金融工程原理-future hedge (2)

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第二章金融工程基本原理《金融工程》PPT课件

➢ 套利机会存在的条件： ➢ （1）如果存在两个资产组合，它们的未来收益（现金流）
相同，但它们的成本（价格）不同，这时市场存在套利机会。 ➢ （2）如果存在两个相同成本（价格）的组合，第一个组合在所有状态下的收益都不低于第二个组合，而且至少存在一种状态，在此状态下第一个组合的收益大于第二个组合，这时市场存在套利机会。 ➢ （3）如果一个组合的构建成本为0，但在所有状态下这个组合的收益都不小于0，而且至少存在一种状态，在此状态下这个组合的收益大于0，则市场存在套利机会。
90
无风险资产：
1 1
1
144 108 81
1 1 1
B：
PB
128
PB1 110
PB2
101
16
无套利定价原理的应用
复制策略的确定用倒推法：
（1）在t=0.5时刻：
当PA＝120时：144x y 128
x 0.5
108x y 110
y 56
PB1 120 0.5 56 116
当PA＝90时：
0 -1个B：-101
合计：
0
1/3A： 27
存款： 74
020
第二节风险中性定价方法
一、风险中性的概念 ➢ 公平博彩 ➢ 如果一个参加者，他刚好可以接受这样一个统计意
义上的公平博彩，他就是风险中性的 ➢ 风险中性投资者投资于风险证券，不需要风险补偿
，只要收益率等于无风险利率就可以了 ➢ 如果市场上的投资者都是风险中性的，则任何一个
持有证券B空头持有动态复制策略多头
-1个B：-128 0.5A： 72 存款： 56
卖出B： 110元买入0.4A：-40元存款68元：-68 合计： 2

金融工程常用术语(中英对照)

金融工程常用术语中英对照AABS Asset-Backed Security 资产支持证券ABS CDO 由ABS所派生出的份额产品Accrual Swap 计息互换Accrued Interest 应计利息Actuaries 保险精算师Adaptive Mesh Model 自适应网格模型Adjusted Present Value 调整现值法Adverse Selection 逆向选择After-tax Interest Rate 税后利润Agency Costs 代理费用American Option 美式期权Amortization 分期偿付Amortization Schedule 分期偿付时间表Amortizing Swap 分期偿还互换Analytic Result 解析结果APR Annual Percentage Rate 年度百分率Annualized Capital Cost 按年折算的资本成本Arbitrage 套利Arbitrageur 套利者Asian Option 亚式期权Ask Price 卖盘价Asset 资产Asset Allocation 资产分配Asset-or-Nothing Call Option 资产或空手看涨期权Asset-or-Nothing Put Option 资产或空手看跌期权Asset Swap 资产互换As-You-Like-It Option 任选期权At-the-Money Option 平值期权Average Price Call Option 平均价格看涨期权Average Price Put Option 平均价格看跌期权Average Strike Option 平均执行价格期权BBackdating 倒填日期Back Testing 回顾测试Backwards Induction 倒推归纳Barrier Option 障碍期权Base Correlation 基础相关系数Basel Committee 巴塞尔委员会Basis 基差Basis Point 基点Basis Risk 基差风险Basis Swap 基差互换Basket Credit Default Swap 篮筐式信用违约互换Basket Option 篮筐式期权Bear Spread 熊市差价Bermudan Option 百慕大式期权Before-tax Interest Rate 税前利率Beta 贝塔Bid-Ask Spread 买入卖出差价Bid Price 买入价Bilateral Clearing 双边结算Binary Credit Default Swap 两点式信用违约互换Binary Option 两值期权Binomial Model 二项式模型Binomial Option Pricing Model 二项期权定价模型Binomial Tree 二叉树Bivariate Normal Distribution 二元正态分布Black’s Approximation 布莱克近似Black’s Model 布莱克模型Black-Scholes-Merton Model 布莱克-斯科尔斯-莫顿模型Bond Option 债券期权Bond Yield 债券收益率Book Value 账面价值Bootstrap Method 票息剥离方法Boston Option 波士顿期权BOT Build-Operate-Transfer 建设-经营-转让Box Spread 合式差价Break-even point 盈亏平衡点Break Forward 断点远期Brownian Motion 布朗运动Bull Spread 牛市差价Butterfly Spread 蝶式差价CCalendar Spread 日历差价Calibration 校正Callable Bond 可赎回债券Call Option 看涨期权Cancelable Swap 可取消互换Cap 上限Cap Rate 上限利率CAPM Capital Asset Pricing Model 资本资产定价模型Caplet 上限单元Capital gain 资本收藏Capital less 资本损失Capital Market 资本市场Capital Market Line 资本市场线Caps 赔付限额Case-Shiller Index 凯斯-席勒指数Cash budget 现金预算Cash cycle time 现金周转时间Cash Dividend 现金股利Cash Flow Mapping 现金流映射Cash-or-Nothing Call Option 现金或空手看涨期权Cash-or-Nothing Put Option 现金或空手看跌期权Cash Settlement 现金交割或现金清算CCP Central Clearing Party 中央结算对手CDD Cooling Degree Days 降温天数CDO Collateralized Debt Obligation 债务抵押债券CDS Credit Default Swap 信用违约互换CEBO Credit Event Binary Option 信用事件两点式期权Central Clearing 中心结算Central Clearing Party 中央结算对手Central Counterparty 中央交易对手CEV Model Constant Elasticity of Variance Model 常方差弹性模型Cheapest-to-Deliver Bond 最便宜可交割债券Cholesky Decomposition 乔里斯基分解Chooser Option 选择人期权Class of Options 期权分类Clean Price of Bond 债券除息价格Clearing House 结算中心Clearing Margin 结算保证金Cliquet Option 棘轮期权CMO Collateralized Mortgage Obligation 见房产抵押债券CMS Constant Maturity Swap 固定期限国债互换Collar 双限Collateral 抵押品Collateralization 抵押品策略Collateralized Debt Obligation 债务抵押债券Collateralized Mortgage Obligation 房产抵押债券Combination 组合Commercial Banks 商业银行Commercial Loan Rate 商业贷款利率Commodity Futures Trading Commission 商品期货交易管理委员会Commodity Swap 商品互换Compound Interest 复利Compounding 复利计息Compounding Frequency 复利利率Compound Correlation 复合相关系数Compound Option 复合期权Confidence interval 置信区间Continuous Probability Distribution 连续概率分布Confirmation 交易确认书Consumption Asset 消费资产Contango 期货溢价Continuous Compounding 连续复利Control Variate Technique 控制变量技术Convenience Yield 便利收益率Conversion Factor 转换因子Convertible Bond 可转换债券Convexity 曲率Convexity Adjustment 曲率调整Cornish-Fisher Expansion 科尼什-费雪展开Copayments 赔付比例Corporation 公司Correlation 相关性Cost of Capital 资本成本Cost of Carry 持有成本Controller 审计官Counterparty 交易对手Coupon 券息Coupon bond 付息债券Covariance 协方差Covarance Matrix 协方差矩阵Covered Call 备保看涨期权Crash phobia 暴跌恐惧症Credit Contagion 信用蔓延Credit Default Swap 信用违约互换Credit Derivative 信用衍生产品Credit Event 信用事件Credit Event Binary Option 信用事件两点式期权Credit Index 信用指数Credit Rating 信用等级Credit Ratings Transition Matrix 信用评级转移矩阵Credit Risk 信用风险Credit Spread Option 信用差价期权CSA Credit Support Annex 信用支持附约CVA Credit Value Adjustment 信用价值调节量Credit Value at Risk 信用风险价值度Cross Hedging 交叉对冲Currency Swap 货币互换Current yield 本期收益率DDay Count 计天方式Day Trade 即日交易DCF Discounted Cash flow Model 现金流折现模型DDM Dividend Discount Model 股利贴现模型DVA Debt Value Adjustment 债务价值调节量Decision Tree 决策树Deductible 免赔额Default Risk 违约风险Defined-benefit Pension Plan 规定受益型养老金计划Defined-contribution Pension Plan 规定缴费型养老金计划Delivery Price 交割价格Delta Hedging Delta对冲Delta-Neutral Portfolio Delta 中性交易组合Derivative 衍生产品Deterministic Variable 确定性变量Diagonal Spread 对角差价Differential Swap 交叉货币度量互换Diffusion Process 扩散过程Dirty Price of Bond 带息价格Discount Bond 折扣债券Discount Instrument 折扣产品Discounted Cash Flow Analysis 贴现现金流分析Discounted Dividend Model 股利贴现模型Diversifiable Risk 可分散风险Diversification 分散化Diversification Principle 分散化原则Diversifying 分散投资Discount Rate 贴现率Dividend 股息Dividend Yield 股息收益率Dodd-Frank Act 多德-弗兰克法案Dollar Duration 绝对额久期DOOM Option DOOM期权Down-and-In Option 下降-敲入期权Down-and-Out Option 下降-敲出期权Downgrade Trigger 降级触发Drift Rate 漂移变化率Duration 久期Duration Matching 久期匹配Dynamic Hedging 动态对冲EEAR/ EFF Effective Annual Rate 实际年利率Early Exercise 提前行使EBIT Earnings Before Interest and Tax 息税前利润Effective Federal Funds Rate 有效联邦基金利率Efficient Portfolio 有效投资组合Efficient Portfolio Frontier 有效投资组合边界Electronic Trading 电子交易Embedded Option 内含期权EMH Efficient Markets Hypothesis 有效市场假说Empirical Research 实证研究Employee Stock Option 雇员股票期权Equilibrium Model 均衡模型Equity Swap 股权互换Equity Tranche 股权份额Equivalent Annual Interest Rate 等价年利率Eurocurrency 欧洲货币Eurodollar 欧洲美元Eurodollar Futures Contract 欧洲美元期货合约Eurodollar Interest Rate 欧洲美元利率Euro LIBOR 欧元同业拆借利率European Option 欧式期权Exchange Option 互换期权Exchange Rate 汇率Exclusions 免赔条款Ex-dividend Date 除息日Exercise Limit 行使限额Exercise Multiple 行使倍数Exercise Price 执行价格Exotic Option 特种期权Expectations Theory 预期理论Expected Shortfall 预期亏损Expected Rate of Return 预期回报率Expected Value of a Variable 变量的期望值Expiration Date 到期日Explicit Finite Difference Method 显式有限差分方法Exponentially Weighted Moving Average Model 指数加权移动平均模型Exponential Weighting 指数加权Exposure 风险敞口Extendable Bond 可展期债券Extendable Swap 可延期互换External Financing 外部投资FFace Value 面值Factor 因子Factor Analysis 因子分析Federal Funds Rate 联邦基金利率FEI Financial Executives Institute 财务执行官组织Finance 金融学Financial Futures 金融期货Financial Guarantees 财务担保Financial Intermediary 金融媒介Financial System 金融系统Finite Difference Method 有限差分法Fixed-Income Instrument 固定收益证券Flat Volatility 单一波动率Flex Option 灵活期权Flexi Cap Flexi上限Floor 下限Floor-Ceiling Agreement 下限上限协议Floor let 下限单元Floor Rate 下限利率Flow of funds 资金流Foreign Currency Option 外汇期权Forward Contract 远期合约Forward Exchange Rate 远期汇率Forward Interest Rate 远期利率Forward Price 远期价格Forward Rate 远期率FRA Forward Rate Agreement 远期利率合约Forward Risk-Neutral World 远期风险中性世界Forward Start Option 远期开始期权Forward Swap 远期互换Fundamental Value 基本价值Futures Commission Merchants 期货佣金经纪人Futures Contract 期货合约Futures Option 期货期权Futures-Style Option 期货式期权FV Final Value 终值GGrowth annuity 增长年金GAP Management 制品管理Gap Option 缺口期权Gaussian Copula Model 高斯Copula 模型Gaussian Quadrature 高斯求积公式Generalize Wiener Process 广义维纳过程Geometric Average 几何平均Geometric Brownian Motion 几何布朗运动Girsanov’s Theorem 哥萨诺夫定理Guaranty Fund 担保基金HHaircut 折扣Hazard Rate 风险率Hedge 对冲Hedge Funds 对冲基金Hedger 对冲者Hedge Ratio 对冲比率Hedgers 套期保值者Historical Simulation 历史模拟Historical Volatility 历史波动率Holiday Calendar 假期日历Human Capital 人力资本IImmediate Annuity 即时年金Implicit Finite Difference Method 隐式有限差分Implied Correlation 隐含相关系数Implied Distribution 隐含分布Implied Dividend 隐含股利Implied Tree 隐含树形Implied Volatility 隐含波动率Inception Profit 起始盈利Index Amortizing Swap 指数递减互换Index Arbitrage 指数套利Index Futures 指数期货Index-linked Bonds 指数化债券Index Option 指数期权Index Principal Swap 指数本金互换Initial Margin 初始保证金Instantaneous Forward Rate 瞬时远期利率Insuring 保险Intangible Assets 无形资产Interest-rate Arbitrage 利率套利Interest Rate Cap 利率上限Interest Rate Collar 利率双限Interest Rate Derivative 利率衍生产品Interest Rate Floor 利率下限Interest Rate Swap 利率互换Internal Financing 内部融资International Swap and Derivatives Association 国际互换和衍生产品协会In-the-Money Option 实值期权Intrinsic Value 内涵价值Inverted Market 反向市场Investment Asset 投资资产Investment Banks 投资银行ISDA International Swap and Derivatives Association 国际互换和衍生产品协会IRR Internal Rate of Return 内部收益率JJump-Diffusion Model 跳跃扩散模型Jump Process 跳跃过程LLaw of One Price 一价原则Liability 负债LIBID London Inter Bank Bid Rate 伦敦同业借款利率LIBOR London Inter Bank Offered Rate 伦敦同业拆出利率LIBOR Curve LIBOR曲线LIBOR-in-Arrears Swap LIBOR后置互换Life Annuity 人寿年金Limited Liability 有限责任Limit Move 涨跌停版变动Limit Order 限价指令Liquidity 流动性Liquidity Preference Theory 流动性偏好理论Liquidity Premium 流动性溢价Liquidity Risk 流动性风险Locals 自营经纪人Lognormal Distribution 对数正态分布Long Hedge 多头对冲Long Position 多头Look back option 回望期权Low Discrepancy Sequence 低偏差序列MMaintenance Margin 维持保证金Margin 保证金Margin Call 保证金催付Market Capitalization Rate 市场资本化利率MSU Market-Leveraged Stock Unit 市场股票凭据Market Maker 做市商Market Model 市场模型Market Portfolio 市场投资组合Market Price of Risk 风险市场价格Market Segmentation Theory 市场分隔理论Market-weighted Stock Indexes 市场加权股票指数Marking to Market 按市场定价Markov Process 马尔科夫过程Martingale 鞅Maturity 期限Maturity Date 到期日Maximum Likelihood Method 极大似然方法Mean Reversion 均值回归Measure 测度Merger 合并Mezzanine Tranche 中层份额Minimum Variance 最小方差组合Modified Duration 修正久期Money Market 货币市场Money Market Account 货币市场帐户Monte Carlo Simulation 蒙特卡罗模拟Moral Hazard 道德风险Mortgage-Backed Security 房产抵押贷款证券Mutual Fund 共同基金NNaked Position 裸露期权Netting 净额结算Net Present Value 净现值Net Worth 净资产No-Arbitrage Assumption 无套利假设No-Arbitrage Interest Rate Model 无套利假设Nominal Future Value 名义终值Nominal Interest Rate 名义利率Nominal Prices 名义价格Nondiversifiable Risk 不可分割风险Nonstationary Model 非平稳模型Non Systemic Risk 非系统风险Normal Backwardation 正常现货溢价NPV Net Present Value 净现值Normal Distribution 正态分布Normal Market 正常市场Notional Principal 面值（本金）Numeraire 计价单位Numerical Procedure 数值方法OOCC Option Clearing Corporation 期权结算中心Offer Price 卖出价格Open Interest 未平仓合约Open Outcry 公开喊价Opportunity Cost of Capital 资金的机会成本Optimal Combination of risky assets 风险资产的最优组合Option 期权Option-Adjusted Spread 期权调整差价Option Class 期权种类Ordinary Annuity 普通年金Out-of-the-Money Option 虚值期权Overnight Indexed Swap 隔夜指数互换Over-the-Counter Market 场外交易市场PPackage 组合期权Par bonds 等价债券Par Value 面值Par Yield 面值收益Parallel Shift 平行移动Parisian Option 巴黎期权Partnership 合伙制Path-Dependent Option 路径依赖型期权Payoff 收益Pay off Diagram 收益图Percent-of-sales method 销售收入百分比法Permanent Income 持久收入Perpetuity 永续年金Perpetual Derivatives 永续衍生品Portfolio Immunization 组合免疫Portfolio Insurance 证券组合保险Portfolio selection 投资组合选择Portfolio theory 投资组合理论Position Limit 头寸限额Premium 期权付费Premium Bond 溢价债券Present Value 现值Principal-agent Problem 委托人-代理人问题Prepayment Function 提前偿付函数Principal 本金Principal Components Analysis 主因子分析Principal Protected Notes 保本型证券Probability Distributions 概念分布Program Trading 程序交易Protective Put 保护看跌期权Pull-to-Par 收敛于面值现象Purchasing-power Parity 购买力评价Pure Discount Bonds 纯贴现债券Put-Call Parity 看跌-看涨期权平价关系式Put Option 看跌期权Puttable Bond 可提前退还债券Puttable Swap 可赎回互换President 总裁PMT Payment（Returns the periodic payment for an annuity）年金PPP Public-Private Partnership 政府和社会资本合作PV Present Value 现值QQuansi-Random Sequences 伪随机序列RRate of Return on capital 资本收益率Rainbow Option 彩虹期权Range-Forward Contract 远期范围合约Ratchet Cap 执行价格调整上限Real Future Value 实际终值Real Interest Rate 实际利率Real Option 实物期权Real Prices 实际价格Rebalancing 再平衡Recovery Rate 回收率Reference Entity 参考实体Reinvestment Rate 再投资利率Residual Claim 剩余索取权Repo 再回购Repo Rate 再回购利率Reset Date 重置日（定息日）RSU Restricted Stock Unit 受限股票单位Reversion Level 回归水平Risk Aversion 风险厌恶Risk-adjusted discount rate 风险调整贴现率Risk Exposure 风险暴露Rights Issue 优先权证Risk-Free Rate 无风险利率Risk Management 风险管理Risk Management Process 风险管理过程Risk-Neutral Valuation 风险中性定价Risk-Neutral World 风险中性世界Roll Back 倒推ROS Ratio of income as percentage of sales 销售利润率ROA Return On Assets 资产收益率ROE Rate of Return on Common Stockholders’ Equity 净资产收益率SScalper 投机者Scenario Analysis 情形分析Securitization 证券化Security Market Line 证券市场线Sensitivity Analysis 敏感性分析Self-financing Investment Strategy 自筹资金投资策略Settlement Price 结算价格Share Repurchase 股票回购Short Hedge 空头头寸对冲Short Position 空头头寸Short Rate 短期利率Short Selling 卖空交易Short-Term Risk-Free Rate 短期无风险利率Shout Option 喊价期权Simple Interest 单利Sole Proprietorship 独资企业Specialist 专家Speculator 投机者Spot futures price parity relation 现货期货价格平价关系。

