Alan would like to speculate on a possible rise in stock price of Garmin. The cu

Question

Alan would like to speculate on a possible rise in stock price of Garmin. The current stock price of Garmin is $42. Alan expects that in one year the stock price of Garmin will be either $48 (up move) or $36 (down move). The excercies price of one-year Eruopena call option of Garmin-$45 and risk-free rate =1% annum. Alan would like to construct a portfolio with the stock and cash from borrowing to replicate the payoff of 100 units of Europeann call option of Garmin.

a.) How many shares of Garmin does Alan need to buy now? b.) How much ($) does Alan need to borrow now? c.) Calulate the percentage margin d.) Calculate the current price of European call option of Garmin per unit in this setting

Explanation / Answer

1) Gross payoff ( up) = max(0,Garmin share price( up) - Exercise price )x 100 units =Max (0,$48 - $45) x 100 = $300
Gross payoff ( down) = max(0,Garmin share price( down) - Exercise price )x 100 units =Max (0,$36 - $45) x 100 = $0
Number of shares Alan need to buy = 100 units x ( Gross payoff up - Gross payoff down)/(Up and down price)
Number of shares = 100 x ($3- $0)/($48-$36) = 25 shares)

2) Borrowing = 25 shares x -$36 (down price)/(1+ 1%(Risk free rate) = $818.18
3) Percentage Margin = Value of stock - loan/ value of stock
Percentage margin = (($45 x 25 shares) - $818.18)/($45 x 25 shares) = 27.27%

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