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The current price of a non-dividend-paying stock is $45.09. Over the next six months it is expected to rise to $55.09 or fall to $9.62. Assume the risk-free rate is zero. An investor sells call options with a strike price of $45.09. What is the value of each call option?

User Landons
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Final answer:

The value of each call option is approximately $-12.74. A negative value means the investor is likely to incur a loss if the stock price does not rise above the strike price.

Step-by-step explanation:

The value of each call option can be calculated using the concept of expected value. The expected value is calculated by multiplying the probability of each outcome by its corresponding payoff, and then summing those values.

In this case, there are two possible outcomes: a rise in the stock price to $55.09 and a fall in the stock price to $9.62. The probability of a rise is 50% and the probability of a fall is also 50%. The payoff for a rise is $55.09 - $45.09 = $10. The payoff for a fall is $9.62 - $45.09 = -$35.47 (negative because the investor sells the stock at a loss).

Using these values, we can calculate the expected value:

Expected value = (Probability of rise * Payoff for rise) + (Probability of fall * Payoff for fall)

Expected value = (0.5 * $10) + (0.5 * -$35.47) = $-12.74

Therefore, the value of each call option is approximately $-12.74. Note that a negative value means that the investor is likely to incur a loss by selling the call options if the stock price does not rise above the strike price.

User HiroIshida
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