《金融工程原理-无套利均衡分析》笔记01---精品管理资料

《金融工程原理－无套利均衡分析》笔记宋逢明第一章无套利均衡分析方法本章重点介绍以下内容：MM命题及无套利均衡分析方法金融产品：包括金融商品(也称为金融工具或有价证券等，如股票、债券、期货、期权、以及互换等）,也包括金融服务(如结算、清算、发行、承销等）。

金融研究的一项核心内容:对金融市场中某项“头寸”进行估值和定价.无套利分析方法（50年代后期，莫迪格里安尼（F。

Modigliani)和米勒（M。

Miller）在研究企业资本结构和企业价值关系时提出的。

分析的基本方法是将这项头寸与市场中其他金融资产头寸组合起来,构建一个在市场均衡时不能产生无风险利润的投资组合，由此测算出该项头寸在市场均衡时的价值即均衡价格.当市场处于非均衡状态时，价格偏离了由供求关系所决定的价值，此时就出现了套利机会.当市场出现套利机会时，所有的市场参与者均会抓住机会套取无风险利润，套利机会很快就会消失，市场重新恢复均衡状态.市场效率越高,重建均衡的速度就越快。

简单地说，当市场处于非均衡状态时，就会出现无风险套利机会；而当市场处于均衡状态时，无风险套利机会消失。

金融工程的核心技术之一：组合分解技术组合分解技术实质上就是用一组金融工具来“复制"另一组金融工具的技术，也就是无套利均衡分析方法的具体化.资本结构及资产负债表融资方式在公司投资于一种资产之前,必须首先获得资金，即融资。

这意味着公司必须筹集资金来支付投资.资产负债表的右边表示公司的融资方式。

公司一般通过发行债券、借款或发行股票来筹集资金，分为负债和和股东权益。

债务证券是公司向债权人借款的债务合同。

权益证券(如普通股和优先股）,是股东对公司剩余现金流量的非合同式索取权。

公司公开发售的股票和债券可以在金融市场上出售。

公司的融资是在金融市场上完成的.按期限的长短可以将负债划分为：短期负债和长期负债短期负债的期限不过一年,一年内必须偿还贷款和债务。

长期负债的期限为一年以上，一年内不必偿还贷款的债务。

金融工程学名词解释

1、头寸指投资人根据其对某一项资产未来价值走势的判断而持有的买入或者卖出该资产的立场在交易中所持有的买卖合约数2、期货(Futures)是包含金融工具或未来交割实物商品销售（一般在商品交易所进行）的金融合约。

