Use Black-Scholes model to determine the price of a European call option. Assume that S0 = $50, rf = .05, T = 6 months, K = $55, and σ = 40%. Please show all work. Please use four decimal places for all calculations.

Answers

Answer 1

The price of a European call option can be determined using the Black-Scholes model. Given the parameters S0 = $50, rf = 0.05, T = 6 months, K = $55, and σ = 0.40, the calculated price of the option is $2.2745.

The Black-Scholes model is used to calculate the price of a European call option based on various parameters. The formula for the price of a European call option is:

C = S0 * N(d1) - K * e^(-rf * T) * N(d2)

Where:

C is the price of the call option

S0 is the current price of the underlying asset

N() represents the cumulative standard normal distribution function

d1 = (ln(S0 / K) + (rf + (σ^2)/2) * T) / (σ * sqrt(T))

d2 = d1 - σ * sqrt(T)

Using the given parameters, we can calculate the values of d1 and d2. Then, we use these values along with the other parameters in the Black-Scholes formula to calculate the price of the option. Substituting the given values into the formula, we have:

d1 = (ln(50 / 55) + (0.05 + (0.40^2)/2) * (0.5)) / (0.40 * sqrt(0.5)) = -0.3184

d2 = -0.3184 - (0.40 * sqrt(0.5)) = -0.6984

Next, we calculate N(d1) and N(d2) using the cumulative standard normal distribution table or a calculator. N(d1) ≈ 0.3745 and N(d2) ≈ 0.2433.

Plugging these values into the Black-Scholes formula, we get:

C = 50 * 0.3745 - 55 * e^(-0.05 * 0.5) * 0.2433 = $2.2745

Therefore, the calculated price of the European call option is approximately $2.2745.

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Related Questions

geometry unit exam a garden wall is 4 feet in height and has a 6-foot shadow. a tree in the garden casts a 24-foot shadow at the same time of day. what is the height of the tree?

Answers

The height of the tree is 16 feet if it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

The shadows at the same time of the day can be compared for the garden wall and a tree as follows;

tree shadow / tree height = wall shadow / wall height

As the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x;

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore the height of the tree is calculated to be 16 feet.

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The height of the tree is 16 feet when it casts a 24 feet shadow at the same time of the day when 4 feet wall casts a 6-foot shadow.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The shadows at the same time of the day can be compared for the garden wall and a tree is given by;

tree shadow / tree height = wall shadow / wall height

Since we know that the height of the wall is given to be 4 feet and it has a 6-foot shadow, and the tree casts a 24-foot shadow, substituting these values in the equation;

24 / x = 6 / 4

Here x represents the height of the tree

Solving for x,

24 / x = 1.5

24 = 1.5 x

x = 24 / 1.5

x = 16

Therefore, the height of the tree is calculated to be 16 feet.

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I have trouble understanding the strategy used to solve this type of equation....

I have trouble understanding the strategy used to solve this type of equation....

Answers

Answer:

Step-by-step explanation:

-3x + 18y = -12

3x - 18y = 4

0 ≠ -8

no solution

What is the solution, if any, to the inequality |3x|20?
all real numbers
solution
no
x>0
x

Answers

Answer:

20×2=40bnmcsshjvghjpiutewqadgjlmbcz

Answer: all real numbers

Step-by-step explanation:

\(y=6x-11 -2x-3y=-7\)

Answers

The value of the variables are x = 2 and y = 1

How to simply the expression

From the information given, we have the simultaneous equations are;

y = 6x -11

-2x - 3y = -7

Now, substitute the value of y in equation 1 to equation 2, we get;

-2x - 3(6x -11) = -7

expand the bracket

-2x - 18x + 33 = -7

collect the like terms

-2x - 18x = -7 - 33

Add the values

-20x = -40

Make 'x' the subject

x = 2

Substitute the values

y = 6x -11

y = 6(2) - 11

y = 1

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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 20 pounds each. There
are 125 boxes in all. If the truck is carrying a total of 3900 pounds in boxes, how many of each type of box is it carrying?

