• 探讨互换运作机制及金融中介在互换市场中的角色：
  • 利率互换 (Interest rate swaps)
  • 货币互换 (Currency swaps)
• 阐释利率互换与货币互换如何转换资产与负债结构
• 探讨作为互换交易理论基础的比较优势理论
• 设计利率互换与货币互换交易结构
• 基于债券组合价格测算利率互换与货币互换的理论价值
• 界定信用（违约）风险并解释其在互换交易中的具体体现

• Discuss the mechanics of swaps and the role of financial intermediaries in swap markets:
  • Interest rate swaps
  • Currency swaps
• Explain how interest rate and currency swaps transform assets and liabilities
• Discuss the comparative advantage argument as rationale for swap transactions
• Design interest rate swaps and currency swaps
• Calculate the value of interest rate and currency swaps in terms of bond prices
• Define credit (default) risk and explain how it relates to swap transactions

25556 金融证券 (FS) – 第 11 讲：利率互换

• 标准普通利率互换 (Plain vanilla swap) 的基本特征
• 违约风险与信用风险暴露 (Default risk & credit exposure)
• 运用互换合约作为风险对冲工具
• 比较优势理论论点 (The comparative advantage argument)
• 互换交易商与做市商的市场角色
• 互换利率的推导与确定
• 运用互换改变现金流风险特征的实际案例演示

25556 Financial Securities (FS) – Lecture 11: Interest Rate Swaps

• Features of a plain vanilla swap
• Default risk and credit exposure
• Using swaps as a hedging instrument
• The comparative advantage argument
• The role of swap dealers and market makers
• Deriving the swap rate
• Demonstration of the use of a swap to alter cash flow profiles

• 利率互换的核心结构特征：
  • 期初不交换本金：名义本金 (Notional principal) 仅作为计算利息收付金额的基准尺度。
  • 利息差额净额结算：在每个结算日，交易双方仅结算并支付浮动利息与固定利息的净差额。
  • 期初设定、期末结算 (Reset in advance, paid in arrears)：浮动利率在每个计息期初锁定，产生的实际现金流在计息期末进行支付。
• 核心经济功能：
  • 将负债 (Liability) 由固定利率转换为浮动利率，或由浮动利率转换为固定利率。
  • 将投资资产 (Asset) 由固定利率转换为浮动利率，反之亦然。
• 历史背景：全球首笔正式互换协议于 1981 年在 IBM 与世界银行 (World Bank) 之间签署生效。

• Key structural features of interest rate swaps:
  • No initial exchange of principal: Notional principal serves only as the scale for calculating interest payments.
  • Netting of interest payments: At each settlement date, only the net interest difference changes hands between counterparties.
  • Reset in advance, paid in arrears: Floating interest rates are fixed at the beginning of each period, with the resulting cash flow paid at the end of the period.
• Core economic functions:
  • Convert a liability from fixed rate to floating rate, or from floating rate to fixed rate.
  • Convert an investment (asset) from fixed rate to floating rate, or vice versa.
• Historical note: The first formal swap was executed in 1981 between IBM and the World Bank.

微软 (Microsoft) 达成互换协议：收取 6 个月 LIBOR，同时按半年支付 5% p.a. 固定利率，期限 3 年，名义本金为 $100M（1亿美元）：

• 支付的固定现金流 = $\mathrm{\$}100\text{M}\times 0.05\times 1/2=\mathrm{\$}2.50\text{M}$
• 当前 6 个月 LIBOR = 4.2%：收到的浮动现金流 = $\mathrm{\$}100\text{M}\times 0.042\times 1/2=\mathrm{\$}2.10\text{M}$
• 6 个月后，6 个月 LIBOR = 4.8%：收到的浮动现金流 = $\mathrm{\$}100\text{M}\times 0.048\times 1/2=\mathrm{\$}2.40\text{M}$

图：见 Hull 教材表 7.1，第 176 页。每期浮动现金流由上一行的 LIBOR 决定。

Microsoft agrees to receive 6-month LIBOR and pay a fixed rate of 5% p.a. semi-annually for 3 years on a notional principal of $100 million:

• Fixed cash flow paid = $\mathrm{\$}100\text{M}\times 0.05\times 1/2=\mathrm{\$}2.50\text{M}$
• Current 6-month LIBOR = 4.2%: floating cash flow received = $\mathrm{\$}100\text{M}\times 0.042\times 1/2=\mathrm{\$}2.10\text{M}$
• In 6 months, 6-month LIBOR = 4.8%: floating cash flow received = $\mathrm{\$}100\text{M}\times 0.048\times 1/2=\mathrm{\$}2.40\text{M}$

Figure: see Table 7.1, page 176 (Hull). Each floating flow is set by the LIBOR of the previous row.

