A stock price is currently $50. Over the next six-month period it is expected to go up by 8% or down by 4% . The risk-free interest rate is 4% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $49?
Answers
Since the binomial tree necessitates iterative computations, I'll walk you through the steps of constructing the tree and calculating the option values at each node.
To value the six-month European call option using the binomial tree approach, we must first build a binomial tree and then compute the option value at each node. Here's one approach to the problem:
Define the parameters:
Current stock price (S0) = $50
Strike price (X) = $49
Time to expiration (T) = 6 months
Risk-free interest rate (r) = 4% per annum = 0.04 (continuous compounding)
Upward price movement factor (u) = 1 + 8% = 1.08
Downward price movement factor (d) = 1 - 4% = 0.96
Calculate the parameters for the binomial tree:
Number of time steps (n) = 2 (since there are two three-month periods in the six-month option)
Time step size (Δt) = T/n
Time step size (Δt) = 6/2
Time step size (Δt) = 3 months
Time step size (Δt) = 0.25 years
Calculate the probabilities of upward and downward movements:
Probability of upward movement (p) = (1 + r - d)/(u - d)
Probability of downward movement (1 - p)
Construct the binomial tree:
Start at the initial stock price node (S0)
At each subsequent time step, calculate the stock price using the upward and downward movement factors
Calculate the option value at each node using the formula:
Option value = \(e^{-r \times \triangle t}\) [p × Option value at up node + (1 - p) × Option value at down node]
Backward induction:
Begin at the final nodes (last time step) and work your way backward, using the option value formula from step 4.
When we get to the first node (S₀), the value there indicates the value of the European call option.
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The complete question is:
A stock price is currently $50. Over each of the next two three-month periods it is expected to go up by 8% or down by 4% . The risk-free interest rate is 4% per annum with continuous compounding. What is the value of a six-month European call option with a strike price of $49? Use binomial tree method to solve this problem.
Related Questions
Please answer my question quickly.
Answers
Answer:
b=sqrt7
Step-by-step explanation:
16=9+b^2
Write the equation of the
line that is perpendicular to
y = -7/5x + 1 and goes
through (5, 3)
A) y= 7/5x-4/7
B) y= -7/5x-4/7
C) y= 5/7x-3/7
D) y= 5/7x-4/7
E) y= 1/7x+3
Answers
Answer:
Step-by-step explanation:
The answer is D.
The rule for perpendicular lines is that the slope will be the negative reciprocal. Because this equation is in slope-intercept form, the coefficient of x is the slope. -7/5 becomes 5/7. Our new equation is y=5/7x+b. Plugging in (5,3), we see that b is equal to -4/7. Our equation is then y=5/7x-4/7
true or false: when two numerical figures appear side by side, spelled-out numbers and numerals should be alternated for clarity.
Answers
When two numbers appear side by side, the number and number should be written together for clarity. The statement is true.
The term numeric expression consists of two words, number for a number and expression for a sentence. Therefore, it is a word containing numbers. Teaching mathematics is the combination of numbers and mixed numbers using mathematical operations such as addition, subtraction, division, or division. There are many number expressions such as word form and number form. Numerical expressions are mathematical expressions that contain only numbers and one or more operators.
Examples of symbol operations are addition, subtraction, multiplication, and division. It can be represented by a radical symbol (square root symbol) or a real value.
Equations consist of numbers and contain multiple digits. There is no limit to the number of operators a shared account can have. Some numbers use only one operator of the two numbers, while others may have more than one operator. The only requirement for a numeric expression is that it only contains a number and an operator. Some numbers have only one operator code others have two or more.
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Which of the following is the same as 2,088 feet per minute
Answers
Answer: 0.3954 Miles per minute
Step-by-step explanation:
Answer:
Step-by-step explanation:
2088/69=34.8
Brad jarred 12 liters
of jam after 2 days.
How much jam did
Brad jar if he spent 3
days making jam?
Answers
12 divided by 2 is 6.
We know each day Brad jars 6.
6 x 3 = 18
Answer:
18 liters
Step-by-step explanation:
We can use ratios to solve
12 liters x liters
----------- = -----------
2 days 3 days
Using cross products
12 *3 = 2x
36 =2x
Divide by 2
36/2 = 2x/2
18 =x
18 liters
in order from least to greatest: 7/11, 0.7 and 60%.
Answers
First is to express all values the same way. For example, convert the fraction and percentage into decimal numbers:
60% → divide it by 100 and you get 0.6
7/11=0.63
Now you can order them
0.6<0.63<0.7
Using the original expressions you get that:
60%<7/11<0.7
The United Kingdom Forestry Commission reports that 43% hectares of woodland area in the United Kingdom had certification identifying them as "sustainably managed" in 2016. Suppose an employee took a simple random sample of 400 of the hectares and saw that the records showed that 47% of the sampled hectares had that certification in 2016. Identify your information:
N =
400
P =
0. 43
Check Conditions:
10% Condition:
We assume 400 hectares is less than 10% of all hectares
Large Counts Condition:
400(0. 43) and 400(1-0. 43) are both < 10
Is this approximately normal?
Yes, BECAUSE the 10% condition is met!
Find the Important Values:
Mean of p-hat:
Standard Deviation of p-hat:
0. 0248
Assuming that the Forestry Commission's report is accurate, what is the approximate probability that more than 47% of the sample would have had the certification in 2016?
Draw Conclusions:
Is there strong evidence against the claimed value of 43%?
Since our probability of
is
than 5%, there
strong evidence against the claimed
Answers
There is not strong evidence against the claimed value of 43%.
N = 400
P = 0.43
Check Conditions:
10% Condition: We assume 400 hectares is less than 10% of all hectares, so this condition is met.
Large Counts Condition: 400(0.43) = 172 and 400(1-0.43) = 228 are both greater than 10, so this condition is met.
Is this approximately normal? Yes, because both the 10% condition and the Large Counts condition are met.
Find the Important Values:
Mean of p-hat: 0.43
Standard Deviation of p-hat: sqrt((0.43)(1-0.43)/400) = 0.0248
Assuming that the Forestry Commission's report is accurate, what is the approximate probability that more than 47% of the sample would have had the certification in 2016?
We need to find the z-score for 0.47: z = (0.47-0.43)/0.0248 = 1.61
Using a z-table, we find that the probability of getting a z-score greater than 1.61 is 0.0537.
Since our probability of 0.0537 is greater than 5%, there is not strong evidence against the claimed value of 43%.
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Calculate the volume of the triangular prism shown below. Give your answer in cm³. 5 cm 7 cm 9 cm 4 cm
Answers
The volume of the given triangular prism is 315 cm³.
The volume of a triangular prism, we need to multiply the base area of the triangular base by the height of the prism.
The triangular base has a base length of 5 cm and a height of 7 cm, and the height of the prism is 9 cm.
Calculate the area of the triangular base.
The area of a triangle can be calculated using the formula:
Area = (base length × height) / 2
Plugging in the values, we have:
Area = (5 cm × 7 cm) / 2
Area = 35 cm²
Calculate the volume of the prism.
The volume of a prism can be calculated by multiplying the base area by the height of the prism.
Volume = Base area × Height
Volume = 35 cm² × 9 cm
Volume = 315 cm³
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Find the value of x.
15 points !
Answers
Answer:
22
Step-by-step explanation: babab
Simplify each expression.
(2+i)(4-5 i)
Answers
The simplified expression for (2+i)(4-5i) is 13 - 6i. To simplify the expression (2+i)(4-5i), we can use the distributive property of multiplication over addition.
First, we multiply the real parts: 2 * 4 = 8.
Then, we multiply the imaginary parts: i * (-5i) = -5i².
Since i² is defined as -1, we have -5i² = -5(-1) = 5.
Finally, we combine the real and imaginary parts: 8 + 5i.
Therefore, the simplified expression is 8 + 5i.
However, if we prefer to express the answer in the standard form a + bi, where a and b are real numbers, we can rewrite 8 + 5i as 13 - 6i by rearranging the terms. This form is commonly preferred because it allows for easier comparison and computation of complex numbers.
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High school students from grades 9–10 and 11–12 were asked to choose the kind of band to have play at a school dance: rap, rock, or country. Their choices were as follows: Grades 9–10—Rap: 40; Rock: 30; Country: 55 Grades 11–12—Rap: 60; Rock: 25; Country: 35 Which of the following is a correct two-way frequency table for the data? Band preference for school dance Rap Rock Country Row totals Grades 9–10 0. 28 0. 21 0. 38 0. 86 Grades 11–12 0. 41 0. 17 0. 24 0. 83 Column totals 0. 69 0. 38 0. 62 1 Band preference for school dance Rap Rock Country Row totals Grades 9–10 0. 40 0. 55 0. 61 0. 86 Grades 11–12 0. 60 0. 45 0. 39 0. 83 Column totals 1 1 1 1 Band preference for school dance Rap Rock Country Row totals Grades 9–10 40 30 55 125 Grades 11–12 60 25 35 120 Column totals 100 55 90 245 Band Preference for School Dance Rap Rock Country Row totals Grades 9–10 0. 32 0. 24 0. 44 1 Grades 11–12 0. 50 0. 21 0. 29 1 Column totals 0. 69 0. 38 0. 62 1.
