Homework Help is Here – Start Your Trial Now!
Math
Statistics
ng the m.g.f. for a normal random variable and w that, for Ia = I{Y > a}, we have that E[YIa] ≤e+o² ( log a- σ ain an upper bound for E[(Y - K)+], where (x)¯ e background: a European call option gives you tock. S. at some future time T for a price K. T

ng the m.g.f. for a normal random variable and w that, for Ia = I{Y > a}, we have that E[YIa] ≤e+o² ( log a- σ ain an upper bound for E[(Y - K)+], where (x)¯ e background: a European call option gives you tock. S. at some future time T for a price K. T

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
100%
Let X~ N(μ, o²), and let y = ex. i) Using the m.g.f. for a normal random variable and the Cauchy-Schwarz inequality, show that, for Ia = I{Y > a}, we have that E[YIa] ≤ ¹+² (_loga-μ)² ii) Obtain an upper bound for E[(Y – K)+], where (x)+ = max{x, 0}, and K > 0. Some background: a European call option gives you the right to purchase one share of stock, S, at some future time T for a price K. The price of such an option is the expected payoff e¯rTE[(S – K)+], where r is the interest rate. The result in (ii) can be used to bound the option price under the widely used assumption that the stock price S has a log-normal distribution.
Transcribed Image Text:Let X~ N(μ, o²), and let y = ex. i) Using the m.g.f. for a normal random variable and the Cauchy-Schwarz inequality, show that, for Ia = I{Y > a}, we have that E[YIa] ≤ ¹+² (_loga-μ)² ii) Obtain an upper bound for E[(Y – K)+], where (x)+ = max{x, 0}, and K > 0. Some background: a European call option gives you the right to purchase one share of stock, S, at some future time T for a price K. The price of such an option is the expected payoff e¯rTE[(S – K)+], where r is the interest rate. The result in (ii) can be used to bound the option price under the widely used assumption that the stock price S has a log-normal distribution.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS