• 阐述远期合约、期货合约以及期权合约的基本特征
• 概述场内交易所市场与场外交易 (OTC) 市场
• 探讨期货市场机制
  • 解释每日逐日盯市 (Marking-to-Market) 结算流程
  • 结合保证金账户交易细则讨论保证金运作机制
  • 定义并对比正常市场与反向市场 – 升水 (Contango) 与贴水 (Backwardation)
• 解释衍生品市场参与者的经济活动：
  • 套期保值者 (Hedgers) • 投机者 (Speculators) • 套利者 (Arbitrageurs)
• 分析基础套利机会与定价边界

• Describe the basic characteristics of forward, futures and option contracts
• Overview exchange markets and over-the-counter markets
• Discuss futures markets
  • Explain the daily marking-to-market process
  • Discuss the margin process with reference to margin account transactions
  • Define and contrast normal markets and inverted markets – backwardation and contango
• Explain the activities of the derivatives users:
  • Hedgers • Speculators • Arbitrageurs
• Analyze basic arbitrage opportunities

• 阐述期货的本质及其与远期合约的关系
• 理解套期保值者和投机者如何利用期货市场
• 阐述悉尼期货交易所 (SFE) 采用的交易与结算安排
• 理解以下期货合约，并说明如何用它们进行套期保值
  • BAB 期货（银行承兑汇票期货）
  • SPI 期货（股价指数期货）

• Explain the nature of futures and their relationship to forwards
• Understand how the futures market can be used by hedgers and speculators
• Explain the trading and settlement arrangements used by the SFE (Sydney Futures Exchange)
• Understand the following futures contracts and explain how they can be used for hedging
  • BAB futures (bank accepted bills)
  • SPI futures (Share Price Index)

• 衍生品 (Derivative) 是一种金融工具，其价值取决于（或衍生自）另一种更基础的资产的价值。这种资产叫基础资产 (Underlying Asset)，教材里也常叫“标的资产”。
• 四大基础衍生工具模块：
  • 期货合约 (Futures Contracts)： 在交易所集中交易的标准化协议，约定在未来特定日期以特定价格买入或卖出基础资产。
  • 远期合约 (Forward Contracts)： 在场外市场 (OTC) 私下达成的双边定制协议，约定在未来买入或卖出基础资产。
  • 互换合约 (Swaps)： 双方私下达成的协议，约定在未来多个日期之间周期性互换现金流。
  • 期权合约 (Options)： 赋予买方在未来特定日期或之前以约定价格买入（看涨期权）或卖出（看跌期权）基础资产的权利（而非义务）的合约。

• A derivative is a financial instrument whose value depends on (or derives from) the values of other, more basic underlying assets.
• Four fundamental derivative building blocks:
  • Futures contracts: Standardised exchange-traded agreements to buy/sell at a specified future date and price.
  • Forward contracts: Customised bilateral over-the-counter (OTC) agreements to buy/sell in the future.
  • Swaps: Private agreements between two parties to exchange periodic cash flows over multiple dates.
  • Options: Contracts conferring the right (without obligation) to buy (call) or sell (put) an asset.

• 金融证券
  • 股票、债券、货币、股票指数
• 大宗商品
  • 金属（铜、黄金、白银）
  • 农产品（玉米、棉花、橙汁、咖啡、活牛）
  • 木材
• 能源
  • 石油产品、天然气、电力
• 其他 – 保险、天气、信用

投资性资产，还是消费性资产？

• 投资性资产 (Investment Asset)：许多投资者纯粹出于投资目的而持有（如黄金、白银）。
• 消费性资产 (Consumption Asset)：主要为消费而持有（如石油、铜）。

• Financial Securities
  • Stocks, bonds, currencies, stock indices
• Commodities
  • Metals (copper, gold, silver)
  • Agricultural (corn, cotton, orange juice, coffee, cattle)
  • Wood
• Energy
  • Oil products, natural gas, electricity
• Other – Insurance, weather, credit

Investment Asset OR Consumption Asset ?