• 金融机构作为互换市场的做市商 (Market Makers)：
  • 市场上两家拥有完全对称相反需求的企业同时找到银行的概率微乎其微。
  • 绝大多数互换是由金融机构先与单方交易对手达成，此时并无立即可对冲的反向头寸——金融机构对该互换风险进行“仓储” (warehouses the swap)。
  • 金融机构通过收取买卖买卖价差或佣金赚取利润（通常为 3–4 个基点，bps）。
• 金融机构对未平仓风险敞口的动态对冲：
  • 市场风险（利率风险）：利用利率期货（如欧洲美元期货或银行承兑汇票期货）、政府国债以及反向互换交易实施动态对冲。
  • 信用（违约）风险：通过要求交易对手缴纳抵押品（信用支持协议 CSA）、签署净额结算协议，以及在信用违约互换 (CDS) 市场买入保护来管理。

• FIs act as Market Makers for swaps:
  • It is very unlikely that two counterparties with exact offsetting needs will approach the bank simultaneously.
  • Most swaps are entered into by the FI with one counterparty without an immediately offsetting position – the FI “warehouses” the swap.
  • The FI charges a bid-ask spread or commission (typically 3–4 basis points).
• The FI must actively hedge its open risk:
  • Market Risk (Interest Rate Risk): Hedged dynamically using interest rate futures (e.g. Eurodollar or bank bill futures), government bonds, and offsetting swap transactions.
  • Credit (Default) Risk: Managed by demanding collateral (credit support annex – CSA), netting agreements, and hedging in credit default swap (CDS) markets.

假定金融中介机构要求收取 3 个基点 (0.03%) 的年度佣金，由交易双方平均分摊，各承担 0.015%：

• 微软 (Microsoft) 向金融机构支付 5.015%（而非 5.000%）：
  微软净借款成本：$(\text{LIBOR}+0.1\mathrm{\%})-\text{LIBOR}+5.015\mathrm{\%}=5.115\mathrm{\%}$（无金融机构时为 5.10%，多付 0.015%）。
• 英特尔 (Intel) 从金融机构收取 4.985%（而非 5.000%）：
  英特尔净借款成本：$5.20\mathrm{\%}-4.985\mathrm{\%}+\text{LIBOR}=\text{LIBOR}+0.215\mathrm{\%}$（无金融机构时为 LIBOR + 0.20%，多付 0.015%）。
• 金融机构银行利润：收取 5.015% • 支付 4.985% • 净利差 = $5.015\mathrm{\%}-4.985\mathrm{\%}=0.030\mathrm{\%}$ (3 bps)。

Suppose the FI requires a 3 basis points (0.03%) annual commission, split equally as 0.015% to each party:

• Microsoft pays the FI 5.015% (instead of 5.000%).
  Net MS borrowing cost: $(\text{LIBOR}+0.1\mathrm{\%})-\text{LIBOR}+5.015\mathrm{\%}=5.115\mathrm{\%}$ (instead of 5.10% without the FI: 0.015% worse off).
• Intel receives 4.985% from the FI (instead of 5.000%).
  Net Intel borrowing cost: $5.20\mathrm{\%}-4.985\mathrm{\%}+\text{LIBOR}=\text{LIBOR}+0.215\mathrm{\%}$ (instead of LIBOR + 0.20% without the FI: 0.015% worse off).
• FI Bank Profit: Receives 5.015% • Pays 4.985% • Net spread = $5.015\mathrm{\%}-4.985\mathrm{\%}=0.030\mathrm{\%}$ (3 bps).

市场向两家公司提供的直接借款利率报价如下：

• 剖析借款利差的显著差异：
  • AAACorp 在固定利率市场借款利率低 1.20%，但在浮动利率市场仅低 0.70%。
  • AAACorp 在固定利率市场具有比较优势。
  • BBBCorp 在浮动利率市场具有比较优势。
• AAACorp 现有一笔固定利率贷款，但希望借入浮动利率资金。
• BBBCorp 现有一笔浮动利率贷款，但希望借入固定利率资金。
• 互换使双方可在各自具有比较优势的市场借款，并转换各自负债的性质：
  • AAACorp 获得相对更优的浮动利率；
  • BBBCorp 获得相对更优的固定利率。

The following borrowing rates are offered to two corporations:

• Notice the spread differential:
  • AAACorp pays 1.20% less in the fixed market, but only 0.70% less in the floating market.
  • AAACorp has a comparative advantage in the FIXED market.
  • BBBCorp has a comparative advantage in the FLOATING market.
• AAACorp has a fixed rate loan but wants to borrow floating.
• BBBCorp has a floating rate loan but wants to borrow fixed.
• A swap allows each party to borrow where it has a comparative advantage and transform the nature of its liability:
  • AAACorp accesses a comparatively better floating rate;
  • BBBCorp gains access to a comparatively better fixed rate.

