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Alexxx [7]
2 years ago
8

You are attempting to value a call option with an exercise price of $100 and one year to expiration. The underlying stock pays n

o dividends, its current price is $100, and you believe it has a 50% chance of increasing to $130 and a 50% chance of decreasing to $70. The risk-free rate of interest is 10%. Calculate the call option's value using the two-state stock price model. (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Business
1 answer:
natka813 [3]2 years ago
3 0

Answer:

$18.18

Explanation:

Calculation to determine the call option's value using the two-state stock price model

Based on the information given since the two possible stock prices are: S+ = $130 Increase and and S- = $70 decrease which means that If the exercise price is the amount of $100 the first step will be to determine the corresponding two possible call values.

First step is to determine the corresponding two possible call values.

Hence, the corresponding two possible call values are:

Cu = ($130-$100) and Cd = $0

Cu = $30 and Cd = $0

Second step is to Calculate the hedge ratio using this formula

Hedge ratio= (Cu - Cd)/(uS0 - dS0)

Hedge ratio= (30- 0)/(130 - 70)

Hedge ratio=30/60

Hedge ratio= 0.50

Third step is form the cost of the riskless portfolio and end-of-year value

Cost of the riskless portfolio = (S0 - 2C0)

Cost of the riskless portfolio = 100 - 2C0

End-of-year value =$70

Fourth step is to calculate the present value of $70 with a one-year interest rate of 10%:

Present value=$70/1.10

Present value= $63.64

Now let estimate the call option's value by first Setting the value of the hedged position to equal to the present value

Call option's value=$100 - 2C0 = $63.64

Hence,

C0=$100-$63.64/2

C0=$36.36/2

C0=$18.18

Therefore the call option's value using the two-state stock price model will be $18.18

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4 0
1 year ago
How many days will it take for $1500 to earn $16 interest if it is deposited in a bank paying simple interest at the rate of 4%/
JulsSmile [24]

Answer:

97 days

Explanation:

In simple interest method, the interest is calculated by the following formula

I= P x R x T

I= interest

P = principal amount

R =interest rate

T= Time

In this case

I=$16

P=$1500$

R= 4% or 0.04%

T= time

$16= $1500 x 0.04 x Time

$16 =60 x Time

Time = 16/60

time = 0.2666 year.

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8 0
2 years ago
Moody Farms just paid a dividend of $3.95 on its stock. The growth rate in dividends is expected to be a constant 5 percent per
Amiraneli [1.4K]

Answer:

$81.52

Explanation:

The current share price is the present value of future dividends as well as the present value of the terminal value of dividends beyond year 6 as shown thus:

Current dividend=$3.95

Year 1 dividend=$3.95*(1+5%)=$4.15

Year 2 dividend=$4.15*(1+5%)=$4.36

Year 3 dividend=$4.36*(1+5%)=$4.58

The required rate of return(discount rate) for the dividends in the FIRST 3 years above is 14%

Year 4 dividend=$4.58*(1+5%)=$4.81

Year 5 dividend=$4.81*(1+5%)=$5.05

Year 6 dividend=$5.05*(1+5%)=$5.30

The required rate of return(discount rate) for the dividends in the NEXT 3 years above is 12%

Terminal value of dividend=Year 6 dividend*(1+growth rate)/(rate of return-growth rate)

growth rate=5%

rate of return=10%(rate of return thereafter)

terminal value=$5.30*(1+5%)/(10%-5%)

terminal value=$111.30

current share price=$4.15/(1+14%)+$4.36/(1+14%)^2+$4.58/(1+14%)^3+$4.81/(1+12%)^4+$5.05/(1+12%)^5+$5.30/(1+12%)^6+$111.30/(1+10%)^6

current share price=$81.52

5 0
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