期货合约对一种指数或商品在未来某一日期的价值。

吃货指庄家在低价时暗中买进股票，叫做吃货。

3.对冲对冲（hedge）指特意减低另一项投资的风险的投资。

它是一种在减低商业风险的同时仍然能在投资中获利的手法。

一般对冲是同时进行两笔行情相关、方向相反、数量相当、盈亏相抵的交易。

4.远期汇率远期汇率也称期汇率，是交易双方达成外汇买卖协议，约定在未来某一时间进行外汇实际交割所使用的汇率。

5.债券可转让的债务证券，通常是由政府或者准政府机构为筹资而发行。

债券的持有人将资金借贷出去一个特定时期以获得固定的利率。

债券的本息在事先约定的到期日得到偿还。

债券可以在股票市场上交易转让。

6、股票是股份证书的简称，是股份公司为筹集资金而发行给股东作为持股凭证并借以取得股息和红利的一种有价证券。

每股股票都代表股东对企业拥有一个基本单位的所有权。

7.实物期券实物期权，一种期权，其底层证券是既非股票又非期货的实物商品。

这实物商品自身（货币，债券，货物）构成了该期权的底层实体。

8.远期交易远期交易（Forward Transaction）是指买卖双方签订远期合同，规定在未来某一时期进行交易的一种交易方式。

9.风险杠率指在同样的空方或者多方头寸时，由于投资人采用了不同的方式，使其承担的风险放大了不同的比例10远期合约是20世纪80年代初兴起的一种保值工具，它是一种交易双方约定在未来的某一确定时间，以确定的价格买卖一定数量的某种金融资产的合约。

合约中要规定交易的标的物、有效期和交割时的执行价格等项内容。

11、商品期货商品期货是指标的物为实物商品的期货合约。

商品期货交易，是在期货交易所内买卖特定商品的标准化合同的交易方式。

12.外汇期货外汇期货，又称为货币期货，是一种在最终交易日按照当时的汇率将一种货币兑换成另外一种货币的期货合约。

《金融工程》第2章金融工程的基本框架与分析方法

低于某一水平，交易者必须按时补齐到起始水平。
否则，交易所将会强行平仓。而远期合约则无需
开立保证金账户。
➢ 期货合约的逐日盯市和保证金制度的结合使用，
使得期货合约与相同到期日的远期合约相比，其
信用风险大大减少。

4、期权合约
期权合约使其持有者有权在预定的日期按预定的
价格买卖某种资产。

涨
未来有权利买资产
合的，则为保值结果。

注1：远期合约存在信用风险，而且信用风险是交易双方
都要承担的；
注2：远期合约在到期之前，双方不存在任何现金支付。

3、期货合约
与远期合约一样，期货合约也使它的交易者能按
预定的价格在规定的到期日买卖某种资产，也可
区分为多头交易和空头交易。
因此期货合约的损益图与远期合约的损益图一致。
第一步：套利者借入一笔1年期资金（假定为10万元），
利率为8%；
第二步：签订远期利率合约，规定该交易者可按9%的价
格1年后从市场借入资金10.08万元；
第三步：按10%的利率贷出10万元资金2年期；
第四步：两年后收回2年期贷款，得本息12.1万元[10
(1+10%)2]，并用10.9872万元[10.08 (1+9%)]偿还1年
镑，偿还1.03英镑的本息后，获利0.02英镑。
这种套利活动的进行，势必会使英镑的利率上升，人民币
的利率下降，英镑即期汇率下跌，英镑远期汇率上升。因
此，1:8不是均衡的远期汇率。

3、金融工具定价
假设三个零息票债券面值均为100元，当前的市场价
格分别为：1年后到期的零息票债券当前价格为98元；

《金融工程》第四章远期与期货的运用

17
合约到期日的选择
一般原则：对于实物交割的期货而言，要避免
在期货到期的月份中持有期货头寸，以防止逼
仓。
在到期时间无法完全吻合时，通常选择比所需
的套期保值月份略晚但尽量接近的期货品种。
所需套期保值时间较长时，可使用套期保值展
期，但可能给套期保值者带来额外的风险。
18
合约数量的选择
相关性
规模的调整
数量 N 还应考虑具体头寸规模
N
n
QH
H
QH
QG
G
QG
rH
H0
QH
rH
VH
rG
G0
QG
rG
VG
（4.6）
需要交易的期货合约份数 N 就是使得现货头寸总
价值变动等于期货头寸总价值变动的量。
22
最小方差套保比率公式
如果我们将风险定义为“方差”，那么最小方差套保比率就
是最优套保比率。其计算公式为
2

n
时无法完全对冲的价格风险。
但通过套期保值，投资者将其所承担的风险由现
货价格的不确定变化转变为基差的不确定变化，
而基差变动的程度总是远远小于现货价格的变动
程度，因此不完美的套期保值虽然无法完全对冲
风险，但还是在很大程度上降低了风险。
14
基差的变化
表4-1
套期保值类型
多头套期保值
空头套期保值
套期保值盈利性与基差
可能由于期货合约的标准数量无法完全对冲现货的价
格风险。
讨论最优套期保值比率时，通常不考虑数量风险。
相比远期，期货更不易实现完美套期保值。
11
基差风险
1 单位现货空头 +1 单位期货多头的套保收益

hedge作为金融术语的解释

hedge作为金融术语的解释嘿，你知道吗，hedge 这个词在金融术语里可有着特别重要的意义呢！它就像是给你的财富上了一道保险！比如说吧，你有一大笔钱投资在股票市场里，就像你拥有了一艘在大海上航行的船（这就是个类比哦）。

可是大海的风浪是很难预测的呀，有时候会波涛汹涌。

这时候，hedge 就像是给你的船装上了一个稳定器。

想象一下，市场突然下跌，你的股票价值也跟着大幅缩水，哎呀，那可真让人头疼！但如果你提前使用了 hedge 策略，那就不一样啦！它能帮你减少这种损失呢。

就好比在大暴雨要来的时候，你提前准备好了雨伞，不至于被淋成落汤鸡。

hedge 可以通过很多方式来实现呀。

比如利用期货合约，这就好像你给自己的财富找了个“保镖”。

或者使用期权，这就像是给你的投资加上了一层“防护膜”。

很多聪明的投资者都会运用 hedge 呢！他们可不想让自己的财富像坐过山车一样大起大落。

他们会精心地规划和布局，就像下棋一样，每一步都深思熟虑。

“哎呀，我可不能让我的钱随便冒险，得用 hedge 来保护一下！”他们会这样说。

在金融的世界里，hedge 真的是太重要啦！它能让你在风云变幻的市场中更加从容不迫，不至于被风浪打得晕头转向。

难道你不想学习一下怎么运用它来保护自己的财富吗？我的观点很明确呀，hedge 就是
金融领域里的一个超级有用的工具，学会它，用好它，能让我们在投资的道路上走得更稳、更安心！。

金融工程--课后习题详解

⾦融⼯程--课后习题详解七．习题1. 布莱克－舒尔斯定价模型的主要缺陷有哪些？2. 交易成本的存在对期权价格有什么影响？3. 怎样理解下⾯这个观点：组合中⼀份衍⽣证券合约的价值往往取决于该组合中其他合约的价值？4. 什么是波动率微笑、波动率期限结构和波动率矩阵？它们的作⽤何在？5. 当波动率是随机的且和股票价格正相关时，⼈们在市场上可能会观察到怎样的隐含波动率？6. 假设⼀个股票价格遵循复合期权模型，隐含波动率会是怎样的形状？7. 如果我们对随机波动率的概念进⼀步深⼊下去，使得波动率的波动率也是随机的，结果会如何？8. 设前⼀天收盘时S&P500为1040，指数的每天波动率为1％，GARCH(1,1)模型中的参数为0.06α=，0.92β=，0.000002ω=。

如果当天收盘时S&P500为1060，则新的波动率估计为多少？（设µ＝0）9. 不确定参数模型的定价思想是什么？10. 如何理解跳跃扩散模型和崩盘模型？11. 期权交易者常常喜欢把深度虚值期权看作基于波动率的期权，为什么？答案：1. （1）交易成本的假设：BS 模型假定⽆交易成本，可以连续进⾏动态的套期保值，但事实上交易成本总是客观存在的。

（2）波动率为常数的假设：实际上波动率本⾝就是⼀个随机变量。

（3）不确定的参数：BS 模型假设波动率、利率、股利等参数都是已知的常数（或是已知的确定函数）。

但事实上它们都不是⼀个常数，最为典型的波动率甚⾄也不是⼀个时间和标的资产价格的确定函数，并且完全⽆法在市场观察到，也⽆法预测。

（4）资产价格的连续变动：在实际中，不连续是常见的，资产价格常常出现跳跃。

2. 交易成本的存在，会影响我们进⾏套期保值的次数和期权价格：交易成本⼀⽅⾯会使得调整次数受到限制，使基于连续组合调整的BS 模型定价成为⼀种近似；另⼀⽅⾯，交易成本也直接影响到期权价格本⾝，使得合理的期权价格成为⼀个区间⽽不是单个数值。

hedge金融术语意思

hedge金融术语意思
Hedge是对冲的意思。

金融学上，对冲（hedge）指特意减低另一项投资的风险的投资。

它是一种在减低商业风险的同时仍然能在投资中获利的手法。

一般对冲是同时进行两笔行情相关、方向相反、数量相当、盈亏相抵的交易。

行情相关是指影响两种商品价格行情的市场供求关系存在同一性，供求关系若发生变化，同时会影响两种商品的价格，且价格变化的方向大体一致。

方向相反指两笔交易的买卖方向相反，这样无论价格向什么方向变化，总是一盈一亏。

当然要做到盈亏相抵，两笔交易的数量大小须根据各自价格变动的幅度来确定，大体做到数量相当。

在金融交易当中的对冲，锁单交易。

这个交易手法是最常见也是最简单的“对冲”应用。

此方法多半是为了规避风险。

例如买外汇市场买进了人民币对美元（多头），但是发现于预期的方向相反了，但是手中的单子又不舍得平仓，并且估计可能价格还是会回来，此时就下一单卖出人民币对美元（空头），这样等于原来亏损的被锁住了，不管价格的涨跌永远只会亏损当前的这么多了。

