NATURE OF MATHEMATICS LL + WEBASSIGN
13th Edition
ISBN: 9780357325865
Author: SMITH
Publisher: CENGAGE L
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Textbook Question
Chapter 9.1, Problem 41PS
The edges of a cube form a three-dimensional network. Are the edges of a cube traversable?
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Question 1. Your manager asks you to explain why the Black-Scholes model may be inappro-
priate for pricing options in practice. Give one reason that would substantiate this claim?
Question 2. We consider stock #1 and stock #2 in the model of Problem 2. Your manager
asks you to pick only one of them to invest in based on the model provided. Which one do you
choose and why ?
Question 3. Let (St) to be an asset modeled by the Black-Scholes SDE. Let Ft be the price
at time t of a European put with maturity T and strike price K. Then, the discounted option
price process (ert Ft) t20 is a martingale. True or False? (Explain your answer.)
Question 4. You are considering pricing an American put option using a Black-Scholes model
for the underlying stock. An explicit formula for the price doesn't exist. In just a few words (no
more than 2 sentences), explain how you would proceed to price it.
Question 5. We model a short rate with a Ho-Lee model drt = ln(1+t) dt +2dWt. Then the
interest rate…
In this problem, we consider a Brownian motion (W+) t≥0. We consider a stock model (St)t>0
given (under the measure P) by
d.St 0.03 St dt + 0.2 St dwt,
with So 2. We assume that the interest rate is r = 0.06. The purpose of this problem is to
price an option on this stock (which we name cubic put). This option is European-type, with
maturity 3 months (i.e. T = 0.25 years), and payoff given by
F = (8-5)+
(a) Write the Stochastic Differential Equation satisfied by (St) under the risk-neutral measure
Q. (You don't need to prove it, simply give the answer.)
(b) Give the price of a regular European put on (St) with maturity 3 months and strike K = 2.
(c) Let X =
S. Find the Stochastic Differential Equation satisfied by the process (Xt)
under the measure Q.
(d) Find an explicit expression for X₁ = S3 under measure Q.
(e) Using the results above, find the price of the cubic put option mentioned above.
(f) Is the price in (e) the same as in question (b)? (Explain why.)
3. Consider the polynomial equation 6-iz+7z² - iz³ +z = 0 for which the roots are 3i, -2i, -i,
and i.