Answers

large box 70, small 55
x+y=125
40x+20y=3900
y=125-x
40x+20(125-x)=3900
40x+2500-20x=3900
20x=1400
x=70
125-70=y
y=55

What is the answer to ... 7x-18=x

Answers

Answer:

x=3

Step-by-step explanation:

7x-18=x

Subtract 7x from each side

7x -18-7x = x-7x

-18 = -6x

divide each side by -6

-18/-6 = -6x/-6

3 =x

answer this correctly and i will give brainliest

answer this correctly and i will give brainliest

Answers

10^13 cause you add the exponents together
10^13 because of exponents

Please can’t you help me!!
REALY FAST PLEASE

Please cant you help me!!REALY FAST PLEASE

Answers

Answer:

65%

Step-by-step explanation:

this is because the decrease of price is 247 amd if u divide by original its 65%

What has to be true if you want to convert one rate to another rate?​

Answers

Answer:

i think it might be the "units of the first rate are both/all distinct from that of the converted rate, but it still represents the same measurement."

Step-by-step explanation:

For a sample of size 17, state the mean and the standard deviation of the sampling distribution of the sample mean. mean of the sampling distribution of the sample mean when n = 17: ____ standard deviation of the sampling distribution of the sample mean when n - 17 rounded to two decimal places: _____

Answers

For a sample of size 17, the mean of the sampling distribution of the sample mean is equal to the population mean. Since the population mean is not given in the question, it cannot be determined.

Standard deviation of the sampling distribution of the sample mean = population standard deviation / square root of sample size. Thus, the standard deviation of the sampling distribution of the sample mean when n = 17 is: To find the standard deviation of the sampling distribution of the sample mean when n = 17, we need to use th

e formula: Standard deviation of the sampling distribution of the sample mean = population standard deviation / square root of sample size Given that the population standard deviation is not provided in the question, it cannot be calculated. Therefore, we cannot find the standard deviation of the sampling distribution of the sample mean when n = 17.

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how many times does the quadratic function below intersect the x-axis?
y=x^2+10x+25​

how many times does the quadratic function below intersect the x-axis?y=x^2+10x+25

Answers

To find how many times the quadratic function intersects the x-axis, set y = 0

y = x^2+10x+25
0 = x^2+10x+25
Factor the right hand side
0 = (x+5)(x+5)
x + 5 = 0
x = - 5

Therefore, the quadratic equation intersects the x-axis at one point (x = -5)

Answer:

A. 1

Step-by-step explanation:

To find the x-intercept, substitute 0 for y and solve for x.

x-intercept(s): (-5,0)

Considering (-5,0) is the only intersection on the x-axis, 1 is your answer.

If you want a visual of this, I recommend you use the Desmos graphing calculator to input your equation. It will show you what the curved line looks like.

find the solution of the system of equation . 3x-y=19 3x-4y=-5

Answers

Answer:

x=9 , y=8

Step-by-step explanation:

\(x=\frac{19+y}{3}\)

\(3\cdot \frac{19+y}{3}-4y=-5\)

\(19-3y=-5\)

\(y=8\)

and now

\(x=\frac{19+y}{3}\)

\(x=9\)

If I get 10 dollars a week how much money will I have saved up in 9-years I WILL GIVE 55 POINTS

Answers

Answer:

$4,680

Step-by-step explanation:

Rate : 10 dollars a week

Per year : 10 x 52 = $5209 x 520 = $4,680

You will have saved up $4,680 in 9 years.

Work the following word problem. Set up the problem in numerical form before you solve it. Then find and reduce the answer. How many times will 1/5 go into 3

Answers

Answer:

15 times of \(\frac{1}{5}\) go into 3.

Step-by-step explanation:

Consider the provided information.

How many times will \(\frac{1}{5}\) go into 3?

First setup the problem in numerical form.

Let x denote the required number of times.