• Investment assets are held by many investors purely for investment (e.g. gold, silver).
• Consumption assets are held primarily for consumption (e.g. oil, copper).

• 优点：提供交割日期多样的标准化合约；没有信用风险
• 缺点：需要缴纳保证金；无法按需定制合约

• Advantages: provide standardized contracts on a range of delivery dates; no credit risk
• Disadvantages: attract margin requirements; no freedom to tailor contracts

• 交易所之外的重要替代渠道
• 由交易商组成、通过电话和计算机联网的交易网络，交易商无需实际碰面
• 交易通常发生在金融机构、企业财务主管和基金经理之间
• 优点
  • 更大的自由度 – 合约条款可根据客户需求量身定制（不受交易所规格限制）
  • 无需缴纳保证金
• 缺点
  • 信用风险（一方不履约的风险；通常适用 ISDA 主协议）；可通过抵押品（担保）降低
• 2008 年以来 …
  • 场外市场已纳入监管
  • 标准化的场外产品在互换执行设施 (SEF) 上交易
  • 所有交易必须向中央数据库报告

• Important alternative to exchanges
• Telephone and computer-linked network of dealers who do not meet physically
• Trades are usually between financial institutions, corporate treasurers, and fund managers
• Advantages
  • More freedom – contract terms are tailored to the needs of the client (not exchange specific)
  • No need for margin payments
• Disadvantages
  • Credit risk (the risk that one of the parties will not honor the contract; documented under ISDA Master Agreements); this can be reduced by collateralization
• Since 2008 …
  • OTC markets have become regulated
  • Standardized OTC products trade on swap execution facilities (SEFs)
  • All trades must be reported to a central registry

资料来源：国际清算银行 (BIS)。图中场外市场为名义本金总额，交易所市场为基础资产价值。

• 名义本金 (Notional Principal)：用于计算衍生品现金流的参考金额。

Source: Bank for International Settlements. Chart shows total principal amounts for OTC markets and value of underlying assets for exchange markets.

• Notional principal: the reference dollar amount on which derivative cash flows are calculated.

远期合约是一种场外 (OTC) 协议，约定在未来某一时间 $T$ 按某一价格 $K$（远期价格）买入或卖出某种资产。

• 同意买入的一方 $A$ 持有多头头寸 (Long Position)。
• 同意卖出的一方 $B$ 持有空头头寸 (Short Position)。
• 订立远期合约在初始时刻不需要任何前期现金流支出（初始时刻合约价值 $f_0=0$）。图中 $S_T$ 为到期日 $T$ 的现货价格。

A forward contract is an OTC agreement to buy or sell an asset at a certain time $T$ in the future for a certain price $K$ – the forward price.

• The party $A$ that has agreed to buy has a long position.
• The party $B$ that has agreed to sell has a short position.
• Entering a forward contract requires zero upfront cash flow (the contract value at initiation $f_0=0$). In the chart, $S_T$ is the spot price at maturity $T$.

期货合约是一种协议，约定在未来某一时间 $T$ 按某一价格（期货价格 $F_t$，$t$ 为某一时点，$t=0$ 为今天）买入或卖出某种资产。

• 期货价格在今天观察到，但对应的是将在未来进行的交易
  • 期货价格由供求关系决定，与现货价格的决定方式相同
• 期货合约在交易所交易
  • 交易所规定交割日 $T$，并规定以交割基础资产（商品期货）或现金结算（金融期货）的方式了结
  • 每日结算：逐日盯市 (Marking-to-Market)
  • 结算所通过合约更替 (Novation) 保证双方履约（成为每一位买方的卖方，以及每一位卖方的买方）
• 绝大多数期货合约在到期前被平仓，而不是实物交割。平仓是指进行一笔对冲（反向）交易
  • 并由此产生现金盈亏

A futures contract is an agreement to buy or sell an asset at a certain time $T$ in the future for a certain price – the futures price $F_t$ ($t$ is a point in time; $t=0$ is today).