(a) Verify the relations between this roots and the coefficients of the polynomial.
(b) Find the annulus region in which the roots lie.
Chapter 9 Solutions
NATURE OF MATHEMATICS LL + WEBASSIGN
Ch. 9.1 - Level 1 IN YOUR OWN WORDS Describe the Konigsberg...Ch. 9.1 - Prob. 2PSCh. 9.1 - Level 1 IN YOUR OWN WORDS Describe the solution to...Ch. 9.1 - Prob. 4PSCh. 9.1 - Prob. 5PSCh. 9.1 - Prob. 6PSCh. 9.1 - Prob. 7PSCh. 9.1 - Prob. 8PSCh. 9.1 - Prob. 9PSCh. 9.1 - Prob. 10PS
Ch. 9.1 - Which of the networks in Problem 6-11 have Euler...Ch. 9.1 - Prob. 12PSCh. 9.1 - Prob. 13PSCh. 9.1 - Prob. 14PSCh. 9.1 - Prob. 15PSCh. 9.1 - Prob. 16PSCh. 9.1 - Prob. 17PSCh. 9.1 - Prob. 18PSCh. 9.1 - Prob. 19PSCh. 9.1 - Prob. 20PSCh. 9.1 - Prob. 21PSCh. 9.1 - Prob. 22PSCh. 9.1 - Prob. 23PSCh. 9.1 - Prob. 24PSCh. 9.1 - Prob. 25PSCh. 9.1 - Prob. 26PSCh. 9.1 - Prob. 27PSCh. 9.1 - Prob. 28PSCh. 9.1 - Prob. 29PSCh. 9.1 - Prob. 30PSCh. 9.1 - Prob. 31PSCh. 9.1 - Prob. 32PSCh. 9.1 - HISTORICAL QUEST Travelers Dodecahedron This...Ch. 9.1 - HISTORICAL QUEST Is there an Euler circuit for the...Ch. 9.1 - Prob. 35PSCh. 9.1 - Prob. 36PSCh. 9.1 - Prob. 37PSCh. 9.1 - Prob. 38PSCh. 9.1 - Prob. 39PSCh. 9.1 - Prob. 40PSCh. 9.1 - The edges of a cube form a three-dimensional...Ch. 9.1 - A saleswoman wants to visit eastern cities, New...Ch. 9.1 - Prob. 43PSCh. 9.1 - Prob. 44PSCh. 9.1 - Repeat Problem 44 using the brute-force method....Ch. 9.1 - Count the number of vertices, edges arcs, and...Ch. 9.1 - The saleswoman in Problem 42 needs to add Atlanta...Ch. 9.1 - A quality control inspector must visit franchises...Ch. 9.1 - Prob. 49PSCh. 9.1 - Prob. 50PSCh. 9.1 - On a planet far, far away, Luke finds himself in a...Ch. 9.1 - How many paths are there to room n in Problem 51?...Ch. 9.1 - Emil Torday told the story of seeing some African...Ch. 9.1 - Prob. 54PSCh. 9.1 - Prob. 55PSCh. 9.1 - Prob. 56PSCh. 9.1 - Prob. 57PSCh. 9.1 - Prob. 58PSCh. 9.1 - Prob. 59PSCh. 9.1 - Prob. 60PSCh. 9.2 - Prob. 1PSCh. 9.2 - Prob. 2PSCh. 9.2 - Prob. 3PSCh. 9.2 - Prob. 4PSCh. 9.2 - Prob. 5PSCh. 9.2 - Prob. 6PSCh. 9.2 - Prob. 7PSCh. 9.2 - Prob. 8PSCh. 9.2 - Prob. 9PSCh. 9.2 - Prob. 10PSCh. 9.2 - Prob. 11PSCh. 9.2 - Prob. 12PSCh. 9.2 - Prob. 13PSCh. 9.2 - Prob. 14PSCh. 9.2 - Prob. 15PSCh. 9.2 - Prob. 16PSCh. 9.2 - Prob. 17PSCh. 9.2 - Prob. 18PSCh. 9.2 - Prob. 19PSCh. 9.2 - Prob. 20PSCh. 9.2 - Prob. 21PSCh. 9.2 - Prob. 22PSCh. 9.2 - Prob. 23PSCh. 9.2 - Prob. 24PSCh. 9.2 - Prob. 25PSCh. 9.2 - Prob. 