Then, according to the given information, we have

x × \(\frac{1}{5}\) = 3

⇒ x = 3 × 5 = 15

Thus, 15 times of \(\frac{1}{5}\) go into 3.

What is the x-intercept of the line y +2 = 3(x + 1)​

Answers

Answer:

Step-by-step explanation:

y+2=3(x+1)

y+2=3x+3

y+3x+5

y=mx+b

m=x-intercept

x-intercept=3

Answer:

  (-1/3, 0)

Step-by-step explanation:

You want the x-intercept of the line y +2 = 3(x + 1)​.

X-intercept

The x-intercept is the point where the graph intersects the x-axis. The value of y is zero there. It can be found by solving the equation for x with 0 substituted for y.

  0 +2 = 3(x +1) . . . . . substitute y=0 in the given equation

  2/3 = x +1 . . . . . . . . divide by 3

  -1/3 = x . . . . . . . . . . subtract 1

The x-intercept is x=-1/3. The point there is (-1/3, 0).

What is the x-intercept of the line y +2 = 3(x + 1)

NEED HELP ASAP AS SOON AS POSSIBLE, WILL GIVE 69 POINTS
A city park commission received a donation of playground equipment from a parents' organization. The area of the playground needs to be 256 square yards for the children to use it safely. The playground will be rectangular.

The city will also put a fence around the playground. The perimeter, P, of the fence includes the gates. To save money, the city wants the least perimeter of fencing for the area of 256 square yards.

Jovana was trying to find a formula for that perimeter with one side 8 yards longer than the other side using the area. In which step did she make a mistake?

Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
Step 7:
Explain her mistake. What is the correct formula?

NEED HELP ASAP AS SOON AS POSSIBLE, WILL GIVE 69 POINTSA city park commission received a donation of

Answers

Mark Brainliest please

Answer:



Explanation

Jovana needs to solve the equation x(x+8) = 256 for x

To do so, first distribute and get everything to one side

x*(x+8) = 256
x*x+x*8 = 256
x^2+8x = 256
x^2+8x-256 = 0

Now use the quadratic formula (a = 1, b = 8, c = -256)

x=−b±b2−4ac/√2a

x=−(8)±82−4(1)(−256)/√2(1)

x=−8±1088/√2

x≈−8±32.98485/2

x≈−8+32.98485/2 or x≈−8−32.98485/2

x≈24.98485/2 or x≈−40.98483/2

x≈12.49242 or x≈−20.49242

Another approach is to graph x^2+8x-256 and locate the roots as shown below
wwwdotdesmosdotcom/calculator/0miqroxamw
which leads to the same approximate solutions

Ignore the negative solution because a negative length or width makes no sense.

So the only practical x value is roughly 12.49242

If x = 12.49242, then
x+8 = 12.49242+8 = 20.49242

Therefore
Width = W = 12.49242
Length = L = 20.49242
which are approximate

The perimeter is approximately
P = 2*(L+W)
P = 2*(20.49242+12.49242)
P = 65.96968

Side Note:
A = L*W = 20.49242*12.49242 = 255.9999174564
which is fairly close to 256

what might you conclude about the clarity of the water from 1950 to 1980 based on this correlation? (10 points)

Answers

Based on the information provided in the question, it is not clear what correlation is being referred to. To accurately conclude the clarity of the water from 1950 to 1980 based on a correlation, we would need more specific information about the correlation itself.


However, if we assume that the correlation being referred to is between a particular factor and the clarity of the water, we can make some general statements about how the clarity of the water might be affected during that time period.

1. If the correlation indicates a positive relationship between the factor and the clarity of the water, we might conclude that the water became clearer from 1950 to 1980. This could suggest that measures were taken to improve water quality, such as implementing stricter pollution control regulations or enhancing water treatment processes.

2. On the other hand, if the correlation indicates a negative relationship between the factor and the clarity of the water, we might conclude that the water became less clear from 1950 to 1980. This could suggest that factors such as increased pollution, deforestation, or other human activities negatively impacted water quality during that time period.