• Futures prices are observed today but refer to transactions to be carried out in the future
  • Futures price is determined by supply and demand, in the same way as the spot price
• Futures contracts are traded on exchanges
  • The exchange specifies delivery date $T$ and settlement by delivery of the underlying (commodity futures) or by cash settlement (financial futures)
  • Are settled daily: marking-to-market
  • The clearinghouse guarantees both sides by novation (buyer to every seller, seller to every buyer)
• Most futures contracts are closed out before maturity, rather than settled by physical delivery. Closing out a futures position involves entering into an offsetting trade
  • resulting in a cash profit or loss

随着时间推移，市场参与者持续交易在 $T$ 时刻买入/卖出资产的期货合约。

• 现货价格 $S_t$ 是资产在 $t$ 时刻立即交割的价格（$S_0$ 为今天的现货价格）
• 期货价格 $F_t$ 是在 $t$ 时刻订立、于 $T$ 时刻交割资产的期货合约所约定的交割价格

注意 $F_0=K$

• 由于期货合约的卖方可以在到期时交割实物资产，期货价格与现货价格在到期时必须相等（$F_T=S_T$）。否则，套利者可以获得无风险利润：
  • $F_T>S_T$：买入现货、做空期货并交割，利润为 $F_T-S_T$
  • $F_T<S_T$：卖空资产、买入期货并接受交割，利润为 $S_T-F_T$

As time goes by, market participants continue trading futures contracts to buy/sell the asset at $T$.

• The spot price $S_t$ is the asset price at time $t$ for immediate delivery ($S_0$ is today's spot price)
• The futures price $F_t$ is the agreed delivery price for a futures contract initiated at $t$, for asset delivery at $T$

Note that $F_0=K$

• Since the seller of the futures contract can deliver the physical asset at maturity, the futures price and the spot price must be the same at that time ($F_T=S_T$). If not, arbitrageurs could make risk-free profits:
  • $F_T>S_T$: buy the asset spot, short futures, deliver; profit $F_T-S_T$
  • $F_T<S_T$: short sell the asset, buy futures, take delivery; profit $S_T-F_T$

• 保证金是投资者存入其经纪人账户的现金或可流通证券；它是履约担保 (Performance Bond)，而非贷款或购货首付款
  • 初始保证金 (Initial Margin)：开仓时存入
  • 维持保证金 (Maintenance Margin)：触发追加保证金通知前账户的最低余额（通常约为初始保证金的 75%–80%）
  • 追加保证金通知（变动保证金，Margin Call）：余额跌破维持保证金时，投资者必须存入资金，将余额恢复至初始保证金水平
• 保证金账户余额随每日结算（逐日盯市）而调整
• 保证金账户可以获得利息
• 保证金通过减少违约时的损失来控制信用风险
• 结算所（SFE 结算公司，Clearinghouse）
  • 经纪商在结算所持有结算保证金账户
  • 对所有会员的头寸进行净额结算，并记录当天的全部交易

• A margin is cash or marketable securities deposited by an investor with his/her broker; it is a performance bond, not a loan or down payment
  • Initial margin: deposited when the position is opened
  • Maintenance margin: the minimum balance before a margin call (typically about 75–80% of initial margin)
  • Margin call (variation margin): if the balance falls below maintenance margin, the investor must deposit funds to restore it to the initial margin
• The balance in the margin account is adjusted to reflect daily settlement (marking-to-market)
• Interest is earned on margin accounts
• Margins control credit risk, by reducing the loss in the event of default
• Clearinghouse (SFE Clearing Corporation)
  • Broker holds a clearing margin account with the Clearinghouse
  • Netting positions of all members and keep track of all transactions in one day