Answers
The correct two-way frequency table for the data on Band preference for school dance is Option D):
Band preference for school dance
RAP ROCK COUNTRY TOTAL
Grades 9-10 40 30 55 125
Grades 11-12 60 25 35 120
TOTAL 100 55 90 245
What is a two-way frequency table?A two-way frequency table is a frequency table that displays frequencies for two different categories of data about a single group.
In the twop-way frequency table, one category is represented by the rows and the columns represent the other category.
Thus, Option D shows the correct two-way frequency table.
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What triangle is formed by the points (3,2), (4,7), and (5,6)?
10
9
8
7
6
5
4
3
2
1
0
10
9
8
C
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9 10
0 1 2 3 4 5 6 7 8 9 10
Answers
Answer:
See attachement
Step-by-step explanation:
I can't interpret the table of options. A drawing is attached.
A video club costs $25 to join. Each video that is rented costs $2.50. Let v represent the
number of videos. Identify the independent and dependent variables. Then, write a rule
in function notation for the situation.
Answers
Answer:
Independent: videos rented; Dependent: total cost; f(v) = 2.5v + 25
Step-by-step explanation:
plz mark as brainliest i tryed my best im sure its right
Find x. Round your answer to the nearest tenth of a degree.
Answers
The measure of the angle that is missing from the given triangle would be =56.4°
How to calculate the measure of the missing angle of the triangle?To calculate the measure of the missing angle of the given triangle, the sine rule must be obeyed such as given below;
a/sinA = b/sinB
where;
a = 5
A = X
b = 6
B = 90°
That is ;
5/sinX = 6/sin90°
sinX = 5×1/6
= 0.8333
X = Sin-1(0.8333)
= 56.4°
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wo points in the xy plane have Cartesian coordinates (5.50,−7.00)m and (−6.50,6.50)m. (a) Determine the distance between these points. m (b) Determine their polar coordinates. (5.50,−7.00)r= (5.50,−7.00)θ= oounterclockwise from the +x-axis (−6.50,6.50)r= (−6.50,6.50)θ=∘ counterclockwise from the +x-axis
Answers
Let's solve the given questions step by step. The distance between the two points is approximately 18.06 meters. The polar coordinates for this point are approximately (9.19, -45 degrees).
(a) To determine the distance between two points in the xy-plane, we can use the distance formula, which is derived from the Pythagorean theorem. The distance (d) between the points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates provided, we can substitute the values and calculate the distance between the two points:
d = √((-6.50 - 5.50)^2 + (6.50 - (-7.00))^2)
= √((-12)^2 + (13.50)^2)
= √(144 + 182.25)
= √326.25
≈ 18.06 m
Therefore, the distance between the two points is approximately 18.06 meters.
(b) The polar coordinates of a point represent its distance from the origin (r) and the angle it makes with the positive x-axis (θ) measured counterclockwise.
For the first point (5.50, -7.00)m, we can calculate the polar coordinates as follows:
r = √((5.50)^2 + (-7.00)^2) ≈ 8.71 m
θ = arctan(-7.00/5.50) ≈ -52.13 degrees
The polar coordinates for this point are approximately (8.71, -52.13 degrees).
Similarly, for the second point (-6.50, 6.50)m:
r = √((-6.50)^2 + (6.50)^2) ≈ 9.19 m
θ = arctan(6.50/-6.50) ≈ -45 degrees
The polar coordinates for this point are approximately (9.19, -45 degrees).
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Find the percent change from the first value to the second.
30; 39
Answers
Answer:
Change in percent = 30%
Step-by-step explanation:
Given:
First value = 30
Second value = 39
Find:
Change in percent
Computation:
Change in percent = [(Second value - First value) / First value]100
Change in percent = [(39 - 30) / 30]100
Change in percent = [(9) / 30]100
Change in percent = 30%
help me please
solve: -11x^2-44=0
Answers
Answer:
1.1 Factoring: x2-44
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 44 is not a square !!
Step-by-step explanation:
There are 25 people in a room and 5 are men. Express the number of men in the group as a fraction. 25/5 5/25 15/25
Answers
Answer:
its 4/10
Step-by-step explanation:
SOMEONE HELP WITH THIS PLEASE!!
Answers
Answer:
Step-by-step explanation:
you just have to evaluate the expression and then solve it
Jane opened a savings account with 700 and was paid simple interest at an annual rate of 2% . When Jane closed the account, she was paid 70 in interest. How long was the account open for, in years?