• 方法 1 – 总体借款成本对比法：
  • 无互换方案：AAA 直接借浮动 (LIBOR − 0.10%) + BBB 直接借固定 (5.20%)
    借款总成本 = $\text{LIBOR}+5.10\mathrm{\%}$。
  • 有互换方案：AAA 直接借固定 (4.00%) + BBB 直接借浮动 (LIBOR + 0.60%)
    借款总成本 = $\text{LIBOR}+4.60\mathrm{\%}$。
  • 互换总收益 (Total Gain)：$(\text{LIBOR}+5.10\mathrm{\%})-(\text{LIBOR}+4.60\mathrm{\%})=0.50\mathrm{\%}$ p.a.。
• 方法 2 – 利差之差法：
  • 固定市场利差：$a=5.20\mathrm{\%}-4.00\mathrm{\%}=1.20\mathrm{\%}$。
  • 浮动市场利差：$b=(\text{LIBOR}+0.60\mathrm{\%})-(\text{LIBOR}-0.10\mathrm{\%})=0.70\mathrm{\%}$。
  • 互换总收益：$a-b=1.20\mathrm{\%}-0.70\mathrm{\%}=0.50\mathrm{\%}$。
• 收益分配机制：
  • 若金融中介机构收取 0.04% 的佣金：
  • 待分配净收益 = $0.50\mathrm{\%}-0.04\mathrm{\%}=0.46\mathrm{\%}$。双方对半均摊： $$\frac{0.46\mathrm{\%}}{2}=0.23\mathrm{\%}\text{ 每家公司节省的借款成本}$$

• Method 1 – Total Borrowing Cost Comparison:
  • Without swap: AAA borrows floating (LIBOR − 0.10%) + BBB borrows fixed (5.20%)
    Total cost = $\text{LIBOR}+5.10\mathrm{\%}$.
  • With swap: AAA borrows fixed (4.00%) + BBB borrows floating (LIBOR + 0.60%)
    Total cost = $\text{LIBOR}+4.60\mathrm{\%}$.
  • Total Gain: $(\text{LIBOR}+5.10\mathrm{\%})-(\text{LIBOR}+4.60\mathrm{\%})=0.50\mathrm{\%}$ p.a.
• Method 2 – Difference of Spreads:
  • Fixed spread: $a=5.20\mathrm{\%}-4.00\mathrm{\%}=1.20\mathrm{\%}$.
  • Floating spread: $b=(\text{LIBOR}+0.60\mathrm{\%})-(\text{LIBOR}-0.10\mathrm{\%})=0.70\mathrm{\%}$.
  • Total Gain: $a-b=1.20\mathrm{\%}-0.70\mathrm{\%}=0.50\mathrm{\%}$.
• Sharing the Gain:
  • If FI intermediary requires 0.04% commission:
  • Remaining benefit = $0.50\mathrm{\%}-0.04\mathrm{\%}=0.46\mathrm{\%}$. Split equally: $$\frac{0.46\mathrm{\%}}{2}=0.23\mathrm{\%}\text{ saving for each company}$$

两家公司相对于各自直接借款市场均实现 0.23% 的成本节省，这就是互换的比较优势（图中 $L$ 表示 LIBOR，如 $L-0.33\mathrm{\%}$ 即 LIBOR − 0.33%）：

• 第 1 步：AAA 在市场按 4.00% 固定借款；BBB 按 LIBOR + 0.60% 浮动借款。
• 第 2 步：金融中介向 AAA 支付 4.00%（冲抵其固定利息），向 BBB 支付 (LIBOR + 0.60%)。
• 第 3 步：AAA 向金融中介支付 $(\text{LIBOR}-0.10\mathrm{\%})-0.23\mathrm{\%}=\text{LIBOR}-0.33\mathrm{\%}$。
  BBB 向金融中介支付 $5.20\mathrm{\%}-0.23\mathrm{\%}=4.97\mathrm{\%}$。
• 金融中介利润：$(4.97\mathrm{\%}-4.00\mathrm{\%})+(\text{LIBOR}-0.33\mathrm{\%}-\text{LIBOR}-0.60\mathrm{\%})$
  $=0.97\mathrm{\%}-0.93\mathrm{\%}=0.04\mathrm{\%}$ (4 bps)。

Both companies achieve a 0.23% saving relative to their direct borrowing markets. This is the comparative advantage of the swap (in the diagram, $L$ means LIBOR, e.g. $L-0.33\mathrm{\%}$ is LIBOR − 0.33%):

• Step 1: AAA borrows at 4.00% fixed; BBB borrows at LIBOR + 0.60% from market.
• Step 2: FI passes 4.00% to AAA (reimbursing fixed) and (LIBOR + 0.60%) to BBB.
• Step 3: AAA pays FI $(\text{LIBOR}-0.10\mathrm{\%})-0.23\mathrm{\%}=\text{LIBOR}-0.33\mathrm{\%}$.
  BBB pays FI $5.20\mathrm{\%}-0.23\mathrm{\%}=4.97\mathrm{\%}$.
• FI Profit: $(4.97\mathrm{\%}-4.00\mathrm{\%})+(\text{LIBOR}-0.33\mathrm{\%}-\text{LIBOR}-0.60\mathrm{\%})$
  $=0.97\mathrm{\%}-0.93\mathrm{\%}=0.04\mathrm{\%}$ (4 bps).