• 6 月 5 日：投资者买入 2 张 12 月到期黄金期货合约（多头）
  • 合约规模 = 100 盎司
  • 期货价格 = 400 美元
  • 初始保证金 = 每张合约 2,000 美元，合计 4,000 美元
  • 维持保证金 = 每张合约 1,500 美元，合计 3,000 美元
• 6 月 26 日：投资者通过卖出 2 张 12 月到期黄金期货合约（空头）平仓
  • 期货价格 = 392.30 美元
• 投资者亏损 = (392.30 − 400) × 200 = 1,540 美元

• On June 5: investor enters a long position in two December gold futures contracts
  • Contract size = 100 oz
  • Futures price = USD 400
  • Initial margin = USD 2,000 per contract or USD 4,000 in total
  • Maintenance margin = USD 1,500 per contract or USD 3,000 in total
• On June 26: investor closes out the position by entering a short position in two December gold futures contracts
  • Futures price = USD 392.30
• Investor loss = USD (392.30 − 400) × 200 = USD 1,540

远期曲线给出某一天不同到期期限的期货价格。

图：2011 年 7 月 25 日 COMEX 黄金期货合约行情（来源：ifs.marketcenter.com）

• 正常市场 (Normal Market)
  • 远期曲线向上倾斜
  • 近月期货价格低于远月期货价格
  • 市场处于期货升水 (Contango)：期货价格高于现货价格

The forward curve gives the futures prices on a given day, for a range of different maturities.

Figure: Listing for COMX gold futures contracts on 25 July 2011 (Source: ifs.marketcenter.com)

• Normal market
  • Forward curve is upward sloping
  • Futures prices for near months are lower than for later months
  • The market is in contango: futures prices trade higher than spot prices

图：2013 年 7 月 4 日 NYMEX 原油期货合约行情（来源：ifs.marketcenter.com）

• 反向市场 (Inverted Market)
  • 远期曲线向下倾斜
  • 远月期货价格低于近月期货价格
  • 市场处于期货贴水 (Backwardation)：期货价格低于现货价格

Figure: Listing for NYMEX crude oil futures contracts on 4 July 2013 (Source: ifs.marketcenter.com)

• Inverted market
  • Forward curve is downward-sloping
  • Futures prices for distant months are lower than for near months
  • The market is in backwardation: futures prices trade lower than spot prices

• 期权是一种合约，赋予持有人在某一日期之前（美式）或在某一日期当天（欧式）($T$)，按某一价格 ($K$，期权的执行价；这里 $K$ 不再是远期交割价) 买入/卖出基础资产的权利（而非义务）
  • 买方为获得这一权利，向卖方（立权人 Writer）支付期权费（权利金）
  • 欧式：仅能在到期日行权；美式：到期日及之前任何时间均可行权
• 期权矩阵 (Options Matrix)

• An option is a contract which confers a right (not an obligation) to buy/sell an underlying asset by (American) or at (European) a certain date ($T$) for a certain price ($K$, the option's strike price; here $K$ is no longer the forward delivery price)
  • The buyer pays the seller (writer) a premium for this right
  • European: exercised only on the expiration date; American: at any time up to and including it
• Options Matrix

• 套期保值 (Hedging)
  • 针对已经拥有或计划买卖的资产，防范价格发生不利变动；降低风险、锁定价格
• 投机 (Speculation)
  • 根据对未来价格变动的判断在市场上建立头寸，从预期的价格变动中获利
  • 承担风险以期获利；杠杆放大收益
  • 投机为衍生品市场提供流动性
• 套利 (Arbitrage)
  • 利用短期市场低效率获取无风险利润（同时建立相互对冲的头寸）
  • 消除市场价格差异
• 改变负债的性质（例如互换）
• 交易者类型
  • 套期保值者、投机者、套利者
  • 做市商、共同基金、对冲基金

