2. Let m m i=1 GA G₁ = II Si " where Si = eª¿Zi, i = 1, 2, . . ., m, Z1, Z2, ...., Zm ~ am are constants. Show that N(0, 1) are independent, a1, a2, In(GA) N(u, σ²), ~ and find μ, o², cov(ln(GA), In(S)) and E[max(GA-K,0)] in terms of a1, a2,,..., am and K in the case of E[max(GA – K, 0)]. Note: The result in this question may be used to design a control variate for the arithmetic mean call (or put) option.
2. Let m m i=1 GA G₁ = II Si " where Si = eª¿Zi, i = 1, 2, . . ., m, Z1, Z2, ...., Zm ~ am are constants. Show that N(0, 1) are independent, a1, a2, In(GA) N(u, σ²), ~ and find μ, o², cov(ln(GA), In(S)) and E[max(GA-K,0)] in terms of a1, a2,,..., am and K in the case of E[max(GA – K, 0)]. Note: The result in this question may be used to design a control variate for the arithmetic mean call (or put) option.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Show that
ln(GA) ∼ N (μ, σ2),
and find μ, σ2, cov(ln(GA), ln(Si)) and E[max(GA−K, 0)] in terms of a1, a2, , . . . , am
and K in the case of E[max(GA − K, 0)]
EXPLAIN IN FULL DETAIL EACH STEP BY STEP
![2.
Let
m
m
i=1
GA
G₁ = II Si
"
where Si = eª¿Zi, i = 1, 2, . . ., m,
Z1, Z2,
...., Zm
~
am are constants.
Show that
N(0, 1) are independent, a1, a2,
In(GA) N(u, σ²),
~
and find μ, o², cov(ln(GA), In(S)) and E[max(GA-K,0)] in terms of a1, a2,,..., am
and K in the case of E[max(GA – K, 0)].
Note: The result in this question may be used to design a control variate for
the arithmetic mean call (or put) option.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F643c9073-bfc9-41d3-b50c-3b14187fea75%2F17b96864-6a67-43ec-9544-91be21bcf377%2Fm00wv6b_processed.png&w=3840&q=75)
Transcribed Image Text:2.
Let
m
m
i=1
GA
G₁ = II Si
"
where Si = eª¿Zi, i = 1, 2, . . ., m,
Z1, Z2,
...., Zm
~
am are constants.
Show that
N(0, 1) are independent, a1, a2,
In(GA) N(u, σ²),
~
and find μ, o², cov(ln(GA), In(S)) and E[max(GA-K,0)] in terms of a1, a2,,..., am
and K in the case of E[max(GA – K, 0)].
Note: The result in this question may be used to design a control variate for
the arithmetic mean call (or put) option.
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