那么其中高手就在于，能够有策略的解锁单子（看准时期交割单子），使得本来亏损的钱变成了盈利。

金融工程相关习题及答案

⾦融⼯程相关习题及答案Chapter 1 Market Organization and Structure PRACTICE PROBLEMS FOR CHAPTER 11. Akihiko Takabe has designed a sophisticated forecasting model, which predicts the movements in the overall stock market, in the hope of earning a return in excess of a fair return for the risk involved. He uses the predictions of the model to decide whether to buy, hold, or sell the shares of an index fund that aims to replicate the movements of the stock market. Takabe would best be characterized as a (n):A. hedger.B. investor.C. information-motivated trader.2. James Beach is young and has substantial wealth. A significant proportion of his stock portfolio consists of emerging market stocks that offer relatively high expected returns at the cost of relatively high risk. Beach believes that investment in emerging market stocks is appropriate for him given his ability and willingness to take risk. Which of the following labels most appropriately describes Beach?A. Hedger.B. Investor.C. Information-motivated trader.3. Lisa Smith owns a manufacturing company in the United States. Her company has sold goods to a customer in Brazil and will be paid in Brazilian real (BRL) in three months. Smith is concerned about the possibility of the BRL depreciating more than expected against the U.S. dollar (USD). Therefore, she is planning to sell three-month futures contracts on the BRL. The seller of such contracts generally gains when the BRL depreciates against the USD. If Smith were to sell these future contracts, she would most appropriately be described as a (n):A. hedger.B. investor.C. information-motivated trader.4. Which of the following is not a function of the financial system?A. To regulate arbitrageurs’ profits (excess returns).B. To help the economy achieve allocational efficiency.C. To facilitate borrowing by businesses to fund current operations.5. An investor primarily invests in stocks of publicly traded companies. The investor wants to increase the diversification of his portfolio. A friend has recommended investing in real estate properties. The purchase of real estate would best be characterized as a transaction in the:A. derivative investment market.B. traditional investment market.C. alternative investment market.6. A hedge fund holds its excess cash in 90-day commercial paper and negotiable certificates of deposit. The cash management policy of the hedge fund is best described as using:A. capital market instruments.B. money market instruments.C. intermediate-term debt instruments.7. An oil and gas exploration and production company announces that it is offering 30 million shares to the public at $45.50each. This transaction is most likely a sale in the:A. futures market.B. primary market.C. secondary market.8. Consider a mutual fund that invests primarily in fixed-income securities that have been determined to be appropriate given the fund’s investment goal. Which of the following is least likely to be a part of this fund?A. Warrants.B. Commercial paper.C. Repurchase agreements.9. A friend has asked you to explain the differences between open-end and closed-end funds. Which of the following will you most likely include in your explanation?A. Closed-end funds are unavailable to new investors.B. When investors sell the shares of an open-end fund, they can receive a discount or a premium to the fund’s net asset value.C. When selling shares, investors in an open-end fund sell the shares back to the fund whereas investors in a closed-end fund sell the shares to others in the secondary market.10. The usefulness of a forward contract is limited by some problems. Which of the following is most likely one of those problems?A. Once you have entered into a forward contract, it is difficult to exit from the contract.B. Entering into a forward contract requires the long party to deposit an initial amount with the short party.C. If the price of the underlying asset moves adversely from the perspective of the long party, periodic payments must be made to the short party.11. Tony Harris is planning to start trading in commodities. He has heard about the use of futures contracts on commodities and is learning more about them. Which of the following is Harris least likely to find associated with a futures contract?A. Existence of counterparty risk.B. Standardized contractual terms.C. Payment of an initial margin to enter into a contract.12. A German company that exports machinery is expecting to receive $10 million in three months. The firm converts all its foreign currency receipts into euros. The chief financial officer of the company wishes to lock in a minimum fixed rate for converting the $10 million to euro but also wants to keep the flexibility to use the future spot rate if it is favorable. What hedging transaction is most likely to achieve this objective?A. Selling dollars forward.B. Buying put options on the dollar.C. Selling futures contracts on dollars.13. A book publisher requires substantial quantities of paper. The publisher and a paper producer have entered into an agreement for the publisher to buy and the producer to supply a given quantity of paper four months later at a price agreed upon today. This agreement is a:A. futures contract.B. forward contract.C. commodity swap.14. The Standard & Poor’s Depos itary Receipts (SPDRs) is an investment that tracks the S&P 500 stock market index. Purchases and sales of SPDRs during an average trading day are best described as:A. primary market transactions in a pooled investment.B. secondary market transactions in a pooled investment.C. secondary market transactions in an actively managed investment.15. The Standard & Poor’s Depositary Receipts (SPDRs) is an exchange-traded fund in the United States that is designed to track the S&P 500 stock market index. The current price of a share of SPDRs is $113. A trader has just bought call options on shares of SPDRs for a premium of $3 per share. The call options expire in five months and have an exercise price of $120 per share. On the expiration date, the trader will exercise the call options (ignore any transaction costs) if and only if the shares of SPDRs are trading:A. below $120 per share.B. above $120 per share.C. above $123 per share.16. Which of the following statements about exchange-traded funds is most correct?A. Exchange-traded funds are not backed by any assets.B. The investment companies that create exchange-traded funds are financial intermediaries.C. The transaction costs of trading shares of exchange-traded funds are substantially greater than the combined costs of trading the underlying assets of the fund.17. Jason Schmidt works for a hedge fund and he specializes in finding profit opportunities that are the result of inefficiencies in the market for convertible bonds—bonds that can be conver ted into a predetermined amount of a company’s common stock. Schmidt tries to find convertibles that are priced inefficiently relative to the underlying stock. The trading strategy involves the simultaneous purchase of the convertible bond and the short sale of the underlying common stock. The above process could best be described as:A. hedging.B. arbitrage.C. securitization.18. Pierre-Louis Robert just purchased a call option on shares of the Michelin Group.A few days ago he wrote a put option on Michelin shares. The call and put options have the same exercise price, expiration date, and number of shares underlying. Considering both positions, Robert’s exposure to the risk of the stock of the Michelin Group is:A. long.B. short.C. neutral.19. An online brokerage firm has set the minimum margin requirement at 55 percent. What is the maximum leverage ratio associated with a position financed by this minimum margin requirement?A. 1.55.B. 1.82.C. 2.22.20. A trader has purchased 200 shares of a non-dividend-paying firm on margin at a price of $50 per share. The leverage ratio is 2.5. Six months later, the trader sells these shares at $60 per share. Ignoring the interest paid on the borrowed amount and the transaction costs, what was the return to the trader during the six-month period?A. 20 percent.B. 33.33 percent.C. 50 percent.21. Jason Williams purchased 500 shares of a company at $32 per share. The stock was bought on 75 percent margin. One month later, Williams had to pay interest on the amount borrowed at a rate of 2 percent per month. At that time, Williams receiveda dividend of $0.50 per share. Immediately after that he sold the shares at $28 per share. He paid commissions of $10 on the purchase and $10 on the sale of the stock. What was the rate of return on this investment for the one-month period?A. ?12.5 percent.B. –15.4 percent.C. –50.1 percent.22. Caroline Rogers believes the price of Gamma Corp. stock will go down in the near future. She has decided to sell short 200 shares of Gamma Corp. at the current market price of €47. The initial margin requirement is 40 percent. Which of the following is an appropriate statement regarding the margin requirement that Rogers is subject to on this short sale?A. She will need to c ontribute €3,760 as margin.B. She will need to contribute €5,640 as margin.C. She will only need to leave the proceeds from the short sale as deposit and does not need to contribute any additional funds.23. The current price of a stock is $25 per share. You have $10,000 to invest. You borrow an additional $10,000 from your broker and invest $20,000 in the stock. If the maintenance margin is 30 percent, at what price will a margin call first occur?A. $9.62.B. $17.86.C. $19.71.24. You have placed a sell market-on-open order—a market order that would automatically be submitted at the market’s open tomorrow and would fill at the market price. Your instruction, to sell the shares at the market open, is a(n):A. execution instruction.B. validity instruction.C. clearing instruction.25. A market has the following limit orders standing on its book for a particular stock. The bid and ask sizes are number of shares in hundreds.What is the market?A. 9.73 bid, offered at 10.14.B. 9.81 bid, offered at 10.10.C. 9.95 bid, offered at 10.02.26. Consider the following limit order book for a stock. The bid and ask sizes are number of shares in hundredsA new buy limit order is placed for 300 shares at ￥123.40. This limit order issaid to:A. take the market.B. make the market.C. make a new market.27. Currently, the market in a stock is "$54.62 bid, offered at $54.71." A new sell limit order is placed at $54.62. This limit order is said to:A. take the market.B. make the market.C. make a new market.28. Jim White has sold short 100 shares of Super Stores at a price of$42 per share. He has also simultaneously placed a "good-till-cancelled, stop 50, limit 55 buy" order. Assume that if the stop condition specified by White is satisfied and the order becomes valid, it will get executed. Excluding transaction costs, what is the maximum possible loss that White can have?A. $800.B. $1,300.C. Unlimited.29. You own shares of a company that are currently trading at $30 a share. Your technical analysis of the shares indicates a support level of $27.50. That is, if the price of the shares is going down, it is more likely to stay above this level rather than fall below it. If the price does fall below this level, however, you believe that the price may continue to decline. You have no immediate intent to sell the shares but are concerned about the possibility of a huge loss if the share price declines below thesupport level. Which of the following types of orders could you place to most appropriately address your concern?A. Short sell order.B. Good-till-cancelled stop sell order.C. Good-till-cancelled stop buy order.30. In an underwritten offering, the risk that the entire issue may not be sold to the public at the stipulated offering price is borne by the:A. issuer.B. investment bank.C. buyers of the part of the issue that is sold.31 . A British company listed on the Alternative Investment Market of the London Stock Exchange, announced the sale of 6,686,665 shares to a small group of qualified investors at ￡0.025 per share. Which of the following best describesA. Shelf registration.B. Private placement.C. Initial public offering.32. A German publicly traded company, to raise new capital, gave its existing shareholders the opportunity to subscribe for new shares. The existing