一、教学目标

金融数学是应用统计学专业（风险管理与精算方向）的必修课程，也是经济金融保险等相关专业的本科生应该掌握的基本内容，是后续专业学习的先修课程。通过本课程的学习，学生应该熟悉利息度量的基本方法，能够进行基本的现金流分析，计算投资收益率，构造债务偿还表，掌握债券、远期、期货、互换和期权的分析方法，熟悉利率的期限结构及其应用，掌握应用久期和凸度进行利率风险管理的基本原理和方法。

 

二、学习要求

（1）学生在课前需要根据教学进度表预习教材内容，每周的教材阅读进度大约为15-20页。课后认真完成指定的作业，每周大约2-3个题目。

（2）每周的课后学习时间不应少于4小时。

（3）本课程从大二第一学期开始就可以修读，是学习寿险精算的基础课程。

（4）修读本课程的学生需要掌握一元微积分基础知识和Excel电子表格的基本应用。

 

三、课堂教学进度和教学建议

 

四、教材和参考书的使用说明

【1】孟生旺，《金融数学》第五版，中国人民大学出版社，2015。本书是该门课程的主要教材，除去期权交易策略、Black-Schole模型、随机利率之外，其他章节都属于教学和考核内容，建议学生系统阅读。

【2】黄达，《金融学》第三版，中国人民大学出版社，2014。本书是该门课程的先修课程教材。尚未修读《金融学》课程的学生在课外应该重点阅读下列的章节：

第四章 利率及其决定

第一节 利息

第二节 利率及其种类

第三节 利率的决定

第四节 利率的作用

第五节 利率的度量

第六节 利率的风险结构

第七节 利率的期限结构

第九章 金融市场

第一节 金融市场及其要素

第二节 货币市场

第三节 资本市场

第四节 证券价格与证券价格指数

第五节 资本市场的效率

第六节 衍生工具市场

第七节 投资基金

第八节 外汇市场与黄金市场

第十章 资产组合与资产定价

第一节 风险与资产组合

第二节 证券价值评估

第三节 资产定价模型

第四节 期权定价模型

【3】约翰·赫尔（John C.Hull）著；王勇，索吾林 译， 期权、期货及其他衍生产品（原书第9版），机械工业出版社，2014。本书是金融数学课程的补充学习材料，不属于考试范围，仅供学有余力的学生选读其中的部分章节，目的在于强化对金融衍生工具的深入理解。建议学生优先选读下列章节：

第1章　引言

第2章　期货市场的运作机制

第3章　利用期货的对冲策略

第4章　利率

第5章　如何确定远期和期货价格

第6章　利率期货

第7章　互换

第10章　期权市场机制

第11章　股票期权的性质

第12章　期权交易策略

第13章　二叉树

第14章　维纳过程和伊藤引理

第15章　布莱克-斯科尔斯-默顿模型

【4】 Chris Ruckman, Joe Francis. Financial Mathematics, BBP Professional Education. 2005。该书的内容与《金融数学》教材比较接近，主要帮助参加SOA或CAS Financial Mathematics课程考试的学生熟悉英文专业术语。CAS关于Financial Mathematics课程考试的下述要求中也包含了最关键的金融数学专业术语：

（1）For time value of money, define and recognize the definitions of the following terms:

a. Interest rate (rate of interest)

b. Simple interest

c. Compound interest

d. Accumulation function

e. Future value

f. Current/present value

g. Net present value

h. Discount factor

i. Discount rate (rate of discount)

j. Nominal rate convertible m-thly

k. Effective rate

l. Inflation and real rate of interest

m. Force of interest

n. Equation of value

（2）For time value of money, the candidate will be able to:

a. Given any three of interest rate, period of time, present value, or future value, calculate the remaining item based on simple or compound interest. Solve time value of money equations involving variable force of interest.

b. Given any one of the effective interest rate, the nominal interest rate convertible m-thly, the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, calculate all of the other items.

c. Write the equation of value given a set of cash flows and an interest rate.

（3）For annuity/cash flows with payments that are not contingent, define and recognize the definitions of the following terms:

a. Annuity-immediate

b. Annuity-due

c. Perpetuity

d. Payable m-thly, or continuously

e. Level payment annuity

f. Arithmetically increasing/decreasing payment annuity

g. Geometrically increasing/decreasing payment annuity

h. Term of annuity

（4）For each of the following types of annuity/cash flows, given sufficient information of immediate or due payments, present value, future value, current value, interest rate, payment amount, and term, the candidate will be able to calculate any remaining item:

a. Level annuity, finite term

b. Level perpetuity

c. Non-level annuity/cash flows:

i) Arithmetic progression, finite term

ii) Arithmetic progression, perpetuity

iii) Geometric progression, finite term

iv) Geometric progression, perpetuity

v) Other non-level annuities/cash flows

（5）For loans, define and recognize the definitions of the following terms:

a. Principal

b. Interest

c. Term

d. Outstanding balance

e. Final payment (drop payment, balloon payment)

f. Amortization

g. Sinking fund

（6）For loans, the candidate will be able to do the following:

a. Given any four of term, interest rate, payment amount, payment period, and principal, calculate the remaining item.

b. Calculate the outstanding balance at any point in time.

c. Calculate the amount of interest and principal repayment in a given payment.

d. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.

e. Perform calculations similar to a-d when refinancing is involved.

