per $1
Troubadour’s position is a short position of $1,000,000, so the short position has a positive value of (¥0.239963/$) x $1,000,000 = ¥239,963 because the forward rate has fallen since the contract initiation.
老师您好，FRA不是应该单利折现的么？