• 替代互换设计方案：
  • 双方直接交换纯粹的 LIBOR，仅调整固定利率端现金流；金融中介赚取 4.37% − 4.33% = 0.04%（图中 $L$ 表示 LIBOR）。
• 对比较优势理论的深刻批判与局限性：
  • 期限错配风险 (Maturity Mismatch)：AAA 与 BBB 在固定市场获得的 4.0% 和 5.2% 利率是长达数年（如 5 年）的长期固定借贷承诺。
  • 展期信贷风险 (Rollover Risk)：浮动利率（LIBOR − 0.10% 和 LIBOR + 0.60%）本质上是 6 个月期的短期借款便利。借款人的信用利差每隔 6 个月就要被贷款银行重新评估！
  • 若 BBB 的信用评级发生恶化，银行将单方面调高 LIBOR 之上的浮动利差，因此 BBB 并未真正锁定 5 年期固定借款成本。
  • 所谓的“比较优势”在很大程度上反映了贷款银行保留的权利：当借款人资信下降时，银行有权提高利差甚至终止信贷额度。

• Alternative Swap Designs:
  • The parties exchange plain LIBOR and adjust the fixed legs; the FI earns 4.37% − 4.33% = 0.04% (in the diagram, $L$ means LIBOR).
• Criticisms of the Comparative Advantage Argument:
  • Maturity Mismatch: The 4.0% and 5.2% fixed rates available to AAA and BBB are multi-year (e.g. 5-year) fixed commitments.
  • Rollover Risk: The floating rates (LIBOR − 0.10% and LIBOR + 0.60%) are 6-month borrowing facilities. The credit spread is reviewed every 6 months!
  • If BBB's credit rating deteriorates, its bank lender will increase the spread above LIBOR, so BBB does not truly lock in a fixed rate for 5 years.
  • The apparent comparative advantage reflects the lender's option to increase credit spreads or cancel floating credit lines if credit quality drops.

利率互换在理论上可分解为两份债券的价值差额进行估值：

• 固定利率债券 ($B_{\text{fix}}$)：按常规债券定价法，利用无风险零息利率曲线折现所有未来的固定票息及本金现金流。
• 浮动利率债券 ($B_{\text{fl}}$)：利用其最根本的定价特性——浮动利率债券在每次付息日刚过之后，其理论价值恰好等于面值 (Par)： $$B_{\text{fl}}=(L+k^{\ast })e^{-r{t}_1}$$ 其中 $L$ 为名义本金（此处 $L$ 不再表示 LIBOR），$k^{\ast }$ 为在上一重置日已确定的下一次浮动利息支付额，$t_1$ 为距离下一次付息的时间。
• 互换合约净价值：
  $$V_{\text{swap}}=B_{\text{fl}}-B_{\text{fix}}\text{（针对收取浮动利率、支付固定利率方）}$$ $$V_{\text{swap}}=B_{\text{fix}}-B_{\text{fl}}\text{（针对收取固定利率、支付浮动利率方）}$$
  例：收取浮动现金流、支付固定现金流的互换，相当于持有一份浮动利率债券的多头、一份固定利率债券的空头，因此 $V_{\text{swap}}=B_{\text{fl}}-B_{\text{fix}}$。
• 备选估值法：互换亦可等价分解为一系列远期利率协议 (FRAs) 的投资组合进行分别定价——自学内容（Hull 教材第 187 页）。

An interest rate swap can be valued as the difference between two bonds:

• Fixed-rate bond ($B_{\text{fix}}$): Valued in the usual way by discounting all scheduled fixed coupon and principal cash flows using the zero curve.
• Floating-rate bond ($B_{\text{fl}}$): Valued by using the fundamental property that a floating-rate bond is worth exactly par immediately after every payment date: $B_{\text{fl}}=(L+k^{\ast })e^{-r{t}_1}$, where $L$ is notional principal (here $L$ no longer means LIBOR), $k^{\ast }$ is the known upcoming floating payment set at the last reset date, and $t_1$ is time until the next payment.
• Net Swap Value:
  $$V_{\text{swap}}=B_{\text{fl}}-B_{\text{fix}}\text{(for party receiving floating, paying fixed)}$$ $$V_{\text{swap}}=B_{\text{fix}}-B_{\text{fl}}\text{(for party receiving fixed, paying floating)}$$
  Example: receiving floating and paying fixed = long a floating-rate bond, short a fixed-rate bond.
• Alternative: a portfolio of Forward Rate Agreements (FRAs) – own study (Hull, p. 187).

