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Hyundai Engineering & Construction's current stock price is 18,000 won, with a 70 percent chance of becoming 19,800 won a year later and a 30 percent chance of becoming 15,300 won. Hyundai Engineering & Construction shares are traded with an exercise price of 19,000 won and a one-year call option. This stock does not pay dividends within a year, and the risk-free interest rate is 8%.

1. What is the difference between the maximum and minimum values of Lee Moo-sik's portfolio after one year, if he owns one share of Hyundai Engineering & Construction and sold one unit of its call option?

Answer:

2. How many units of sale of call options are required to form a risk-free hedge portfolio for one share of Hyundai Engineering & Construction? (Display up to the third decimal place)

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3. What is the price of the call option for Hyundai Engineering & Construction shares? (Indicate up to the third decimal place)

Answer:

4. Suppose a put option with the same conditions as the call option for Hyundai Engineering & Construction shares is being traded. How many units of put options can Lee Moo-sik, who owns one share of Hyundai Engineering & Construction, use to form a risk-free hedge portfolio? (Display up to the third decimal place)

Answer:

5. What is the put option price for Hyundai Engineering & Construction shares in the above problem? (Indicate up to the second decimal place)

Answer:

Answer :

The value of σ (volatility). Without this value, it's not possible to accurately calculate the call option price. Therefore, we cannot determine the difference between the maximum and minimum values of Lee Moo-sik's portfolio after one year.

To find the difference between the maximum and minimum values of Lee Moo-sik's portfolio after one year, we need to calculate the portfolio value in both scenarios and subtract the minimum value from the maximum value.

1. Calculate the portfolio value if the stock price becomes 19,800 won (70% chance):
Portfolio value = Number of shares × Stock price - Cost of call option
Since Lee Moo-sik owns one share of Hyundai Engineering & Construction, the portfolio value in this scenario would be:
Portfolio value = 1 × 19,800 - Cost of call option

2. Calculate the portfolio value if the stock price becomes 15,300 won (30% chance):
Portfolio value = Number of shares × Stock price - Cost of call option
In this scenario, the portfolio value would be:
Portfolio value = 1 × 15,300 - Cost of call option
Now, let's calculate the maximum and minimum values of Lee Moo-sik's portfolio after one year:
Maximum value = Portfolio value if stock price becomes 19,800 won
Minimum value = Portfolio value if stock price becomes 15,300 won

To find the cost of the call option, we can use the Black-Scholes model. The formula to calculate the call option price is:
Call option price = [tex]S₀ × N(d₁) - X × e^{(-rT)} × N(d₂)[/tex]
Where:
S₀ = Current stock price (18,000 won)
X = Exercise price (19,000 won)
r = Risk-free interest rate (8% or 0.08)
T = Time to expiration (1 year)

d₁ = [ln(S₀ / X) + (r + (σ²/2)) × T] / (σ × sqrt(T))
d₂ = d₁ - σ × sqrt(T)

In this problem, we don't have the value of σ (volatility). Without this value, it's not possible to accurately calculate the call option price. Therefore, we cannot determine the difference between the maximum and minimum values of Lee Moo-sik's portfolio after one year.

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