• Hedging
  • Seek protection against unfavourable price changes in an asset already owned or planned to be bought/sold; reduce risk and lock in the price
• Speculation
  • Take a position in the market by betting on future price movements to earn profits from expected price changes
  • Take risk in the hopes of profit; leverage magnifies returns
  • Speculation provides liquidity in derivatives markets
• Arbitrage
  • Make risk-free profits by taking advantage of short-term market inefficiencies (simultaneous offsetting positions)
  • Eliminates market price discrepancies
• To change the nature of a liability (e.g. swaps)
• Types of traders
  • Hedgers, speculators, arbitrageurs
  • Market makers, mutual funds, hedge funds

• 一家美国公司将在 3 个月后为从英国进口的商品支付 1,000 万英镑。3 个月期远期汇率为 1.6192。
• 公司决定通过持有远期合约多头来套期保值
  • 锁定 1.6192 的汇率
  • 将 3 个月后支付的价款固定为 16,192,000 美元（10,000,000 × 1.6192）
• 利用远期合约套期保值消除了不确定性；但不能保证套期保值的结果更好
  • 若 3 个月后的汇率 < 1.6192：不套期保值的结果更好
  • 若 3 个月后的汇率 > 1.6192：套期保值的结果更好

• A US company will pay £10 million for imports from Britain in 3 months. The 3-month forward exchange rate is 1.6192.
• The company decides to hedge by using a long position in a forward contract
  • To lock in an exchange rate of 1.6192
  • Fixes the price paid in 3 months to USD 16,192,000 (10,000,000 × 1.6192)
• Hedging using forwards removes the uncertainty; there is no assurance that the outcome with hedging will be better
  • If exchange rate in 3 months < 1.6192: outcome without hedging is better
  • If exchange rate in 3 months > 1.6192: outcome with hedging is better

• 某投资者持有 1,000 股微软股票，当前每股价值 28 美元。一份执行价格为 27.50 美元的 2 个月期看跌期权价格为 1 美元。
• 投资者决定买入 10 张看跌期权合约（每张 100 股）进行套期保值。

• 股价 $20：行使看跌期权，以 $27.50 卖出 1,000 股：$27,500 − $1,000 = $26,500
• 股价 $35：看跌期权作废，在市场上卖出股票得 $35,000 − $1,000 = $34,000

• An investor owns 1,000 Microsoft shares currently worth $28 per share. A two-month put with a strike price of $27.50 costs $1.
• The investor decides to hedge by buying 10 put option contracts (100 shares each).

• Stock price $20: exercise the puts, sell 1,000 shares at $27.50: $27,500 − $1,000 = $26,500
• Stock price $35: puts expire worthless, sell the shares for $35,000 − $1,000 = $34,000

• 一位美国投机者认为英镑 (£) 将在未来 2 个月内升值，并愿意投机 250,000 英镑。
• 有哪些可选策略？
  • 今天买入 250,000 英镑，存入生息账户，日后再卖出。
  • 持有英镑期货合约的多头头寸。
• 两种策略的盈亏相同；区别在于
  • 买入英镑需要前期投资（例如即期汇率 1.4400 时需 360,000 美元）
  • 期货策略所需的前期投资较少（仅需保证金）：以杠杆建立大额投机头寸（例如 4 张 CME 合约，每张 62,500 英镑，保证金每张 5,000 美元，共 20,000 美元）

• A US speculator believes that the £ will rise over the next 2 months and he is willing to speculate on £250,000.
• What are the alternative strategies?
  • Buy £250,000 today, invest them in an interest-bearing account and sell it later.
  • Long position in futures contracts on £.
• The profit/loss from both strategies is the same; the difference is that
  • Buying £ requires up-front investment (e.g. $360,000 at a spot rate of 1.4400)
  • The futures strategy requires less up-front investment (only margin): leverage to take a large speculative position (e.g. 4 CME contracts of £62,500 with $5,000 margin each = $20,000)

