Question

You own a lot in Key West, Florida, that is currently unused. Similar lots have recently sold for $1,340,000. Over the past five years, the price of land in the area has increased 8 percent per year, with an annual standard deviation of 31 percent. You have approached a buyer and would like the option to sell the land in 12 months for $1,490,000. The risk-free rate of interest is 4 percent per year, compounded continuously.

  

What is the price of the put option necessary to guarantee your sales price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Price of put option

$

Answer 1

	Option price=	SN(d1) - Xe-r t N(d2)
	d1 =	[ ln(S/X) + ( r+ v2 /2) t ]/ v t0.5
	d2 =	d1 - v t0.5
	Where
S=	Current stock price=	1340000
X=	Exercise price=	1490000
r=	Risk free interest rate=	4%
v=	Standard devriation=	31%
t=	time to expiration (in years) =	1.0000
d1 =	[ ln(1340000/1490000) + ( 0.04 + (0.31^2)/2 ) *1] / [0.31*1^ 0.5 ]
d1 =	[ -0.106107 + 0.08805 ] /0.31
d1 =	-0.058247
d2 =	-0.058247 - 0.31 * 1^0.5
	-0.368247
N(d1) =	N( -0.058247 ) =	0.47678
N(d2) =	N( -0.368247 ) =	0.35634
Option price=	1340000*0.476776024059086-1490000*(e^-0.04*1) *0.356344610880169
	128,745.39

Price of call option (right to purchase) is $128,745.39

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