26PSCh. 9.2 - Prob. 27PSCh. 9.2 - Prob. 28PSCh. 9.2 - Prob. 29PSCh. 9.2 - Prob. 30PSCh. 9.2 - Prob. 31PSCh. 9.2 - Prob. 32PSCh. 9.2 - Prob. 33PSCh. 9.2 - Prob. 34PSCh. 9.2 - Prob. 35PSCh. 9.2 - Prob. 36PSCh. 9.2 - Prob. 37PSCh. 9.2 - Prob. 38PSCh. 9.2 - Prob. 39PSCh. 9.2 - Prob. 40PSCh. 9.2 - Prob. 41PSCh. 9.2 - Prob. 42PSCh. 9.2 - Prob. 43PSCh. 9.2 - Prob. 44PSCh. 9.2 - Prob. 45PSCh. 9.2 - Prob. 46PSCh. 9.2 - Prob. 47PSCh. 9.2 - Prob. 48PSCh. 9.2 - Prob. 49PSCh. 9.2 - Suppose you wish to install a drip sprinkler...Ch. 9.2 - Prob. 51PSCh. 9.2 - Prob. 52PSCh. 9.2 - Prob. 53PSCh. 9.2 - Prob. 54PSCh. 9.2 - Prob. 55PSCh. 9.2 - Prob. 56PSCh. 9.2 - Prob. 57PSCh. 9.2 - Prob. 58PSCh. 9.2 - Prob. 59PSCh. 9.2 - Prob. 60PSCh. 9.3 - Prob. 1PSCh. 9.3 - Prob. 2PSCh. 9.3 - Prob. 3PSCh. 9.3 - IN YOUR OWN WORDS What is a tessellation?Ch. 9.3 - Prob. 5PSCh. 9.3 - Prob. 6PSCh. 9.3 - Prob. 7PSCh. 9.3 - Prob. 8PSCh. 9.3 - Prob. 9PSCh. 9.3 - Prob. 10PSCh. 9.3 - Prob. 11PSCh. 9.3 - Prob. 12PSCh. 9.3 - Prob. 13PSCh. 9.3 - Prob. 14PSCh. 9.3 - Prob. 15PSCh. 9.3 - Prob. 16PSCh. 9.3 - Prob. 17PSCh. 9.3 - Prob. 18PSCh. 9.3 - Prob. 19PSCh. 9.3 - Prob. 20PSCh. 9.3 - Prob. 21PSCh. 9.3 - Prob. 22PSCh. 9.3 - Prob. 23PSCh. 9.3 - Prob. 24PSCh. 9.3 - Prob. 25PSCh. 9.3 - Prob. 26PSCh. 9.3 - Prob. 27PSCh. 9.3 - Prob. 28PSCh. 9.3 - Prob. 29PSCh. 9.3 - Group the letters of the alphabet in the fonts...Ch. 9.3 - Prob. 31PSCh. 9.3 - Prob. 32PSCh. 9.3 - Prob. 33PSCh. 9.3 - Prob. 34PSCh. 9.3 - Prob. 35PSCh. 9.3 - Prob. 36PSCh. 9.3 - Prob. 37PSCh. 9.3 - Prob. 38PSCh. 9.3 - Prob. 39PSCh. 9.3 - Prob. 40PSCh. 9.3 - Prob. 41PSCh. 9.3 - Prob. 42PSCh. 9.3 - Prob. 43PSCh. 9.3 - Prob. 44PSCh. 9.3 - Prob. 45PSCh. 9.3 - Prob. 46PSCh. 9.3 - Prob. 47PSCh. 9.3 - Prob. 48PSCh. 9.3 - Prob. 49PSCh. 9.3 - Prob. 50PSCh. 9.3 - Prob. 51PSCh. 9.3 - Prob. 52PSCh. 9.3 - Prob. 53PSCh. 9.3 - Prob. 54PSCh. 9.3 - Prob. 55PSCh. 9.3 - Prob. 56PSCh. 9.3 - Prob. 57PSCh. 9.3 - Prob. 58PSCh. 9.3 - Prob. 59PSCh. 9.3 - Prob. 60PSCh. 9.CR - Prob. 1CRCh. 9.CR - Prob. 2CRCh. 9.CR - Prob. 3CRCh. 9.CR - Prob. 4CRCh. 9.CR - Prob. 5CRCh. 9.CR - Prob. 6CRCh. 9.CR - Prob. 7CRCh. 9.CR - Prob. 8CRCh. 9.CR - Prob. 9CRCh. 9.CR - Prob. 10CRCh. 9.CR - Prob. 11CRCh. 9.CR - Prob. 12CRCh. 9.CR - Prob. 13CRCh. 9.CR - Prob. 14CRCh. 9.CR - Prob. 15CRCh. 9.CR - Prob. 16CRCh. 9.CR - Prob. 17CRCh. 9.CR - Prob. 18CRCh. 9.CR - Prob. 19CRCh. 9.CR - Prob. 20CR
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