• 某投资者有 2,000 美元可供投资，预期亚马逊 (Amazon.com) 的价值将在未来 2 个月内上升。当前股价为 20 美元，执行价格为 22.50 美元的 2 个月期看涨期权价格为 1 美元。有哪些可选策略？
  • 买入 100 股股票
  • 买入 20 张看涨期权合约（2,000 份看涨期权）

• An investor with $2,000 to invest expects the value of Amazon.com to increase over the next 2 months. The current stock price is $20 and the price of a 2-month call option with a strike of $22.50 is $1. What are the alternative strategies?
  • Buy 100 shares
  • Long 20 call option contracts (2,000 call options)

• $S_0=\mathrm{\$}20$；2 个月期、执行价格 $K=\mathrm{\$}22.50$ 的看涨期权价格为 $c=\mathrm{\$}1.00$。投资预算 $2,000。
• 策略 A：以 $2,000 买入 100 股股票。策略 B：以 $2,000 买入 2,000 份看涨期权（20 张合约）。
• 2 个月后的不同情景：

  到期股票价格	策略 A (买入 100 股股票)	策略 B (买入 2,000 份看涨期权)
  下跌至 $15	持仓市值 $1,500 (亏损：-$500 / -25%)	期权价值 $0 (全额亏损：-$2,000 / -100%)
  上涨至 $27	持仓市值 $2,700 (盈利：+$700 / +35%)	期权价值 $2,000\times \mathrm{\$}4.50=\mathrm{\$}9,000$ (盈利：+$7,000 / +350%)

• $S_0=\mathrm{\$}20$; 2-month call with strike $K=\mathrm{\$}22.50$ costs $c=\mathrm{\$}1.00$. Budget $2,000.
• Strategy A: buy 100 shares for $2,000. Strategy B: buy 2,000 call options (20 contracts) for $2,000.
• Outcome scenarios at 2 months:

  Terminal Stock Price	Strategy A (100 Shares)	Strategy B (2,000 Calls)
  Drops to $15	Value $1,500 (Loss: -$500 / -25%)	Value $0 (Total Loss: -$2,000 / -100%)
  Rises to $27	Value $2,700 (Gain: +$700 / +35%)	Value $2,000\times \mathrm{\$}4.50=\mathrm{\$}9,000$ (Gain: +$7,000 / +350%)

• 期货投机特征：
  • 前期资本投入极小（仅需缴纳履约保证金）。
  • 线性损益结构：潜在收益无上限，但潜在亏损同样无底线，且可能远远超过最初存入的保证金本金。
• 期权投机特征：
  • 前期最大损失严格限定于已支付的期权费权利金。
  • 非线性损益结构：潜在收益无上限；下行亏损有限，最大仅为 100% 权利金；上行杠杆在股价大幅突破时可带来数倍爆发性回报（>300%）。
  • 但前提是股价必须大幅超越执行价格，足以抵消购买期权所支付的时间价值。

• Futures Speculation:
  • Small upfront investment (only margin deposit required).
  • Linear payoff: Potential gain is unlimited, but potential loss is also unlimited and can exceed initial margin.
• Options Speculation:
  • Upfront cost is strictly limited to the option premium paid.
  • Non-linear payoff: Potential gain is unlimited, while downside loss is strictly capped at 100% of premium (limited loss); upside leverage can deliver explosive returns (>300%).
  • However, requires stock to move significantly beyond the strike price to overcome the time value paid.

