9 a outcome s t x s t x stock s t d s t d put x s t

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9. a. Outcome S T X S T > X Stock S T + D S T + D Put X – S T 0 Total X + D S T + D b. Outcome S T X S T > X Call 0 S T – X Zeros X + D X + D Total X + D S T + D The total payoffs for the two strategies are equal regardless of whether S T exceeds X. c.The cost of establishing the stock-plus-put portfolio is: S 0 + P The cost of establishing the call-plus-zero portfolio is: C + PV(X + D) Therefore: S 0 + P = C + PV(X + D) This result is identical to equation 20.2. 20-4
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Chapter 20 - Options Markets: Introduction 10. a. Position S T < X 1 X 1 S T X 2 X 2 < S T X 3 X 3 < S T Long call (X 1 ) 0 S T – X 1 S T – X 1 S T – X 1 Short 2 calls (X 2 ) 0 0 –2(S T – X 2 ) –2(S T – X 2 ) Long call (X 3 ) 0 0 0 S T – X 3 Total 0 S T – X 1 2X 2 – X 1 – S T (X 2 –X 1 ) – (X 3 –X 2 ) = 0 X 2 – X 1 S T X 1 X 2 Payoff X 3 b. Position S T < X 1 X 1 S T X 2 X 2 < S T Buy call (X 2 ) 0 0 S T – X 2 Buy put (X 1 ) X 1 – S T 0 0 Total X 1 – S T 0 S T – X 2 X 1 S T X 1 X 2 Payoff 20-5
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Chapter 20 - Options Markets: Introduction 11. Position S T < X 1 X 1 S T X 2 X 2 < S T Buy call (X 2 ) 0 0 S T – X 2 Sell call (X 1 ) 0 –(S T – X 1 ) –(S T – X 1 ) Total 0 X 1 – S T X 1 – X 2 Payo ff 0 S T X 1 X 2 Payo ff (X 2 –X 1 ) 12. a.By writing covered call options, Jones receives premium income of $30,000. If, in January, the price of the stock is less than or equal to $45, then Jones will have his stock plus the premium income. But the most he can have at that time is ($450,000 + $30,000) because the stock will be called away from him if the stock price exceeds $45. (We are ignoring here any interest earned over this short period of time on the premium income received from writing the option.) The payoff structure is: Stock price Portfolio value less than $45 10,000 times stock price + $30,000 greater than $45 $450,000 + $30,000 = $480,000 This strategy offers some extra premium income but leaves Jones subject to substantial downside risk. At an extreme, if the stock price fell to zero, Jones would be left with only $30,000. This strategy also puts a cap on the final value at $480,000, but this is more than sufficient to purchase the house. b. By buying put options with a $35 strike price, Jones will be paying $30,000 in premiums in order to insure a minimum level for the final value of his position. That minimum value is: ($35 × 10,000) – $30,000 = $320,000 This strategy allows for upside gain, but exposes Jones to the possibility of a moderate loss equal to the cost of the puts. The payoff structure is: Stock price Portfolio value less than $35 $350,000 – $30,000 = $320,000 greater than $35 10,000 times stock price – $30,000 20-6
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Chapter 20 - Options Markets: Introduction c.The net cost of the collar is zero. The value of the portfolio will be as follows: Stock price Portfolio value less than $35 $350,000 between $35 and $45 10,000 times stock price greater than $45 $450,000 If the stock price is less than or equal to $35, then the collar preserves the $350,000 principal. If the price exceeds $45, then Jones gains up to a cap of $450,000. In between $35 and $45, his proceeds equal 10,000 times the stock price.
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