（7）For bonds, define and recognize the definitions of the following terms:

a. Price

b. Redemption value

c. Par/Face value

d. Coupon and coupon rate

e. Term

f. Yield rate

g. Callable/non-callable

h. Book value

i. Accumulation of discount and amortization of premium

（8）For bonds, given sufficient partial information about the items listed below, the candidate will be able to calculate any of the remaining items.

a. Price, book value, amortization of premium, and accumulation of discount

b. Redemption value and face value

c. Yield rate

d. Coupon and coupon rate

e. Term of bond, point in time that a bond has a given book value, amortization of premium, or accumulation of discount

（9）For general cash flows and portfolios, define and recognize the definitions of the following terms:

a. Yield rate/rate of return

b. Dollar-weighted rate of return/Time-weighted rate of return

c. Current value

d. Duration (Macaulay and modified)

e. Convexity (Macaulay and modified)

f. Portfolio and investment year allocation methods

g. Spot rate

h. Forward rate

i. Yield curve

j. Stock price and stock dividend

（10）For general cash flows and portfolios, the candidate will be able to do the following:

a. Calculate the portfolio yield rate.

b. Calculate the dollar-weighted and time-weighted rates of return.

c. Calculate the duration and convexity of a set of cash flows.

d. Calculate either Macaulay or modified duration given the other.

e. Use duration and convexity to approximate the change in present value due to a change in interest rate.

f. Calculate the price of a stock using the dividend discount model.

（11）For immunization, define and recognize the definitions of the following terms:

a. Cash-flow matching

b. Immunization (including full immunization)

c. Redington immunization

（12）For immunization, the candidate will be able to do the following:

a. Construct an investment portfolio to fully immunize a set of liability cash flows.

b. Construct an investment portfolio to match present value and duration of a set of liability cash flows.

c. Construct an investment portfolio to exactly match a set of liability cash flows.

（13）For general derivatives, define and recognize the definitions of the following terms:

a. Derivative, underlying asset, and over-the-counter market

b. Ask price, spot price, bid price, and bid-ask spread

c. Short selling, short position, and long position

d. Lease rate

e. Stock index

f. Net profit/payoff

g. Credit risk

h. Dividend

i. Marking-to-market

j. No arbitrage

k. Risk aversion

l. Margin, maintenance margin, and margin call

（14）For general derivatives, evaluate an investor's margin position based on changes in asset values.

（15）For options, define and recognize the definitions of the following terms:

a. Call and put option

b. Expiration and expiration date

c. Strike price/Exercise price

d. European option, American option, and Bermudan option

e. Option writer

f. In-the-money, at-the-money, and out-of-the-money

g. Covered call and naked writing

h. Put-call parity

（16）For options, evaluate the payoff and profit of basic derivative contracts.

（17）For hedging and investment strategies, define and recognize the definitions of the following terms:

a. Hedging and arbitrage

b. Diversifiable and non-diversifiable risk

c. Spreads (including option, bull, bear, vertical, box, and ratio spreads)

d. Collars (including collar width, collared stock, and zero-cost collars)

e. Straddles (including strangles, written straddles, and butterfly spreads)

f. Convertible and mandatorily convertible bonds

（18）For hedging and investment strategies, the candidate will be able to:

a. Explain how derivative securities can be used as tools to manage financial risk

b. Explain the reasons to hedge and not to hedge

c. Evaluate the payoff and profit of different hedging strategies

（19）For forwards and futures, define and recognize the definitions of the following terms:

a. Forward, futures, and prepaid forward contract

b. Outright and fully leveraged purchase

c. Cost of carry

（20）For forwards and futures, the candidate will be able to:

a. Determine the forward price given the prepaid forward price.

b. Explain the relationship between forward price, futures price, and the future stock price

c. Use the concept of no-arbitrage to determine the theoretical value of futures and forwardcontracts

d. Given sufficient information about call premium, put premium, forward price, strike price and interest rate, calculate any remaining item using the put-call parity formula.

（21）For swaps, define and recognize the definitions of the following terms:

a. Swap and prepaid swap

b. Swap term, spread, and notional amount

c. Simple commodity swap

d. Interest rate swap

e. Deferred swap

（22） Use the concept of no-arbitrage to determine the theoretical values of swaps.

 

五、考核方式

（1）平时成绩占30%，期末考试成绩占70%。

（2）期末考试为闭卷笔试，以计算题为主，中文命题。

（3）往年的考试题、练习题、参考答案、SOA和CAS的学习资料可以在孟生旺的新浪博客下载：http://blog.sina.com.cn/mengshw