• 假设：黄金现货价格 $S=\mathrm{\$}1,390$/盎司，1 年期年利率 $r=5\mathrm{\%}$（单利），黄金没有收益也没有仓储成本。
• 市场上 1 年期黄金期货报价：$F_{\text{mkt}}=\mathrm{\$}1,485$。
• 理论远期价格：$F_{\text{theor}}=\mathrm{\$}1,390\times (1+0.05)=\mathrm{\$}1,459.50$。
• 由于 $F_{\text{mkt}}>F_{\text{theor}}$，黄金期货价格被高估！是否存在套利机会？有：“现货-期货正向套利 (Cash-and-Carry)”。

  现在 ($t=0$)	1 年后 ($T=1$)
  以 5% 年利率借入 $1,390，期限 1 年	偿还贷款：$\mathrm{\$}1,390\times 1.05=-\mathrm{\$}1,459.50$
  以 $1,390 买入 1 盎司黄金	按期货合约交付黄金
  以 $1,485 卖出（做空）1 年期黄金期货合约	收取期货价格：$+\mathrm{\$}1,485.00$
  今日净现金流 = $0	套利利润 = $(1,485 − 1,459.50) = 每盎司 $25.50

• Assume: spot price of gold $S=\mathrm{\$}1,390$/oz, 1-year interest rate $r=5\mathrm{\%}$ per annum (simple interest), no income or storage costs for gold.
• Quoted 1-year futures price: $F_{\text{mkt}}=\mathrm{\$}1,485$.
• Theoretical forward price: $F_{\text{theor}}=\mathrm{\$}1,390\times (1+0.05)=\mathrm{\$}1,459.50$.
• Since $F_{\text{mkt}}>F_{\text{theor}}$, gold futures are overpriced! Is there an arbitrage opportunity? Yes: “cash-and-carry” arbitrage.

  Now ($t=0$)	After 1 year ($T=1$)
  Borrow $1,390 at 5% p.a. for 1 year	Repay the loan: $\mathrm{\$}1,390\times 1.05=-\mathrm{\$}1,459.50$
  Buy 1 oz of gold for $1,390	Deliver the gold under the futures contract
  Short a 1-year gold futures contract at $1,485	Receive the futures price: $+\mathrm{\$}1,485.00$
  Net cash flow today = $0	Arbitrage profit = $(1,485 − 1,459.50) = $25.50 per oz

• 假设：$S=\mathrm{\$}1,390$/盎司，$r=5\mathrm{\%}$，黄金没有收益也没有仓储成本；$F_{\text{theor}}=\mathrm{\$}1,459.50$。
• 市场上 1 年期黄金期货报价：$F_{\text{mkt}}=\mathrm{\$}1,390$。
• 由于 $F_{\text{mkt}}<F_{\text{theor}}$，黄金期货价格被低估！是否存在套利机会？有：“反向现货-期货套利 (Reverse Cash-and-Carry)”。

  现在 ($t=0$)	1 年后 ($T=1$)
  卖出（卖空）黄金，得到 $1,390	按期货合约接受黄金交割
  将 $1,390 按 5% 年利率投资 1 年	投资增长为：$\mathrm{\$}1,390\times 1.05=+\mathrm{\$}1,459.50$
  以 $1,390 买入 1 年期黄金期货合约（多头）	支付期货价格：$-\mathrm{\$}1,390.00$
  今日净现金流 = $0	套利利润 = $(1,459.50 − 1,390) = 每盎司 $69.50

• Assume: $S=\mathrm{\$}1,390$/oz, $r=5\mathrm{\%}$ per annum, no income or storage costs for gold; $F_{\text{theor}}=\mathrm{\$}1,459.50$.
• Quoted 1-year futures price: $F_{\text{mkt}}=\mathrm{\$}1,390$.
• Since $F_{\text{mkt}}<F_{\text{theor}}$, gold futures are underpriced! Is there an arbitrage opportunity? Yes: “reverse cash-and-carry” arbitrage.