练习题 Quiz Question 7.2（第 207 页）：收取 6 个月 LIBOR，每半年支付 7% 固定利息，名义本金为 $100M（1亿美元）。剩余期限 10 个月。所有期限的连续复利贴现率均为 $r=5\mathrm{\%}$ p.a.。最近一次确定的 6 个月 LIBOR 为 4.6%。

• 现金流时间点：下一次付息在 4 个月后 ($4/12$)；最终付息及到期在 10 个月后 ($10/12$)。
• 第 1 步：固定利率债券估值 ($B_{\text{fix}}$)：
  • 半年期固定票息：$\mathrm{\$}100\text{M}\times 7\mathrm{\%}\times 6/12=\mathrm{\$}3.5\text{M}$。
  • $B_{\text{fix}}=3.5e^{-0.05\times 4/12}+(100+3.5)e^{-0.05\times 10/12}=3.442+99.276=\mathrm{\$}102.718\text{M}$。
• 第 2 步：浮动利率债券估值 ($B_{\text{fl}}$)：
  • 第 4 个月应付的浮动利息已按 4.6% 锁定：$\mathrm{\$}100\text{M}\times 4.6\mathrm{\%}\times 6/12=\mathrm{\$}2.3\text{M}$。
  • 在第 4 个月付息完毕后，浮动利率债券价值重置为面值 ($100M)。
  • $B_{\text{fl}}=(100+2.3)e^{-0.05\times 4/12}=102.3\times 0.98347=\mathrm{\$}100.609\text{M}$。
• 第 3 步：互换总价值（收取浮动、支付固定方）： $$V_{\text{swap}}=B_{\text{fl}}-B_{\text{fix}}=\mathrm{\$}100.609\text{M}-\mathrm{\$}102.718\text{M}=-\mathrm{\$}2.109\text{M}$$
• 注意：互换利率为 7%——面值 $100M、每半年付息、年票息率 7% 的债券按面值发行，即在互换利率下固定端价值等于面值。

Quiz Question 7.2 (page 207): Receive 6-month LIBOR, pay 7% semi-annually on $100M notional. 10 months remaining. Discount rate $r=5\mathrm{\%}$ p.a. (continuous) for all maturities. Latest LIBOR was 4.6%.

• Payment Dates: Next payment in 4 months ($4/12$); final payment in 10 months ($10/12$).
• Step 1: Value Fixed-Rate Bond ($B_{\text{fix}}$):
  • Semi-annual fixed coupon: $\mathrm{\$}100\text{M}\times 7\mathrm{\%}\times 6/12=\mathrm{\$}3.5\text{M}$.
  • $B_{\text{fix}}=3.5e^{-0.05\times 4/12}+(100+3.5)e^{-0.05\times 10/12}=3.442+99.276=\mathrm{\$}102.718\text{M}$.
• Step 2: Value Floating-Rate Bond ($B_{\text{fl}}$):
  • Floating payment at month 4 was set at 4.6%: $\mathrm{\$}100\text{M}\times 4.6\mathrm{\%}\times 6/12=\mathrm{\$}2.3\text{M}$.
  • At month 4 (after payment), the bond resets to par ($100M).
  • $B_{\text{fl}}=(100+2.3)e^{-0.05\times 4/12}=102.3\times 0.98347=\mathrm{\$}100.609\text{M}$.
• Step 3: Value of the Swap (Receiving Floating, Paying Fixed): $$V_{\text{swap}}=B_{\text{fl}}-B_{\text{fix}}=\mathrm{\$}100.609\text{M}-\mathrm{\$}102.718\text{M}=-\mathrm{\$}2.109\text{M}$$
• Note that: the swap rate is 7% – a $100 million bond with a semi-annual coupon of 7% p.a. sells for par, so the fixed leg is worth par at the swap rate.

Core Principle: You never need to forecast future floating cash flows! Because floating coupon resets to prevailing market rates, the entire floating leg from month 1 to month 13 collapses into par ($10M) at the first reset date.

• 货币互换的核心特征：
  • 期初与到期均交换本金：期初按即期汇率交换本金，到期时按完全相同的期初即期汇率换回本金。
  • 利息支付按币种全额收付：因为收付的是不同货币，利息现金流无法相互冲抵，不能净额结算。
  • 回顾：在利率互换中，本金不交换，利息按净额结算。
• 货币互换的用途：
  • 将负债（投资）从一种货币转换为另一种货币。
  • 例：IBM 同意每年在 1000 万英镑 (£10M) 本金上支付 11% 的英镑利息，并在 1500 万美元 ($15M) 本金上收取 8% 的美元利息，期限 5 年：

• Key features of currency swaps:
  • Principal is exchanged at the beginning (at spot exchange rate) and re-exchanged at maturity at the same initial rate.
  • All interest payments are exchanged in full: Because payments are in different currencies, they cannot be netted.
  • Recall that in an interest rate swap, principal is not exchanged and interest payments are netted.
• It is used to:
  • Convert a liability (investment) from one currency to another.
  • Example: IBM has agreed to pay 11% on a sterling principal of £10 million and receive 8% on a USD principal of $15 million every year for 5 years:

通用汽车 (GM) 与澳洲航空 (Qantas) 在两个货币市场所面临的借款利率报价：

• 利差结构的深度比较：
  • GM 在两个市场均享有绝对借款优势，但在美元市场的优势显著更大 (2.00% vs 0.40%)。
  • GM 在美元借款市场上具有比较优势。
  • 澳洲航空在澳元借款市场上具有比较优势（其在澳元市场的借款劣势仅为 0.40%，而美元劣势高达 2.00%）。
• GM 需要筹集澳元，而澳航需要筹集美元。货币互换能够实现双方融资成本的共同显著下降！

The following borrowing rates are offered to General Motors (US) and Qantas (Australia):

• Notice the spread differential:
  • GM has an absolute advantage in both markets, but its advantage is much larger in USD (2.00% vs 0.40%).
  • GM has a comparative advantage in USD.
  • Qantas has a comparative advantage in AUD (its borrowing disadvantage is only 0.40% in AUD vs 2.00% in USD).
• GM wants AUD borrowing, while Qantas wants USD borrowing. A currency swap achieves mutual interest savings!

