**MATH 2212:** **MATHEMATICS OF FINANCE II**

**Course Type: Core **

** ****Level: 1**

**Semester: 2**

**No. of Credits: 3**

**Pre-requisites: **MATH 2211

**Course Rationale**

Actuaries apply mathematical and statistical techniques to quantitative risk assessment and other problems in finance and business. Actuaries and students of Actuarial Science therefore need to know various fincial products commonly in use as well as various types of financial instruments. Many undergraduate students enter university with little or no knowledge of what things as loans, mortgages, how credit cards work, stocks and bonds are and how they work. Some of this information is provided in Mathematics of Finance I and other courses.

The aim of this course is to provide an understanding of the fundamental concepts of financial derivatives and define the features of options like call, put, forwards and futures. The student will also learn to use hedging in investment and risk management. This course will also present relevant concepts and skills used in the financial field.

**Course Description**

This course covers topics relevant in financial mathematics that include mathematical techniques used to price and hedge derivative securities in modern finance. Assessment of the course will be continuous and students are encouraged to practice questions and read the prescribed reading texts to keep abreast. Assignments will employ the use of actuarial and statistical software to solve business oriented problems.

Assessment is designed to encourage students to work continuously with the course materials. Active learning will be achieved through marked assignments supplemented by problem papers, allowing continuous feedback and guidance on problem solving techniques in tutorials and lectures. Assessment will be based on the marked assignments and in-course tests followed by a final examination based on the whole course. Software used in the actuarial field will be incorporated in the course so that students develop practical skills

The content of this course covers some of the topics examined in the Society of Actuaries **Financial Mathematics (FM)** exam.

**Course Content**

- Yield Rates
- Practical Applications to Consumer Products
- Introduction to general derivatives;
- Options;
- Hedging and investment strategies
- Forwards and futures;
- Swaps;

On completion of these modules the student should be able to:

__Yield Rates__- Define the following terms: yield rate/rate of return, dollar-weighted rate of return/time-weighted rate of return, current value, duration (Macaulay and modified) , convexity, portfolio, spot rate, forward rate, yield curve, stock price, and stock dividend
- Calculate the following:
- Current value of a set of cash flows.
- Portfolio yield rate.
- Dollar-weighted and time-weighted rate of return.
- Duration and convexity of a set of cash flows.
- Either Macaulay or modified duration given the other
- Price of a stock using the dividend discount model.

B.. __Practical Applications__

- Calculate installments for:
- Consumer loans;
- Real estate mortgages;
- Depreciation costs.

__C. General Derivatives __

- Define and recognize the following terms: derivative, underlying asset, over-the-counter market, ask price, bid price, bid-ask spread, short selling, short position, long position, stock index, spot price, net profit/payoff, credit risk, marking-to-market, margin, maintenance margin, and margin call
- Evaluate an investor's margin position based on changes in asset values.

__D.. Options __

- Define and recognize the following terms: call option, put option, expiration, expiration date, strike price/exercise price, European option, American option, Bermudan option, in-the-money, at-the-money, out-of-the-money, covered call, dividends and put-call parity
- Evaluate the payoff and profit of basic derivative contracts.

__E. Forwards and Futures __

- Define and understand the following terms: forward contract, prepaid forward, contract , outright purchase, fully leveraged purchase, implied repo rate, cost of carry, lease rate, futures contract
- Determine forward price from prepaid forward price.
- Explain the relationship between forward price and futures price.
- Explain the relationship between forward price and future stock price.
- Use the concept of no-arbitrage to determine the theoretical value of futures and forwards.
- Given any four of call premium, put premium, forward price, strike price and interest rate, calculate the remaining item using the put-call parity formula.

__F. Swaps __

- Define and understand the different type of swaps:

a. Swap, Prepaid swap

b. Swap term, Swap spread, Notional Amount

c. Simple commodity swap, Interest rate swap

d. Deferred swap

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

__G. Hedging and Investment Strategies __

- Define and understand the following terms:

a. Hedging, Arbitrage

b. Diversifiable risk, non-diversifiable risk

c. Synthetic forwards

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

d. Collars (including zero-cost collars), pay-later strategy

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

f. Convertible bond, mandatorily convertible bond

- Explain how derivative securities can be used as tools to manage financial risk.
- Explain the reasons to hedge and not to hedge.
- Evaluate the payoff and profit of hedging strategies.

**Cognitive skills, Core skills and Professional Awareness**

- Awareness of the principal statistical methods and models used in assessing problems in interest theory for actuarial work
- Possession of the knowledge required to work in the area of finance in the actuarial context
- Application of the appropriate and rigorous use of mathematical modeling to formulate workable solutions to important financial problems

**Assessment Criteria**

Mathematics of Finance II is assessed by combination of coursework (50%) and a single 2-hour written exam at the end of the semester (50%).

**Assessment:** In-course Tests 40%

Assignments and Quizzes 10%

Final Exam 50%

**In-course Tests: **Two 50-minute written papers (20% each) consisting of compulsory questions of varying length

**Assignments:** Two papers to be submitted: One paper on the first part of the course and the other on the second part of the course. Each assignment is worth 5%. Tutorial practice papers will be given every week to be handed in the next week. Tutorial papers are not graded as part of the course work.

**Exam Format:** One two-hour written paper with compulsory questions.

**Teaching Methodology**

__Lectures__: Two lectures per week (50 minutes each)

Lab: One weekly two-hour lab session based on material covered during lectures and introducing students to the use of Excel, Matlab, Maple and Axis to make Actuarial calculations.

**Course Calendar**

Week |
Topic to be taught |
Assessment |

1 |
Introduction to course/Course overview |
Assignment #1 is given |

2 |
Yield rates /Practical Applications |
Assignment #2 is given and Assignment #1 is corrected |

3 |
Introduction to general derivatives |
Assignment #2 is given |

4 |
Options |
Assignment #3 is given and Assignment #2 is corrected |

5 |
Payoff of options |
Assignment #4 is given and Assignment #3 is corrected |

6 |
Definition of Hedging |
Assignment #5 is given and Assignment #4 is corrected |

7 |
Payoff of hedging |
First coursework test is given |

8 |
Hedging in risk management |
Assignment #6 is given and Assignment #5 is corrected |

9 |
Definition of futures and forwards |
Assignment #7 is given and Assignment #6 is corrected |

10 |
Calculating the value of a future |
Assignment #8 is given and Assignment #7 is corrected |

11 |
Calculating the value of a forward |
Assignment #9 is given and Assignment #8 is corrected |

12 |
Definition of swaps |
Second coursework test is given |

13 |
Calculating the value of a swaps Revision/Course Review/Clarification of Issues |
Assignment #10 is given and Assignment #9 is corrected |

**Required Reading **

*Derivative Markets-*Robert L. MacDonald 2^{nd}Edition 2004*Theory of Interest –*Stephen Kellison 3^{rd}Edition 2008.*Mathematics of Investment and Credit –*Samuel A. Broverman 4^{th}Edition 2008.

*Mathematical Interest Theory* – Daniel & Vaaler 2009.

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