  Now ($t=0$)	After 1 year ($T=1$)
  Sell (short sell) gold for $1,390	Take delivery of gold under the futures contract
  Invest $1,390 at 5% p.a. for 1 year	Investment grows to $\mathrm{\$}1,390\times 1.05=+\mathrm{\$}1,459.50$
  Long a 1-year gold futures contract at $1,390	Pay the futures price: $-\mathrm{\$}1,390.00$
  Net cash flow today = $0	Arbitrage profit = $(1,459.50 − 1,390) = $69.50 per oz

• 期货价格应该是多少？
• 若黄金现货价格为 $S$，一份 $T$ 年后交割的期货合约的期货价格为 $F$，则
  $$F=S(1+r{)}^T$$
  其中 $r$ 为 1 年期（本币）单利利率。
• 在我们的例子中，$S=\mathrm{\$}1,390$，$T=1$，$r=0.05$，因此 $F=\mathrm{\$}1,390(1+0.05)=\mathrm{\$}1,459.50$。
• 若 $F>S(1+r{)}^T$：套利者借款买入现货并做空期货（正向现货-期货套利 Cash-and-Carry）。
• 若 $F<S(1+r{)}^T$：套利者卖空现货、贷出所得资金并买入期货（反向现货-期货套利 Reverse Cash-and-Carry）。
• 若采用连续复利（Hull 记号），同一关系写作 $F_0=S_0{e}^{rT}$。

• What should the futures price be?
• If the spot price of gold is $S$ and the futures price for a contract deliverable in $T$ years is $F$, then
  $$F=S(1+r{)}^T$$
  where $r$ is the 1-year (domestic currency) simple interest rate.
• In our examples, $S=\mathrm{\$}1,390$, $T=1$ and $r=0.05$, so that $F=\mathrm{\$}1,390(1+0.05)=\mathrm{\$}1,459.50$.
• If $F>S(1+r{)}^T$: arbitrageurs borrow, buy spot, short futures (cash-and-carry).
• If $F<S(1+r{)}^T$: arbitrageurs short spot, lend the proceeds, buy futures (reverse cash-and-carry).
• With continuous compounding (Hull's notation) the same relation reads $F_0=S_0{e}^{rT}$.

• 参数设定： 原油即期现货价格 $S=\mathrm{\$}85$，利率 $r=5\mathrm{\%}$ p.a.，年化仓储成本 $u=2\mathrm{\%}$ p.a.。
• 情景 1：1 年期期货市场报价 $F=\mathrm{\$}93$：
  • 持有成本决定的理论价格上限：$F_{\text{max}}=85\times (1+0.05+0.02)=\mathrm{\$}90.95$。
  • 由于 $\mathrm{\$}93>\mathrm{\$}90.95$，正向现货-期货套利完全可行（借款、买入原油、储存储备、做空期货 → 锁定确定性无风险利润）。
• 情景 2：1 年期期货市场报价 $F=\mathrm{\$}82$：
  • 此时是否存在无风险套利机会？不存在！
  • 反向现货-期货套利不可行（原油是消费性资产，并非总能卖空）：普通市场参与者极难在现货市场直接借入并卖空实物原油；而商业库存持有者由于需要维持生产运营的便利收益 (Convenience Yield)，也不愿清空出售现货库存。

• Setup: Spot oil $S=\mathrm{\$}85$, $r=5\mathrm{\%}$ p.a., storage cost $u=2\mathrm{\%}$ p.a.
• Scenario 1: Quoted 1-year futures $F=\mathrm{\$}93$:
  • Cost of carry upper bound: $F_{\text{max}}=85\times (1+0.05+0.02)=\mathrm{\$}90.95$.
  • Since $\mathrm{\$}93>\mathrm{\$}90.95$, cash-and-carry arbitrage WORKS (borrow, buy oil, store, sell futures → guaranteed profit).
• Scenario 2: Quoted 1-year futures $F=\mathrm{\$}82$:
  • Is there an arbitrage opportunity? NO!
  • Reverse cash-and-carry is not available: short-selling oil is not always possible because oil is a consumption asset – market participants cannot easily short sell physical crude oil, and commercial inventory holders will not sell stock due to operational convenience yield.