• 总收益测算：
  • 无互换方案：GM 直接借澳元 (7.60%) + 澳航直接借美元 (7.00%)
    两家合计借款成本 = $7.60\mathrm{\%}+7.00\mathrm{\%}=14.60\mathrm{\%}$。
  • 有互换方案：GM 借美元 (5.00%) + 澳航借澳元 (8.00%)
    两家合计借款成本 = $5.00\mathrm{\%}+8.00\mathrm{\%}=13.00\mathrm{\%}$。
  • 互换总收益：$14.60\mathrm{\%}-13.00\mathrm{\%}=1.60\mathrm{\%}$。
  • 备选方法：
    • GM 获得澳航澳元利率的收益：$b=8\mathrm{\%}-7.60\mathrm{\%}=0.40\mathrm{\%}$。
    • 澳航获得 GM 美元利率的收益：$a=7\mathrm{\%}-5\mathrm{\%}=2\mathrm{\%}$。
    • 互换总收益：$a-b=2\mathrm{\%}-0.40\mathrm{\%}=1.60\mathrm{\%}$。
• 中介机构收益扣除与企业净收益分配：
  • 假定金融中介机构收取 0.20% 的做市佣金：
  • 待分摊的净收益 = $1.60\mathrm{\%}-0.20\mathrm{\%}=1.40\mathrm{\%}$。
  • 双方平均均摊： $$\frac{1.40\mathrm{\%}}{2}=0.70\mathrm{\%}\text{ 每家公司实现的利息节省}$$
  • GM 目标澳元综合借款成本：$7.60\mathrm{\%}-0.70\mathrm{\%}=6.90\mathrm{\%}$。
  • 澳航目标美元综合借款成本：$7.00\mathrm{\%}-0.70\mathrm{\%}=6.30\mathrm{\%}$。

• Total Gain Calculation:
  • Without swap: GM borrows AUD directly at 7.60% + Qantas borrows USD directly at 7.00%
    Total borrowing cost = $7.60\mathrm{\%}+7.00\mathrm{\%}=14.60\mathrm{\%}$.
  • With swap: GM borrows USD at 5.00% + Qantas borrows AUD at 8.00%
    Total borrowing cost = $5.00\mathrm{\%}+8.00\mathrm{\%}=13.00\mathrm{\%}$.
  • Total Gain: $14.60\mathrm{\%}-13.00\mathrm{\%}=1.60\mathrm{\%}$.
  • Alternative way:
    • Benefit to GM of accessing Qantas's AUD rate: $b=8\mathrm{\%}-7.60\mathrm{\%}=0.40\mathrm{\%}$.
    • Benefit to Qantas of accessing GM's USD rate: $a=7\mathrm{\%}-5\mathrm{\%}=2\mathrm{\%}$.
    • Total gain from the swap: $a-b=2\mathrm{\%}-0.40\mathrm{\%}=1.60\mathrm{\%}$.
• Intermediary Commission & Net Benefit:
  • Suppose the FI charges 0.20% commission:
  • Net gain to be shared = $1.60\mathrm{\%}-0.20\mathrm{\%}=1.40\mathrm{\%}$.
  • Divided equally: $$\frac{1.40\mathrm{\%}}{2}=0.70\mathrm{\%}\text{ saving for each company}$$
  • GM target borrowing cost: $7.60\mathrm{\%}-0.70\mathrm{\%}=6.90\mathrm{\%}$ in AUD.
  • Qantas target borrowing cost: $7.00\mathrm{\%}-0.70\mathrm{\%}=6.30\mathrm{\%}$ in USD.

包含金融中介收取 0.20% 利差时的互换交易结构设计：

• 第 1 步：GM 在本土借入 5.00% 美元；澳航在本土市场借入 8.00% 澳元。
• 第 2 步：GM 从金融机构收取 5.00% 美元（冲抵外部借款）；澳航从金融机构收取 8.00% 澳元（冲抵外部借款）。
• 第 3 步：GM 向金融机构支付澳元 $7.60\mathrm{\%}-0.70\mathrm{\%}=6.90\mathrm{\%}$；澳航向金融机构支付美元 $7.00\mathrm{\%}-0.70\mathrm{\%}=6.30\mathrm{\%}$。
• 金融中介利润：收取美元 6.3% • 支付美元 5.0% (+1.3% USD)；收取澳元 6.9% • 支付澳元 8.0% (−1.1% AUD)。净年利润 = $1.30\mathrm{\%}-1.10\mathrm{\%}=0.20\mathrm{\%}$。

双方的借款利率都改善了 0.70%。这就是货币互换的比较优势。

Structure of the swap with a Financial Intermediary taking 0.20% spread:

