Before Black schole
Bachelier doctoral dissertation in 1900 contains the formula
S- K
S- K
K- S
C ( S , T ) = SN
- KN
+s T n
s T
s T
s T
Sprenkle (1961) has
C ( S , T ) =e rT SN ( d1 ) - (1 - A) KN ( d 2 )
where \rho is the average growth rate and

Chapter2
MechanicsofFutures
Markets
Options, Futures, and Other Derivatives, 8th
Edition,
1
FuturesContracts
Available on a wide range of assets
Exchange traded
Specifications need to be defined:
Where it can be delivered, &
What can be delivered,
When it

Chapter 14
The Black-Scholes-Merton
Model
1
The Stock Price Assumption
Consider a stock whose price is S
In a short period of time of length t, the
return on the stock is normally distributed:
S
t , 2 t
S
where is expected return and is
volatility
2
The

Chapter 18
The Greek Letters
1
Example
A bank has sold for $300,000 a European call
option on 100,000 shares of a non-dividend
paying stock
S0 = 49, K = 50, r = 5%, = 20%,
T = 20 weeks, = 13%
The Black-Scholes-Merton value of the option is
$240,000
How do

FERM531 - Homework 5 Solutions
1. A The buyer will not have a net prot unless the net stock price
exceeds $34. The other statements are true. At $30 the option will be
exercised, but the writer will only lose money in a net sense when the
stock price exce

Chapter 11
Trading Strategies Involving
Options
1
Strategies to be Considered
Bond plus option to create principal
protected note
Stock plus option
Two or more options of the same type (a
spread)
Two or more options of different types (a
combination)
2
Pr

FERM531 - Homework 4 Solutions
1. C A put option is out of the money if S > X and in the money if
S < X. The other statements are true.
2. C American and European options both give the holder the right to
exercise the option at expiration. An American opt

FERM531 - Homework 5
You do not have to turn it in.
1. A call option sells for $4 on a $25 stock with a strike price of $30.
Which of the following statements is least accurate?
(a) At expiration, the buyer of the call will not make a prot unless
the stoc

Chapter 9
Mechanics of Options
Markets
1
Review of Option Types
A call is an option to buy
A put is an option to sell
A European option can be exercised only at
the end of its life
An American option can be exercised at any
time
2
Option Positions
Long ca

FERM531 - Homework 4
You do not have to turn it in.
1. Which of the following statements about moneyness is least accurate?
When:
(a) S X is > 0, a call option is in the money.
(b) S X is = 0, a call option is at the money.
(c) S > X, a put option is in t

Chapter 7
Swaps
1
Nature of Swaps
A swap is an agreement to exchange
cash flows at specified future times
according to certain specified rules
2
An Example of a Plain Vanilla Interest
Rate Swap
An agreement by Microsoft to receive 6month LIBOR & pay a fix

Chapter 4
Interest Rates
1
Types of Rates
Treasury rates
LIBOR rates
Repo rates
2
Treasury Rates
Rates on instruments issued by a government
in its own currency
3
LIBOR and LIBID
LIBOR is the rate of interest at which a bank
is prepared to deposit money w

FERM 531 - Homework 3 Solutions
1. A current yield =
71.25
1,023.47
= 0.06962 = 6.962%.
2. C 1, 023.47 =
8
35.625
i=1 (1+Y T M/2)i
+
1,000
(1+Y T M/2)8
3. C 1, 023.47 =
4
35.625
i=1 (1+Y T C/2)i
+
1,010
(1+Y T C/2)4
Y T C = 6.334%.
4. B 1, 023.47 =
4
35.

FERM 531 - Homework 3
You do not have to turn it in.
Use the following data to answer questions 1 through 4
An analyst observes a Widget&Co. 7.125%, 4-year, semiannual-pay bond
trading at 102.347% of par (where par is $1,000). The bond is callable at
101

FERM 531 - Homework 2 Solutions
1. B c = 1, 000
0.10
2
2. B bond value =
= $50
2
100
i=1 0 (1+0.15)i
+
1,000
(1+0.15)20
= $687.03
3. A $828.40
4. C Bond A = $743.22 and Bond B = $1, 172.04. Because the coupon on
Bond A is less than its required yield, th

FERM 531 - Homework 2
You do not have to turn it in.
1. An analyst observes a 5-year, 10% coupon bond with semiannual payments. The face value is $1, 000. How much is the each coupon payment?
(a) $25
(b) $50
(c) $100
2. A 20-year, 10% annual-pay bond has

Chapter 1
Introduction
1
What is a Derivative?
A derivative is an instrument whose value
depends on, or is derived from, the value of
another asset.
Examples: futures, forwards, swaps, options,
exotics
2
Why Derivatives Are Important
Derivatives play a ke

FERM 531 - Homework 1 Solutions
1. C A derivatives value is derived from another asset.
2. C Exchange-traded derivatives have relatively low default risk because
the clearinghouse stands between the counter parties involved in most
contracts.
3. C This no

FERM 531 - Homework 1
You do not have to turn it in.
1. Which of the following most accurately describes a derivative security?
A derivative:
(a) always increase risk.
(b) has no expiration date.
(c) has a payo based on another asset.
2. Which of the foll

FINANCIAL ENGINEERING - WEEK 3
INTRODUCTION TO OPTIMAL INVESTMENT
MUZAFFER AKAT
In this chapter we provide an introduction to the theory of optimal investment in nite
one-period models. We assume throughout that a nite one-period model with k basic risky

FINANCIAL ENGINEERING - WEEK 2
ARBITRAGE-FREE PRICING IN ONE-PERIOD
FINITE MODELS
MUZAFFER AKAT
The simplest nancial models involving random evolution of prices are those in which there
are only two trading times and the prices of the basic securities are

FERM 506 - Homework 2
1. Suppose you are a representative of a nancial company, which can invest in a nancial
market, where one can borrow and lend money for any period of time according to the
eective annual interest rate R = 6%. One can also buy or sell

FERM 506 - Homework 1
1. Consider a one-period trinomial model, where there are three assets: the bank account,
a stock S and a standard call option C on the stock with maturity T = 1. The sample
space consists of 3 elements: = (1 , 2 , 3 ). The interest