3. If the correlation is weak or close to zero, it would be difficult to draw any conclusive statements about the clarity of the water from 1950 to 1980 based solely on this correlation. Other factors or variables not considered in the correlation may have had a significant impact on water clarity during that time.

In summary, without specific information about the correlation being referenced, it is not possible to provide a definitive conclusion about the clarity of the water from 1950 to 1980.

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Can someone help me with this question please??

Can someone help me with this question please??

Answers

Answer:

\(x = \frac{16}{3}\)

Step-by-step explanation:

\(3 \times x = 8 \times 2\\3x = 16\\x = \frac{16}{3}\)

A DVD rental service wants to pay close attention to what movies their customers like the most. Which measure of central tendency will give them the best estimate? Explain.

Answers

Answer:

Mode.

Because it is used to determine the most frequently occurring item which in this case is movie.

Step-by-step explanation:

The 3 measure of central tendencies are namely;

Mean, median mode.

- Mean is defined as the average of a set of data.

- Median is the middle term of a set of data that splits that set of data into 2.

- Mode is the term that occurs most frequently in a set of data.

In this question, we want to find the movies most frequently watched.

Thus, from the definitions above earlier, it is clear that the only way to know this is using the mode.

Use algebra to rewrite the integrand; then integrate and simplify. (Use C for the constant of integration.) integral (3x^2 - 4)^2 x^3 dx Use algebra to rewrite the integrand; then integrate and simplify. (Use C for the constant of integration.) integral 3x + 3/x^7 dx

Answers

(a) After integrating and simplification, the ∫(3x² - 4)² x³ dx is 9(x⁸/8) - 24(x⁵/5) + 16(x⁴/4) + C, and also

(b) The integral ∫(x + 3)/x⁷ dx is = (-1/5x⁵) - (1/2x⁶) + C.

Part(a) : We have to integrate : ∫(3x² - 4)² x³ dx,

We simplify using the algebraic-identity,

= ∫(9x² - 24x + 16) x³ dx,

= ∫9x⁷ - 24x⁴ + 16x³ dx,

On integrating,

We get,

= 9(x⁸/8) - 24(x⁵/5) + 16(x⁴/4) + C,

Part (b) : We have to integrate : ∫(x + 3)/x⁷ dx,

On simplification,

We get,

= ∫(x/x⁷ + 3/x⁷)dx,

= ∫(1/x⁶ + 3/x⁷)dx,

= ∫(x⁻⁶ + 3x⁻⁷)dx,

On integrating,

We get,

= (-1/5x⁵) - (3/6x⁶) + C,

= (-1/5x⁵) - (1/2x⁶) + C,

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The given question is incomplete, the complete question is

(a) Use algebra to rewrite the integrand; then integrate and simplify. (Use C for the constant of integration.)

∫(3x² - 4)² x³ dx,

(b) Use algebra to rewrite the integrand; then integrate and simplify. (Use C for the constant of integration.)

∫(x + 3)/x⁷ dx.

question 19 the list 76, 56, 93, 24, 45, 88, 13, 7 , 37 is sorted using bucket sort with 4 buckets. which buck will contain 45?

Answers

Bucket number 2 will contain 45 after sorting the data.

According to the statement, we are given that a data list is sorted using bucket sort with 4 buckets and we have to find which bucket will contain the number 45.

So, the given data list is:

76, 56, 93, 24, 45, 88, 13, 7, 37

The list of data is sorted into buckets and the data contains numbers from 0 to 100.

We know that the 100 numbers are being sorted with 4 buckets which means each bucket contains 25 numbers.

So, let us consider

BUCKET 1: 0 to 25

It contains data numbers 7, 13, and 24.

Now,

BUCKET 2: 25 to 50

It contains data numbers 37 and 45.

Now,

BUCKET 3: 50 to 75

It contains data number 56.

Now,

BUCKET 4: 75 to 100

It contains data numbers 76, 88, and 93.