• Step 1: GM borrows USD at 5.00%; Qantas borrows AUD at 8.00% from domestic lenders.
• Step 2: GM receives USD 5.00% from FI (offsetting its USD loan); Qantas receives AUD 8.00% from FI (offsetting its AUD loan).
• Step 3: GM pays FI AUD $7.60\mathrm{\%}-0.70\mathrm{\%}=6.90\mathrm{\%}$; Qantas pays FI USD $7.00\mathrm{\%}-0.70\mathrm{\%}=6.30\mathrm{\%}$.
• FI Profit: Receives USD 6.3% • Pays USD 5.0% (+1.3% USD) • Receives AUD 6.9% • Pays AUD 8.0% (−1.1% AUD). Net gain = $1.30\mathrm{\%}-1.10\mathrm{\%}=0.20\mathrm{\%}$.

Both parties have improved their borrowing rate by 0.70%. This is the comparative advantage of the currency swap.

其中一家企业愿意承担部分外汇汇率风险：
假设澳航同意每年支付 1% 澳元以及 5.30% 美元（将利息支出分散在两个币种承担）：

• 通过重新设计不同币种的偿付责任，澳航在主动承担部分外汇风险的同时，实现了量身定制的融资目标。
• 澳航每年支付 1% 澳元和 5.30% 美元。金融机构净收 +USD 0.30%（5.30% − 5.00%），净付 AUD 0.10%（6.90% − 7.00%）：存在小额的剩余币种错配，总利差为 0.20%。

One of the companies wishes to bear foreign exchange risk:
Suppose Qantas agrees to pay 1% p.a. in AUD and 5.30% p.a. in USD (splitting its payments across both currencies):

• By restructuring the currency obligations, Qantas absorbs partial FX risk while obtaining customized financing.
• Qantas pays 1% p.a. in AUD and 5.30% p.a. in USD. The FI nets +USD 0.30% (5.30% − 5.00%) and −AUD 0.10% (6.90% − 7.00%): a small residual currency mismatch, with a total margin of 0.20%.

核心原则：货币互换中，本金必须在期初和到期时按原始即期汇率交换。由于存在全额本金交换，货币互换的信用风险远高于利率互换。

Core Principle: In currency swaps, principal MUST be exchanged at both initiation and maturity at the original spot rate. Credit risk in currency swaps is substantially higher than in interest rate swaps because of full principal exchange.

与利率互换类似，货币互换可以通过以下两种等价方法估值：

• 分解为两份不同货币债券价值的差额。
• 分解为一系列远期利率协议 (FRAs)，即远期外汇合约 (FX Forwards) 的投资组合。

基于债券组合价格的估值法：

• 需要当前即期汇率 $S_0$（定义为每单位外币折合的本币数额，即直接标价法）。
• 令 $B_D$ 为本币债券在本币计价下的价值。
• 令 $B_F$ 为外币债券在外币计价下的价值。
• 例：支付外币 $F$、收取本币 $D$ 的货币互换，相当于持有一份外币债券的空头和一份本币债券的多头。对于收取本币 $D$、支付外币 $F$ 的金融机构：
  $$V_{\text{swap}}=B_D-S_0{B}_F$$
• 对于收取外币 $F$、支付本币 $D$ 的金融机构：
  $$V_{\text{swap}}=S_0{B}_F-B_D$$

Like interest rate swaps, currency swaps can be valued as:

• The difference between the values of two bonds.
• A portfolio of forward rate agreements (FRAs), i.e. forward foreign exchange contracts.

Valuation in Terms of Bond Prices:

• The current spot exchange rate $S_0$ is required (defined as domestic currency per unit of foreign currency).
• Let $B_D$ be the value of the domestic currency bond (in domestic currency).
• Let $B_F$ be the value of the foreign currency bond (in foreign currency).
• Paying foreign currency $F$ and receiving domestic currency $D$ = short a foreign currency bond, long a domestic currency bond:
  $$V_{\text{swap}}=B_D-S_0{B}_F$$
• For a financial institution receiving foreign currency $F$ and paying domestic currency $D$:
  $$V_{\text{swap}}=S_0{B}_F-B_D$$

练习题 Quiz Question 7.5（第 207 页）：某互换每年在 £20M（2000万英镑）本金上支付 10%，在 $30M（3000万美元）本金上收取 6%。剩余期限 15 个月。贴现率：美元 4%，英镑 7%（按年复利，所有期限相同）。当前即期汇率：1 £ = $1.85。

