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OLga [1]
3 years ago
9

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 $120 and a 50% chance of decreasing to $80. The risk-free rate of interest is 10%.Based upon your assumptions, calculate your estimate of the the call option's value using the two-state stock price model.
Business
1 answer:
Anastasy [175]3 years ago
8 0

Answer:

$13.64

Explanation:

Given:

Exercise price,X = $100

Current price = $100

Value when price is up, uS = $120

Value when price is down, dS= $80

Risk free interest rate = 10%

First calculate hedge ratio, H:

H = \frac{C_u - C_d}{uS - dS}

Where,

Cu = uS - X

= 120 - 100

= $20

H = \frac{20 - 0}{120 - 80} = \ftac{1}{2}

A risk free portfolio involves one share and two call options.

Find cost of portfolio:

Cost of portfolio = Cost of stock - Cost of the two cells.

= $100 - 2C

This portfolio is risk free. The table below shows that

_______________

Portforlio 1:

Buy 1 share $80; Write 2 calls: $0; Total: ($80 + 0) $80

____________________

Portforlio 2:

Buy 1 share: $120; Write 2 calls: -$40; Total: ($120 - $40) $80

Check for oresent value of the portfolio:

Present value = \frac{80}{1 + 0.10} = 72.73

Value = exercise price - value of option

$72.73 = $100 - 2C

Find call option, C

C = \frac{100 - 72.73}{2} = 13.64

Call option's value = $13.64

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Price inelasticity is very beneficial for businesses and is important in understanding how they should formulate their pricing strategy. Price inelasticity offers firms greater flexibility with prices as the change in demand remains essentially the same whether prices increase or decrease. If the price goes up or down, you can expect consumers’ buying habits to stay mostly unchanged.

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Less Overall Revenue

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Explanation:

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