Answers
Answer:
5 years
Step-by-step explanation:
N/A
What is 2/3 as a decimal
Answers
Answer:
\(. \frac{}{66} \)
Answer:
0.66666667
Step-by-step explanation:
How do I solve this equation?
Answers
Answer:
x = 132
Step-by-step explanation:
Solve by raising both sides to the multiplicative inverse of the exponent.
\(((x-7)^{\frac{2}{3} } )^{\frac{3}{2} } =25^{\frac{3}{2} }\)
x - 7 = 125
x = 132
which two ratios represents quantities that are proportional? A. 15/10 and 10/15 B. 20/25 and 16/20 C. 5/6 and 17/12 D. 15/21 and 20/24
Answers
20/25 = 4/5
16/20 = 8/10 = 4/5
72= 27+ 9s solve the equation
Answers
Answer:
s=5
Step-by-step explanation:
72=27+9s
Subtract 27 from both sides.
72-27=9s+27-27
45=9s
Divide 9 from both sides.
5=s
Determine the surface area of a rectangular prism with the following dimensions:
Length = 4 cm, Width = 2 cm, Height = 3
A.52 sq. cm
D.20 sq.cm
d. 290 sq. cm
B.104 sq.cm
Answers
Answer:
A. 52 sq. cmStep-by-step explanation:
surface area of a rectangular prism = 2(LW + WH + LH)
where
L = 4cm
W = 2cm
H = 3cm
plugin values into the formula:
As = 2(4*2 + 2*3 + 4*3)
As = 52 sq. cm
Answer:
A.52 sq. cm
Step-by-step explanation:
Given: l = 4 cm, w = 2 cm, h = 3 cm
Surface area of a rectangular prism
=2(l*w + w*h+h*l)
= 2(4*2 + 2*3 + 3*4)
= 2(8 + 6 + 12)
= 2*26
= 52 sq. cm
TRUE / FALSE. when the block is in equilibrium, each spring is stretched an additional ∆x. then the block is set into oscillation with amplitude a; when it passes through its equilibrium point it has a speed v.
Answers
The statement is true.
When the block is in equilibrium, each spring is stretched an additional ∆x. This implies that the forces from the two springs are balanced, and the block is not experiencing any net force in the equilibrium position.
When the block is set into oscillation with amplitude a, it will pass through its equilibrium point during the oscillation. At the equilibrium point, the displacement of the block is zero, and it changes direction. At this point, the block has its maximum speed v, as it is accelerating towards the equilibrium position.
The speed of the block decreases as it moves away from the equilibrium position, reaches zero at the maximum displacement (amplitude), and then starts accelerating towards the equilibrium point again. Therefore, when the block passes through its equilibrium point, it has its maximum speed v.
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Calculate 18% tip on a 6250 dinner bill
Answers
The SAT mathematics scores in the state of Florida for this year are approximately normally distributed with a mean of 500 and a standard deviation of 100
Using the empirical rule, what is the probability that a randomly selected score lies between 500 and 700? Express your answer as a decimal and round to 3 decimal places.
Answers
question: when do you take the SAT test
The ratio of income to expenditure is 6:5, find the savings if the expenditure is 20,000 dollars.
Answers
Savings = $4000
Explanations:The ratio of income to expenditure = 6 : 5
Expenditure = $20000
\(\begin{gathered} \frac{Income}{\text{Expenditure}}\text{ = }\frac{6}{5} \\ \frac{Income}{20000}=\text{ }\frac{6}{5} \\ \frac{Income}{20000}=1.2 \\ \text{Income = 20000(1.2)} \\ \text{Income = }24000 \end{gathered}\)Income = $24000
Savings = Income - Expenditure
Savings = $24000 - $20000
Savings = $4000
if you traveled in space at a speed of 1000 miles per house, how far would you travel in 7.5*10^5 houes
Answers
Traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.
To calculate the distance traveled, we can multiply the speed by the time traveled.
Speed = 1000 miles per hour
Time = 7.5 * 10⁵ hours
Distance = Speed * Time
Distance = 1000 miles/hour * 7.5 * 10⁵ hours
To perform this calculation, we can multiply the numerical values and keep the scientific notation for the result:
Distance = 1000 * 7.5 * 10⁵ miles
Distance = 7.5 * 10⁸ miles
Therefore, traveling at a speed of 1000 miles per hour for 7.5 * 10⁵ hours would result in traveling a distance of 7.5 * 10⁸ miles.
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