FINANCIAL ENGINEERING - WEEK 4
ARBITRAGE-FREE PRICING IN ONE-PERIOD
FINITE MODELS
MUZAFFER AKAT
The simplest financial models involving random evolution of prices are those in which there
are only two
FINANCIAL ENGINEERING - WEEK 3
FORWARD CONTRACTS AND PUT-CALL PARITY
MUZAFFER AKAT
Recall that a forward contract is an agreement between two parties made at some time
concerning the sale of an asset
FERM 505
Dec 26, 2016
Financial Engineering I
Fall 2016
60 minutes
Sample Midterm - Solutions
Name:
Write your answers clearly in the spaces provided. You may use the back of a page for
additional spa
FERM 505
Dec 26, 2016
Financial Engineering I
Fall 2016
60 minutes
Sample Midterm
Name:
Write your answers clearly in the spaces provided. You may use the back of a page for
additional space; please i
FERM 505 - Assignment 0 - Solutions
1. Let T > 0 be given. Let C denote a European call option (on a stock S) with exercise
date T and strike price Kc = $50.00. Let P denote a European put option on t
FERM505 - Assignment 1
Due on April 2nd.
1. Consider a simple financial model with two times, t = 0 and t = 1, and a single stock
S that pays no dividends. There is also a bank with one-period interes
FERM505 - Homework 4
1. Consider a one-period binomial model with r = .1, u = 1.2, d = .9 and S0 = 50.
(a) Find the risk-neutral probabilities p and q
(b) Find the initial price V0 and the number of s
FERM 505 - Homework 2
All interest rates should be interpreted as annualized rates.
1. A 3-year coupon bond was issued two years ago today (i.e. the bond matures one year
from today. The face value of
FERM 505
Dec 26, 2016
Financial Engineering I
Fall 2016
60 minutes
Midterm
Name:
Write your answers clearly in the spaces provided. You may use the back of a page for
additional space; please indicate
FERM505 - Homework 1 - Solutions
1. If the stock goes up to $40 at t = 1,then the value of the put option to the holder is
P1 = $0. If the stock goes down to $25 then the value of the option at t = 1
FERM 505
Dec 26, 2016
Financial Engineering I
Fall 2016
60 minutes
Midterm - Answer Key
Name:
Write your answers clearly in the spaces provided. You may use the back of a page for
additional space; pl
FERM505 - Homework 3
Muzaffer Akat
1. Keller Zabel is offering a new financial instrument called a happy call. It has a payoff
function at time T equal to max(.5ST , ST K), where ST is the stock price
FERM505 - Homework 2 - Solutions
All interest rates should be interpreted as annualized rates.
1. (a) Each coupon payment is C = F q[m]
= 1, 000 .08
= 40 dollars. Arbitrage-free
m
2
price of the bond
FERM505 - Homework 4 - Solutions
1. (a) The risk neutral probabilities are p =
1+rd
ud
=
1+.1.9
1.2.9
= 23 . So q = 1 p = 13 .
(b) Let X = (X0 , 0 ) be the strategy that replicates the option V . Then
FERM 505 - Homework 3 - Solutions
1. Notice that we can rewrite the final payoff of the happy call as
max(.5ST , ST K) = .5ST + max(0, .5ST K)
= .5ST + .5 max(0, ST 2K)
It is clear that we can replica
FERM505 - Assignment 0
Muzaffer Akat
You do not have to turn in.
1. Let T > 0 be given. Let C denote a European call option (on a stock S) with exercise
date T and strike price Kc = $50.00. Let P deno
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
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:
Wher
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 ,
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 Blac
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 o
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
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 righ
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