Question

The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $28. Assume the risk-free rate is 10% per annum (continuously compounded). What, to the nearest cent, is the price of an American put option with a strike price of $33? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

Answer 1

Solution-

First we need to Find Probability-

Probabilty for upward Movement =

Probabilty for upward Movement =

Probabilty for upward Movement = 0.4423

Probabilty for Downward Movement =1 - Probabilty for upward Movement

Probabilty for Downward Movement =1 - 0.4423

Probabilty for Downward Movement = 0.5577

Option Price of PUT as on Today
		A	B	A*B
Current Market Price as on Expiry	Strike Price	Option Price as on Expiry	Probability	Expected Option price as on expiry
36	33	0	0.4423	0.000
28	33	5	0.5577	2.7885
				2.789

Price of American put option as on Today =

Price of American put option as on Today = $2.789 * 0.9512

Price of American put option as on Today = $2.653

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