Columbia University Instructor: Rama CONT Assignment 1. Bond pricing. Assignments should be done individually.
M.S. in Financial Engineering Summer 2011.
IEOR 4706: Foundations of Financial Engineering
The table below shows the term structure of (annually
Columbia University Instructor: Rama CONT
M.S. in Financial Engineering Summer 2011.
IEOR 4706: Foundations of Financial Engineering
Solution for Assignment 3. Arbitrage relations. Part I: Consider an arbitrage-free market in which investors can trade in
Columbia University Department of IEOR Foundations of Financial Engineering E4706, Summer 2010 TR 11am-1:30pm, 633 Mudd Columbia Course Work Web Page Prof. Steven Kou 312 Mudd Building [email protected] Tel: 212-854-4334 Professors Oce Hours: TA: TA e-mai
Columbia University
IEOR 4706: Foundations of Financial Engineering
M.S. in Financial Engineering Summer 2011.
Instructor: Rama CONT TA: Jinbeom Kim Assignment 1. Bond pricing.
Assignments should be done individually. The table below shows the term struct
E4706 Foundations of Financial Engineering
Fall 2014
Homework 1
1. Consider the cash ow (3x, 5, x) (at periods 0, 1, 2 respectively) for
some number x > 0.
(a) Apply the discount factor dk = (1 + r)k , with r = 10%, for
period k. Whats the range of x such
E4706 Foundations of Financial Engineering
Part II
Instructor: Tim Leung
IEOR Department
Columbia University
http:/www.columbia.edu/tl2497
Fall 2014
1 / 78
Tim S.T. Leung
E4706 Financial Engineering
One-Period Binomial Model
Suppose the underlying stock c
AMERICAN OPTIONS IN THE BINOMIAL MODEL (REVISED)
MARK H.A. DAVIS
1. The binomial tree. The tree has N time steps corresponding to times k = 0, 1, . . . , N , and
models an asset price Sk . The price is normalized to S0 = 1, and at each branch in the tree
Credit Rating
The cornerstone of credit risk measurement and management for a nancial institution is the credit rating,
whether supplied by an external credit rating agency
(CRA) or generated by an internal credit model. A
credit rating represents an over
Credit Risk
Credit risk is the risk of an economic loss from the
failure of a counterpartya to fulll its contractual
obligations. For example, credit risk in the loan
portfolio of a bank materializes when a borrower fails
to make a payment, either the per
Credit Default Swaps
CDS contracts are usually documented according
to International Swaps and Derivatives Association
(ISDA) standards and specify the following:
A credit default swap (CDS) is a contract between
two parties, the protection buyer and a pr
Final Cheat Sheet for IEOR E4706: Foundations of FE (Fall 2015)
One-Period Definitions
(1) An elementary security is a security that has date t = 1 payoff of the form ej = (0, . . . , 0, 1, 0, . . . , 0),
where the payoff of 1 occurs in state j.
(2) A con
Lecture on Nov 25
(implied density, and hedging with Greeks)
Tuesday, November 25, 2014
4:11 PM
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IEOR-E4706 Foundations of Financial Engineering
Instructor: Tim Leung1
Assets and Derivatives
Financial market instruments can be classied into two types. First, there are the underlying
assets (or securities), such as stocks, bonds, commodities like gold
E4706 Foundations of Financial Engineering Fall 2014
Handout: Probability Essentials
1
Probability Space
The basic notion in probability theory is that of a random experiment: an experiment whose
outcomes are not known in advance. The set of all possible
2
Credit Risk: Defaultable Securities
Credit risk has seen the biggest growth among derivatives
markets in the last few years.
Credit derivatives market: from $170 billion outstanding
notional in 1997, to almost $1400 billion through 2001.
Defaultable
Greeks - Sensitivity Analysis of Calls & Puts
Thursday, November 06, 2014
3:57 PM
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E4706 Foundations of Financial Engineering
Part II
Instructor: Tim Leung
IEOR Department
Columbia University
http:/www.columbia.edu/tl2497
Fall 2014
1 / 78
Tim S.T. Leung
E4706 Financial Engineering
One-Period Binomial Model
Suppose the underlying stock c
11
C H A P T E R
Introduction to
Binomial Trees
A useful and very popular technique for pricing an option involves constructing a
binomial tree. This is a diagram that represents dierent possible paths that might be
followed by the stock price over the li
r-
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Assume a dim'dtnd CUE
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So
- SEES HUM O h)- i—k Off de’ljggf L”:
_ values at were decma5€d Ed 5
, acacia mhbc: far t>fk arc damaged
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Options: Basic Denitions
There are several binary classications that help
dene an option contract.
A nancial option is a contract conferring on the
holder the right, but not the obligation, to engage
in some transaction, on precisely specied terms,
at som
IEOR 4706: Foundations of Financial Engineering Instructor: Rama CONT
_Lecture_.12;._Defaultriskandrapitaletrneture _ _
Note Title 8H NEON
. St: equity Dt value of debt
Equity + Debt = St + D: = Vt- Link betWeen equity risk and default risk
Empirical
PRODUCT TRAINING
Module VII:
SWAPS
FOR INTERNAL USE ONLY
NOT TO BE DISTRIBUTED EXTERNALLY
MORGAN STANLEY
MORGAN STANLEY
PRODUCT TRAINING FID ANALYST PROGRAMME AUGUST 2000
INTEREST RATE SWAPS
An interest rate swap is an agreement between two parties to
exc