shareholders could purchase two new shares at a subscription price of €4.58 per share for every 15 shares held. This is an example of a(n):A. rights offering.B. private placement.C. initial public offering.33. Consider an order-driven system that allows hidden orders. The following four sell orders on a particular stock are currently in the system's limit order book. Based on the commonly used order precedence hierarchy, which of these orders will have precedence over others?A. Order I (time of arrival of 9:52:01 ).B. Order II (time of arrival of 9:52:08).C. Order III (time of arrival of 9:53:04)34. Zhenhu Li has submitted an immediate-or-cancel buy order for 500 shares of a company at a limit price of CNY 74.25. There are two sell limit orders standing in that stock's order book at that time. One is for 300 shares at a limit price of CNY74.30 and the other is for 400 shares at a limit price of CNY 74.35. How many shares in Li's order would get cancelled?A. None (the order would remain open but unfilled).B. 200 (300 shares would get filled).C. 500 (there would be no fill).35. A market has the following limit orders standing on its book for a particular stock:Ian submits a day order to sell 1,000 shares, limit ￡19.83. Assuming that no more buy orders are submitted on that day after Ian submits his order, what would be Ian's average trade price?A. ￡19.70.36. A financial analyst is examining whether a country's financial market is well functioning. She finds that the transaction costs in this market are low and trading volumes are high. She concludes that the market is quite liquid. In such a market:A. traders will find it hard to make use of their information.B. traders will find it easy to trade and their trading will make the market less informationally efficient.C. traders will find it easy to trade and their trading will make the marketmore informationally efficient.37. The government of a country whose financial markets are in an early stage of development has hired you as a consultant on financial market regulation. Your first task is to prepare a list of the objectives of market regulation. Which of the following is least likely to be included in this list of objectives?A. Minimize agency problems in the financial markets.B. Ensure that financial markets are fair and orderly.C. Ensure that investors in the stock market achieve a rate of return that is at least equal to the risk-free rate of return. Chapter 2 Portfolio Management: An Overview PRACTICE PROBLEMS FOR CHAPTER 21. Investors should use a portfolio approach to:A. reduce risk.B. monitor risk.C. eliminate risk.2. Which of the following is the best reason for an investor to be concerned with the composition of a portfolio?A. Risk reduction.B. Downside risk protection.C. Avoidance of investment disasters.3. With respect to the formation of portfolios, which of the following statements is most accurate?A. Portfolios affect risk less than returns.B. Portfolios affect risk more than returns.C. Portfolios affect risk and returns equally.4. Which of the following institutions will on average have the greatest need for liquidity?A. Banks.B. Investment companies.C. Non-life insurance companies.5. Which of the following institutional investors will most likely have the longest time horizon?A. Defined benefit plan.B. University endowment.C. Life insurance company.6. A defined benefit plan with a large number of retirees is likely to have a high need forA. income.7. Which of the following institutional investors is most likely to manage investmentsin mutual funds?A. Insurance companies.B. Investment companies.C. University endowments.8. With respect to the portfolio management process, the asset allocation is determined in the:A. planning step.B. feedback step.C. execution step9. The planning step of the portfolio management process is least likely to include an assessment of the client'sA. securities.B. constraints.C. risk tolerance.10. With respect to the portfolio management process, the rebalancing of a portfolio's composition is most likely to occur in the:A. planning step.B. feedback step.C. execution step.11. An analyst gathers the following information for the asset allocations of three portfolios:Which of the portfolios is most likely appropriate for a client who has a high degree of risk tolerance?A. Portfolio 1.B. Portfolio 2.C. Portfolio 3.12. Which of the following investment products is most likely to trade at their net asset value per share?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.13. Which of the following financial products is least likely to have a capital gain distribution?A. Exchange traded funds.B. Open-end mutual funds.C. Closed-end mutual funds.14. Which of the following forms of pooled investments is subject to the least amount of regulation?A. Hedge funds.B. Exchange traded funds.C. Closed-end mutual funds.15. Which of the following pooled investments is most likely characterized by a few large investments?A. Hedge funds.B. Buyout funds.C. Venture capital funds.Chapter 3 Portfolio Risk and Return: Part I PRACTICE PROBLEMS FOR CHAPTER 31. An investor purchased 100 shares of a stock for $34.50 per share at the beginning of the quarter. If the investor sold all of the shares for $30.50 per share after receiving a $51.55 dividend payment at the end of the quarter, the holding period return is closest to:A. - 13.0%.B. - 11.6%.C. - 10.1%.2. An analyst obtains the following annual rates of return for a mutual fund:The fund's holding period return over the three-year period is closest to:A. 0.18%.B. 0.55%.C. 0.67%.3. An analyst observes the following annual rates of return for a hedge fund:The hedge fund's annual geometric mean return is closest to:A. 0.52%.B. 1.02%.C. 2.67%.4. Which of the following return calculating methods is best for evaluating the annualized returns of a buy-and-hold strategy of an investor who has made annual deposits to an account for each of the last five years?A. Geometric mean return.B. Arithmetic mean return.C. Money-weighted return.5. An investor evaluating the returns of three recently formed exchange-traded funds gathers the following information:The ETF with the highest annualized rate of return is:A. ETF 1.B. ETF 2.C. ETF 3.6. With respect to capital market theory, which of the following asset characteristics is least likely to impact the variance of an investor's equally weighted portfolio?A. Return on the asset.B. Standard deviation of the asset.C. Covariances of the asset with the other assets in the portfolio.7. A portfolio manager creates the following portfolio:If the correlation of returns between the two securities is 0.40, the expected standard deviation of the portfolio is closest to:A. 10.7%.B. 11.3%.C. 12.1%.8. A portfolio manager creates the following portfolio:If the covariance of returns between the two securities is - 0.0240, the expectedstandard deviation of the portfolio is closest to:A. 2.4%.B. 7.5%.C. 9.2%.The following information relates to Questions 9-10A portfolio manager creates the following portfolio:9. If the standard deviation of the portfolio is 14.40%, the correlation between the two securities is equal to:A. - 1.0.B. 0.0.C. 1.0.10. If the standard deviation of the portfolio is 14.40%, the covariance between the two securities is equal to:A. 0.0006.B. 0.0240.C. 1.0000.The following information relates to Questions 11-14An analyst observes the following historic geometric returns:11 . The real rate of return for equities is closest to:A. 5.4%.B. 5.8%.C. 5.9%.12. The real rate of return for corporate bonds is closest to:A. 4.3%.B. 4.4%.C. 4.5%.13. The risk premium for equities is closest to:A. 5.4%.B. 5.5%.C. 5.6%.14. The risk premium for corporate bonds is closest to:A. 3.5%.B. 3.9%.C. 4.0%.15. With respect to trading costs, liquidity is least likely to impact the:A. stock price.B. bid-ask spreads.C. brokerage commissions.16. Evidence of risk aversion is best illustrated by a risk-return relationship that is:A. negative.B. neutral.C. positive.17. With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is:A. the same for all individuals.B. positive for risk-averse investors.C. equal to zero for risk seeking investors18. With respect to utility theory, the most risk-averse investor will have an indifference curve with the:A. most convexity.B. smallest intercept value.C. greatest slope coefficient.19. With respect to an investor's utility function expressed as:21=E(r)-2u A　, whichof the following values for the measure for risk aversion has the least amount of risk aversion?A. - 4.B. 0.C. 4.The following information relates to Questions 20-23A financial planner has created the following data to illustrate the application of utility theory to portfolio selection:20. A risk-neutral investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.ExpectedStandard Deviation (% )28153021. If an investor's utility function is expressed as U = E(r) ~A& and the measure for risk aversion has a value of- 2, the risk-seeking investor is most likely to choose:A. Investment 2.B. Investment 3.C. Investment 4.22. If an investor's utility function is expressed as U = E(r) - ~A& and the measure for risk aversion has a value of2, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.23. If an investor's utility function is expressed as U =E(r) - ~A& and the measure for risk aversion has a value of4, the risk-averse investor is most likely to choose:A. Investment 1.B. Investment 2.C. Investment 3.24. With respect to the mean-variance portfolio theory, the capital allocation line, CAL, is the combination of the risk-free asset and a portfolio of all:A. risky assets.B. equity securities.C. feasible investments.25. Two individual investors with different levels of risk aversion will have optimal portfolios that are:A. below the capital allocation line.B. on the capital allocation line.C. above the capital allocation line.The following information relates to Questions 26-28A portfolio manager creates the following portfolio:26. If the portfolio of the two securities has an expected return of15%, the proportion invested in Security 1 is:A. 25%.B. 50%.C. 75%.27. If the correlation of returns between the two securities is - 0.15, the expected standard deviation of an equal-weighted portfolio is closest to:A. 13.04%.B. 13.60%.C. 13.87%.28. If the two securities are uncorrelated, the expected standard deviation of anequal-weighted portfolio is closest to:A. 14.00%.B. 14.14%.C. 20.00%.29. As the number of assets in an equally-weighted portfolio increases, the contribution of each individual asset's variance to the volatility of the portfolio:A. increases.B. decreases.C. remains the same.30. With respect to an equally-weighted portfolio made up of a large number of assets, which of the following contributes the most to the volatility of the portfolio?A. Average variance of the individual assets.B. Standard deviation of the individual assets.C. Average covariance between all pairs of assets.31. The correlation between assets in a two-asset portfolio increases during a market decline. If there is no change in the proportion of each asset held in the portfolio or the expected standard deviation of the individual assets, the volatility of the portfolio is most likely to:A. increase.B. decrease.C. remain the same.The following information relates to Questions 32-34An analyst has made the following return projections for each of three possible outcomes with an equal likelihood of occurrence:32. Which pair of assets is perfectly negatively correlated?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.33. If the analyst constructs two-asset portfolios that are equally-weighted, which pair of assets has the lowest expected standard deviation?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.34. If the analyst constructs two-asset portfolios that are equally weighted, which pair of assets provides the least amount of risk reduction?A. Asset 1 and Asset 2.B. Asset 1 and Asset 3.C. Asset 2 and Asset 3.35. Which of the following statements is least accurate? The efficient frontier is the set of all attainable risky assets with the:A. highest expected return for a given level of risk.B. lowest amount of risk for a given level of return.C. highest expected return relative to the risk-free rate.36. The portfolio on the minimum-variance frontier with the lowest standard deviation is:A. unattainable.。

