Math 238 Winter 2009 Problem Set 3 - Solutions
March 4, 2009
Problem 1 Consider a company with N outstanding shares and M outstanding European warrants. Each warrant entitles the holder to purchase shares from the company at time T at a price K per share.
MATH 238 WINTER 2009 PROBLEM SET 1 - SOLUTIONS Problem 1: Let S be the current stock price, K the strike price of the option, T the expiration time of the option, t the current time, ST the stock price at time T , r the risk-free interest rate, c the pric
Math 238, Financial Mathematics Problem set 3
February 5, 2009
These problems are due on Friday February 13. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Consider a company
Math 238, Financial Mathematics Problem Set 4 Solutions
February 28, 2009
Problem 1 Consider the Vasicek (or Ornstein-Uhlenbeck) model for the observed short rate (money market rate) rt which is drt = a(r rt )dt + dWt Here r is the observed equilibrium le
Math 238, Financial Mathematics Problem set 1
January 13, 2009
These problems are due on Tusday January 20. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Let St be the curren
The Journal of Derivatives 1993.1.1:71-84. Downloaded from www.iijournals.com by PRINCETON UNIVERSITY on 11/11/10.
It is illegal to make unauthorized copies of this article, forward to an unauthorized user or to post electronically without Publisher permi
Math 238, Financial Mathematics Homework 5 Solutions
March 17, 2009
Problem 1 For the Vasicek short rate model, the price c(t, T1 , K, T2 ) at time t of a call option maturing at time T1 with strike price K on a zero coupon bond with maturing at time T2 (
Stochastic Processes
Amir Dembo (revised by Kevin Ross)
April 8, 2008
E-mail address: amir@stat.stanford.edu
Department of Statistics, Stanford University, Stanford, CA 94305.
Contents
Preface
5
Chapter 1. Probability, measure and integration
1.1. Probabi
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Math 238, Financial Mathematics Problem set 2
January 27, 2009
These problems are due on Friday January 30, 5:00pm. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. You will need to use M
The Pricing of Options and Corporate Liabilities
Author(s): Fischer Black and Myron Scholes
Reviewed work(s):
Source: Journal of Political Economy, Vol. 81, No. 3 (May - Jun., 1973), pp. 637-654
Published by: The University of Chicago Press
Stable URL: ht
Math 238, Financial Mathematics
Problem set 3
February 11, 2016
These problems are due on Friday February 19, 5:00 pm. You can give them to me in class,
drop them in my office, or put them in my mailbox outside the mathematics department.
Problem 1
Consid
PDEs with Applications to Finance
Spring 2015
Lecture 7
Lecturer: Marta Leniec
E-mail: marta.leniec@math.uu.se
1. Introduction to American Options
Recall that a European option is an option that can be only exercised at the maturity
time T > 0. An America
Problem 3
Consider the pricing of the American perpetual put option. Let the underlying price process
be geometric Brownian motion in the risk neutral setting
dSt = rSt dt + St dWt , S0 = S.
The price of a perpetual American put option with strike price K
CHAPTER 5
American Options
The distinctive feature of an American option is its early exercise privilege,
that is, the holder can exercise the option prior to the date of expiration.
Since the additional right should not be worthless, we expect an America
Appl Math Optim 17:37-60 (1988)
Applied Mathematics
and Optimization
1988 Springer-Verlag New York Inc.
On the Pricing of American Options*
Ioannis Karatzas
Department of Statistics, Columbia University, New York, NY 10027, USA, and
Center for Stochastic
Mathematical Finance, Vol. 1, No. 2 (April 1991), 1—14
OPTIMAL STOPPING AND THE AMERICAN PUT
S. D. JACKA‘
Department of Statistics, University of Warwick, Coventry, England
We show that the problem of pricing the American put is equivalent to solving an
Financial Applications of Random Matrix Theory: a short review
Jean-Philippe Bouchaud, Marc Potters
Science & Finance, Capital Fund Management, 6 Bd Haussmann, 75009 Paris France
I.
arXiv:0910.1205v1 [q-fin.ST] 7 Oct 2009
A.
INTRODUCTION
Setting the stage
SIAM REVIEW
Vol. 15, No. 1, January 1973
MATHEMATICS OF SPECULATIVE PRICE*
PAUL A.
SAMUELSON"
This paper is dedicated to a great mind, L. J. Savage of Yale.
Abstraeto A variety of mathematical methods are applied to economists analyses of speculative
pric
Math 238, Financial Mathematics
Problem set 2
January 25, 2016
These problems are due on Monday February 1, noon. You can give them to me in class, drop
them in my office, or put them in my mailbox outside the mathematics department. You will need
to use
Math 238, Financial Mathematics
Fourth and Final Problem set
February 24, 2016
This problem is due on Friday March 4, 5:00pm. You can give it to me in class, drop it in my
office, or put it in my mailbox outside the mathematics department.
Problem 1
Consi
Math 238, Financial Mathematics
Problem set 1
January 16, 2016
These problems are due on Friday January 22 by 5pm. You can give them to me in class,
drop them in my office 380-383V, or put them in my mailbox outside the mathematics department.
Give refere
MATH 238 WINTER 2009 PROBLEM SET 2 - SOLUTIONS
Problem 1 Derive the put-call parity relation using the Black-Scholes equation and then give a no-arbitrage interpretation of it. Solution Let C (x, t) and P (x, t) denote the solutions of the Black-Scholes e
Math 238, Financial Mathematics Problem set 4
February 17, 2009
These problems are due on Tuesday February 24. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Consider the Vasi
Math 238, Financial Mathematics Final Problem set
March 3, 2009
These problems are due on Tuesday March 10. You can give them to me in class, drop them in my oce, or put them in my mailbox outside the mathematics department. Problem 1 Discuss the pricing
On the pricing and hedging
of volatility derivatives
SAM HOWISON
Mathematical Institute, University of Oxford, 24 29 St. Giles,
OX1 3LB Oxford, UK
Email: howison@maths.ox.ac.uk
AVRAAM RAFAILIDIS
Department of Mathematics, Kings College London,
Strand, Lon
Pricing and Hedging Volatility Derivatives
Mark Broadiea
Ashish Jainb
January 10, 2008
Abstract
This paper studies the pricing and hedging of variance swaps and other volatility derivatives,
including volatility swaps and variance options, in the Heston s
Towards a Theory of Volatility Trading
Peter Carr
Morgan Stanley
1585 Broadway, 6th Floor
New York, NY 10036
(212) 761-7340
carrp@ms.com
Dilip Madan
College of Business and Management
University of Maryland
College Park, MD 20742
(301) 405-2127
dbm@mbs.um
ROBERT E. WHALEY*
Understanding VIX
ABSTRACT
In the recent weeks of market turmoil, financial news services have begun
routinely reporting the level of the CBOEs Market Volatility Index or VIX, for short.
While this new practice is healthy in the sense t