From sorting, the 45 number sort in bucket 2.

So, bucket number 2 will contain 45 after the list is sorted.

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Find the value for each variable.

Find the value for each variable.

Answers

the value of variable x is 55 answer ok . angle q is 35 p is 90

M and P = 90
N and Q = 35
R= 55

Let an = 5n/4n + 1 Determine whether {an) is convergent. convergent divergent

Answers

To determine whether the sequence {an} = 5n/4n + 1 is convergent or divergent, we can analyze its behavior as n approaches infinity.

First, let's rewrite the expression for the nth term of the sequence:

an = 5n / (4n + 1)

As n approaches infinity, the denominator 4n + 1 becomes dominant compared to the numerator 5n. Therefore, we can simplify the expression by neglecting the term 5n:

an ≈ n / (4n + 1)

Now, we can consider the limit of the sequence as n approaches infinity:

lim(n→∞) n / (4n + 1)

To evaluate this limit, we can divide both the numerator and denominator by n:

lim(n→∞) (1 / 4 + 1/n)

As n approaches infinity, the term 1/n approaches zero, leaving us with:

lim(n→∞) 1 / 4 = 1/4

Since the limit of the sequence is a finite value (1/4), we can conclude that the sequence {an} = 5n/4n + 1 is convergent.

In other words, as n gets larger and larger, the terms of the sequence {an} get closer and closer to the limit of 1/4. This indicates that the sequence approaches a fixed value and does not exhibit wild oscillations or diverge to infinity. Therefore, we can say that the sequence is convergent.

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If RSTUV=KLMNO, then TS =_____.

Answers

The given identity RSTUV ≅ KLMNO implies that TS ≅ ML, which means that the length of TS is congruent to the length of ML.

Congruency refers to the property of two geometric figures that have the same shape and size. If two figures are congruent, then their corresponding sides and angles are equal.

In the context of polygons, congruent polygons have the same number of sides and their corresponding sides and angles are equal. In this case, since RSTUV and KLMNO are congruent polygons, their corresponding sides are equal in length, and we can use this property to determine that TS is congruent to ML.

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Evaluate the following.
3 x 7 + 5 + 20 divided 5

Answers

Answer

30

Step-by-step explanation:

PEMDAS

(3x7) + 5 (20/5)

21 + 5 +4= 26+4

30

1.) 9x³ - 12x - 24x
= 3x² - 4x - 8

2.) 16y⁴ - 8y³ + 20y²
= -4y²+ 2y - 5

3.) = n + 7
n + 3

4.) = m - 6
m + 5​

1.) 9x - 12x - 24x= 3x - 4x - 82.) 16y - 8y + 20y= -4y+ 2y - 53.) = n + 7n + 34.) = m - 6m + 5

Answers

Answer:

u reseach in xauthmath

Step-by-step explanation:

i thin 1+n

12 in.
12 in.
The volume of
the figure is
cubic inches.
6 in
10 in.
8 in.
18 in.

12 in.12 in.The volume ofthe figure iscubic inches.6 in10 in.8 in.18 in.

Answers

Answer:

2,304in^3

Step-by-step explanation:

The formula for volume is [ b * l * h ]. We can use the values we are given to find the volume of both rectangles then add them both together.

12 * 12 * 6 = 864in^3

18 * 10 * 8 = 1,440in^3

Add them both together.

864 + 1440 = 2,304in^3

Best of Luck!

aldosterone stimulates the reabsorption of sodium while enhancing potassium secretion.
a. true b. false

Answers

I believe that may be false

Answer:

Step-by-step explanation:

True.

Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.

This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.

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What is the term for breaking a larger number apart into smaller numbers that can be multiplied together to get a specific result?.

Answers

Answer:

factoring

Step-by-step explanation:

What is the value of x

What is the value of x

Answers

Answer:

23. because there is a 90 degree angle and then the 67 degree angle, and triangle law says that all angles add up to 180.

Step-by-step explanation:

Im not smart but hope this helps

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