# Financial Mathematics Exam

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1 2014 Exam 2 Syllabus Financial Mathematics Exam The purpose of the syllabus for this examination is to develop knowledge of the fundamental concepts of financial mathematics and how those concepts are applied in calculating present and accumulated values for various streams of cash flows as a basis for use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. The candidate will also be given an introduction to financial instruments, including derivatives, and the concept of noarbitrage as it relates to financial mathematics. The syllabus for this exam is defined in the form of learning objectives that set forth, usually in broad terms, what the candidate should be able to do in actual practice. Please check the Syllabus Update for this exam for any changes to this syllabus or to other options for obtaining credit for this exam. The Financial Mathematics Exam assumes a basic knowledge of calculus and an introductory knowledge of probability. A. Interest Theory LEARNING OBJECTIVES 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 Exam 2 Syllabus 2013, Casualty Actuarial Society, All Rights Reserved Exam 2-1

2 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 2014 Exam 2 Syllabus Exam 2-2

3 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 Exam 2 Syllabus Exam 2-3

4 B. Financial Economics LEARNING OBJECTIVES 1. 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 2. For general derivatives, evaluate an investor's margin position based on changes in asset values. 3. 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 4. For options, evaluate the payoff and profit of basic derivative contracts. 5. 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 6. 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 7. 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 2014 Exam 2 Syllabus Exam 2-4

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