• 支付时间节点：下一次付息在 3 个月后 ($3/12=0.25$ 年)；最终到期在 15 个月后 ($15/12=1.25$ 年)。
• 第 1 步：美元债券估值 ($B_D$)：
  • 年度利息 = $\mathrm{\$}30\text{M}\times 6\mathrm{\%}=\mathrm{\$}1.8\text{M}$。期末现金流 = $\mathrm{\$}31.8\text{M}$。
  • $B_D=\frac{1.8}{{1.04}^{0.25}}+\frac{31.8}{{1.04}^{1.25}}=1.782+30.279=\mathrm{\$}32.061\text{M}$。
• 第 2 步：英镑债券估值 ($B_F$)：
  • 年度利息 = $\pounds 20\text{M}\times 10\mathrm{\%}=\pounds 2.0\text{M}$。期末现金流 = $\pounds 22.0\text{M}$。
  • $B_F=\frac{2.0}{{1.07}^{0.25}}+\frac{22.0}{{1.07}^{1.25}}=1.966+20.216=\pounds 22.182\text{M}$。
• 第 3 步：互换理论价值测算：
  • 对于支付英镑、收取美元方： $$V_{\text{swap}}=B_D-S_0{B}_F=\mathrm{\$}32.061\text{M}-(1.85\times \pounds 22.182\text{M})$$ $$=\mathrm{\$}32.061\text{M}-\mathrm{\$}41.037\text{M}=-\mathrm{\$}8.976\text{M}$$
  • 对于支付美元、收取英镑方：$V_{\text{swap}}=+\mathrm{\$}8.976\text{M}$。

Quiz Question 7.5 (page 207): Swap pays 10% on £20M, receives 6% on $30M annually. 15 months remaining. Discount rates: 4% in $, 7% in £ (annual compounding, all maturities). Exchange rate: 1 £ = $1.85.

• Payment Dates: Next payment in 3 months ($3/12=0.25$ yr); final payment in 15 months ($15/12=1.25$ yr).
• Step 1: Value Dollar Bond ($B_D$):
  • Annual coupon = $\mathrm{\$}30\text{M}\times 6\mathrm{\%}=\mathrm{\$}1.8\text{M}$. Final flow = $\mathrm{\$}31.8\text{M}$.
  • $B_D=\frac{1.8}{{1.04}^{0.25}}+\frac{31.8}{{1.04}^{1.25}}=1.782+30.279=\mathrm{\$}32.061\text{M}$.
• Step 2: Value Sterling Bond ($B_F$):
  • Annual coupon = $\pounds 20\text{M}\times 10\mathrm{\%}=\pounds 2.0\text{M}$. Final flow = $\pounds 22.0\text{M}$.
  • $B_F=\frac{2.0}{{1.07}^{0.25}}+\frac{22.0}{{1.07}^{1.25}}=1.966+20.216=\pounds 22.182\text{M}$.
• Step 3: Value of the Swap:
  • To party paying £ and receiving $: $$V_{\text{swap}}=B_D-S_0{B}_F=\mathrm{\$}32.061\text{M}-(1.85\times \pounds 22.182\text{M})$$ $$=\mathrm{\$}32.061\text{M}-\mathrm{\$}41.037\text{M}=-\mathrm{\$}8.976\text{M}$$
  • To party paying $ and receiving £: $$V_{\text{swap}}=+\mathrm{\$}8.976\text{M}$$

Core Principle: Value each bond in its own currency first using its domestic risk-free rate, then translate into the common valuation currency using today's spot rate $S_0$. Negative value indicates the FI's obligations in high-yielding AUD exceed its USD receipts.

• 信用风险源于交易对手违约的可能性：
  • 在合约起初时刻，互换理论价值严格为零 ($V_0=0$)，与远期合约类似。
  • 未来某一时点，其价值可能为正也可能为负：市场利率与外汇汇率持续波动，导致互换价值对一方为正，对另一方为负。
• 金融机构面临的非对称信用风险暴露 (Asymmetric Credit Exposure)：
  • 金融机构仅当互换对其具有正价值时，才面临真实的信用风险暴露。
  • 若互换对金融机构的价值为负，对手方绝无理由违约，因为该合约对对手方而言是一项具有正价值的资产：对手方会出售该合约以获取其正价值（若对手方破产，其清算人亦会保留或出售该资产）。
• 互换违约与普通贷款违约损失对比：
  • 互换违约导致的潜在损失远小于同等名义本金贷款的违约损失，因为利率互换中本金从未被实际借贷给对方。
  • 在发生违约时，货币互换造成的损失显著大于利率互换，因为货币互换涉及期末本金的全额收付交换，且两国汇率可能经历极其剧烈的累计漂移。

• Credit risk arises from the possibility of default by a counterparty:
  • At initiation, a swap is worth zero ($V_0=0$), similar to a forward contract.
  • At a future time its value may be either positive or negative: interest rates and currency rates fluctuate, so the swap value becomes positive to one party and negative to the other.
• Asymmetric Credit Exposure for Financial Institutions:
  • An FI is exposed to credit risk only when the swap value is positive to the FI.
  • If the swap value to the FI is negative, the counterparty will not default because the contract is an asset to them: it will sell the contract to profit from its positive value (or bankruptcy administrators will preserve/sell it).
• Default Losses on Swaps vs Loans:
  • Potential losses from defaults on swaps are much smaller than losses on loans of the same notional principal, because principals are not lent out (in IRS).
  • At default, currency swaps generate significantly greater losses than interest rate swaps because principal amounts are exchanged and exchange rates can experience massive cumulative shifts.