You would Ske to hold a protective put position on the stock of Avaion Corporati
ID: 1172481 • Letter: Y
Question
You would Ske to hold a protective put position on the stock of Avaion Corporation to lock in a guarenteed minimum value of $50 at year end Avaion cure stock price will increase by 10% or decrease by 10% The Tbl ate is 5%, ntly sells for $50 Over the neet year, the Unfortunately, no put options re raded on Ava on Co. What portfolio position in stock and T-bill will ensure you a payoff equal to the payot that would be provided by a protective pu with X-$80 O 1 share of stock and $25 in bils O 1share of stock and $50 in bilis O share of stock and $26 19m O share of stock and $25
Explanation / Answer
1st we need to find the price of put
if price goes up then price of stock = $50 + 10% of $50 = $55
Similarly when it goes down then price = $45
Payoff of put is given by max(0, (K - St))
where K is strike price and St is stock price at time t.
Price of put at up = max(0, (50 - 55)) = 0
Price of put at down = max(0, (50 - 45)) = 5
probablity of up is given by belwo formula
p = (e^(r*t) - d)/(u - d)
where r is risk free rate
t is time period
d is probablity of going up and u is probality of going down
p =( e^(.05*1) - .9)/(1.1 - .9)
= .75
probablity of going down = 1 - p = .25
Price of put = e^(-r*t) (p * putup + (1-p) * putdown)
= e^(.05*1) (.75 * 0 + .25*5)
= $1.19
Protective put is buying a put and buying a stock so the correct answer will be option 3.
1/2 share of stock and $26.19 in T-bills.
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