第一章金融工程原理

3.金融工程为金融创新提供了重要的平台
目前还没有一个统一公允的定义。
三个代表性定义：
Finnerty的定义：
“金融工程包括创新型金融工具与金融手段的设计、开发与实施，以及对金融问题给予创造性的解决。”
“创新性”——金融工具、金融手段的设计、开发与实施
“创造性”——金融问题的解决
Galitz的定义：
“金融工程是应用金融工具，将现在的金融结构进行重组以获得人们所希望的结果。”
例1远期外汇定价
•假定市场条件如下：货币市场上英镑利率是5%，美元利率是10%；外汇市场上英镑与美元的即期汇率是1英镑兑换1.5美元（1:1.5）。那么，一年期的远期汇率是否还是1:1.5呢？
•解：如果还是1:1.5，可套利。
（1）借入1英镑，1年后需归还1.05英镑；
（2）将借入的1英镑兑换为1.5美元，存期一年，1年后获本利和1.5×1.1＝1.65美元；再将1.65美元兑换为1.65÷1.5＝1.1英镑
第一章金融工程原理
第一章导论
本章要解决的问题
什么是金融工程学？
促使金融工程发展的因素有哪些？
金融工程师从事哪些业务？
金融工程与金融理论有什么关系？
金融工程包括哪些内容？
一、金融工程的产生
（一）金融理论的几个发展阶段
（二）金融产品的特点
1.金融产品供给和需求的特殊性
2.金融产品定价的特殊性
3.金融产品获得长期稳定收益的困难性
必须满足：
•3.终值与现值
•终值又称将来值，它是指现在的一笔资金在未来一段时间后所具有的价值。
•其计算即复利的本利和，公式为：(bu)
如果是连续复利，
(bu)
•可以理解为现在投资S，未来应该收入多少才能达到平均收益率？

金融工程第3章期货的对冲策略

基差的变动
基差扩大
现货价格的增长大于期货价格的增长
基差减少
期货价格的增长大于现货的价格增长
基差变动的图形
符号定义
在t1 时刻对冲，在 t2 时刻平仓 S1：在 t1 时刻现货的价格
S2：在 t2 时刻现货的价格
F1：在 t1 时刻期货的价格 F2：在 t2 时刻期货的价格 b1：在 t1 时刻的基差 b2：在 t2 时刻的基差
例子
某企业知道在未来的3个月内，商品的价格每上升1美分可以多赚1万美元，而价格每下跌1美分时少赚1万美元
企业应持有一个期货空头来对冲风险
如果价格下跌，期货的盈利将弥补商品因价格下跌而导致的损失而价格上涨时，期货的损失将冲抵商品价格上升带来的好处
期货空头套期保值
空头套期保值（short hedge）
依据前面提到的选择期货合约的准则，公司应该选择 9月份到期的日元期货合约
公司在3月1日卖出4个9月份到期的日元期货合约。当7月底公司收到日元时，公司平仓其期货合约。
由于期货价格与即期价格之差的不确定性产生了所谓的基差风险
我们假定3月1日的期货价格为每日元0.78美分，当期货合约平仓时，现货和期货的价ቤተ መጻሕፍቲ ባይዱ分别为每日元0.72和0.725美分，
该策略将把铜的价格锁定在每磅120美分附近
多头套期保值策略
市场情况 1月15日
某加工商5月15日需要购买100 000磅铜来履行合同。
当前铜的即期价格为每磅140美分 5月份到期的铜期货的价格为每磅120美分
套期保值策略
1月15日：购买4张5月份铜期货合约 5月15日：将1月15日购买的期货平仓
股票持有者相对于企业管理层在风险上的信息劣势佣金和交易成本的影响

金融工程原理

金融工程原理
金融工程原理是一门综合利用数学、统计学和编程技术来解决金融问题的学科。

它涉及金融市场的建模、风险管理、投资组合优化以及金融工具的定价等方面。

金融工程的原理主要有以下几个方面：
1. 随机过程与金融市场模型：金融市场的价格和利率等变量往往是随机的，因此需要掌握随机过程的基本理论，如布朗运动、随机微分方程等。

金融市场模型则是建立在随机过程的基础上，用来描述市场中各种金融产品的价格和变动规律。

2. 金融产品定价与衍生品分析：定价是金融工程中的核心问题之一。

通过建立适当的定价模型，可以对金融产品进行合理的定价。

衍生品分析则是研究衍生品的定价、风险度量和对冲策略等方面的内容。

3. 投资组合优化：投资组合优化是指通过合理的资产配置，以实现预期的风险和收益的平衡。

通过运用数学优化的方法，可以找到最优的投资组合，提高资产配置的效率。

4. 风险管理与金融衍生品：金融市场存在着各种风险，如市场风险、信用风险和操作风险等。

金融工程的原理可以用来衡量和管理这些风险。

金融衍生品则是一种用来管理金融风险的工具，例如期权、期货和掉期等。

5. 统计学与计量经济学方法：金融工程的原理需要运用统计学
和计量经济学的方法来分析金融数据和建立模型。

通过对历史数据的分析，可以得出对未来市场行情和风险的预测。

综上所述，金融工程原理关注于利用数学、统计学和编程技术来解决金融问题。

它的核心包括金融市场模型、金融产品定价、投资组合优化、风险管理和统计学方法等。

通过运用这些原理，可以更好地理解金融市场，优化投资决策，并有效管理风险。

金融工程原理第二章.

2.6 工具
按照金融市场上的惯例可将这些工具划分为以下部分：
(1)固定收益工具。包括银行间存款单，存款、商业票据、银行承兑汇票和国库券。这些被认为是货币市场工具。债券、票据和浮动利率票据是债券市场工具。
(2)股票，包括上市公司发行的不同种类股票。 (3)货币和商品。
(4)衍生品，主要类别是利率、股票、货币和商品的衍生品。
在一定意义上，通过先借款然后再购买资产，一个人拥有的不是资产而是某种敞口。如果资产价格上涨，头寸将有利可图。另一方面，如果价格下降，头寸将出现损失。
2.7 头寸——空头寸融资
图2-3从市场操作者的角度表示了一个空头寸，空头寸时借的是资产。资产价格下降时头寸将盈利，而价格上升时头寸将损失。原因是借的是资产而不是资金。
期货或期权交易所的买卖机制如下：两个池中交易者根据客户的意愿直接进行交易。然后签署交易单并盖上章。直到此时，两个交易者互为交易对方。可是一旦交易单盖上章，清算所将成为他们共同的对方。
作为所有空头和多头的唯一对方，清算所将大大降低对方的违约风险，因为交易所是与清算成员而不是与直接交易商打交道。
B (t , T) = 100
T T R
t （3）
100
365
2.5.2 收益率报价方法
在适当的惯例下，上述表达式可能都是正确的。在美国，债券市场按照公式（1）报收益率，此时RT称作债券等价收益率。涉及银行间存款和贷款的货币市场使用货币市场收益率惯例，并在定价和风险管理中采用公式（2）。商业票据和国库券的收益率按公式（3）报价，该收益率称为贴现率。
2.4 交易机制——确认和结算
订单的确认包括在双方之间传递消息，以使交易在市场从业者之间得到口头上的确认。结算时交换现金以及相关证券，或者只是交换证券。

期权、期货及其他衍生产品课件2金融工程学

The basis arising from the difference between the two assets.
3.17
Choice of Contract

Choose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging.
3.11
Convergence of Futures to Spot
(Hedge initiated at time t1 and closed out at time t2)
Futures Price
Spot Price
Time t1 t2 3.12
Basis Risk

Basis is the difference between spot & futures Basis= Spot price of asset to be hedgedFutures price of contract used When the spot price increases by more than the futures prices, the basis increases,this is referred to as a strengthening of the basis. weakening of the basis Basis risk arises because of the uncertainty about the basis when the hedge is closed out