Suppose the price of a non-dividend paying stock is $100 today and the continuous com- pounding interest rate is r =

Question

Suppose the price of a non-dividend paying stock is $100 today and the continuous com- pounding interest rate is r = 7%. (7a) Find the range for the price of an American put with strike price X = 110 and T = 2. (75) Suppose that the price of an European call with X = 110 and T = 2 is $6, find the range for the price of an American put with the same X and T.

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Step1= Concept of Put and call option Put Option Option holder has the right to sell the asset at strike price he prefers to sell at a price where strike price is higher than spot. American Put Can be exercised anytime hence maximum price=strike price European Put Cannot be exercised before expiry date hence maximum price=present value of strike price Call option Option holder has the right to buy asset at strike price optionholder prefers to exercise when strike price is lower than spot. American call and European Call Maximum price=stock price at the time of exercise Step2 7a range for American Put Minimum value Maximum value Max (0,X-S) X (0,110-100) =$10 $110 Range is between 10 and 110 7b) step 3 Price of European call Max(0,(S - X*e^rt ), S) Value of european call is given $6 =S – 110*e-0.07*2 =S- 110* 0.869358 6=S- 95.6294 S= 6+95.6294= $101.6294 Range for American Put Max (0,X-S),X MAX(0,110-101.6294), 110 RANGE IS BETWEEN $8.3706 AND $110 IMPORTANT POINTS: YOU MAY USE FORMULA =EXP ON EXCEL FOR VALUE OF e X= strike price S= spot price

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Suppose the price of a non-dividend paying stock is $100 today and the continuous com- pounding interest rate is r = 7%

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Archived Solution

Put Option	Option holder has the right to sell the asset at strike price he prefers to sell at a price where strike price is higher than spot.
American Put	Can be exercised anytime hence maximum price=strike price
European Put	Cannot be exercised before expiry date hence maximum price=present value of strike price

Call option	Option holder has the right to buy asset at strike price optionholder prefers to exercise when strike price is lower than spot.
American call and European Call	Maximum price=stock price at the time of exercise

Minimum value	Maximum value
Max (0,X-S)	X
(0,110-100) =$10	$110
Range is between 10 and 110

Price of European call	Max(0,(S - X*e^rt ), S)
Value of european call is given $6	=S – 110e^-0.072 =S- 110* 0.869358 6=S- 95.6294 S= 6+95.6294= $101.6294

Range for American Put	Max (0,X-S),X
	MAX(0,110-101.6294), 110 RANGE IS BETWEEN $8.3706 AND $110