Question

what is the price of a European put if the price of the underlying common stock is $20, the exercise price is $20, the risk free rate is 8%, the variance of the price of the underlying stock is 0.36 and the option expires six months from now? use both
a) a two steps binomial tree
b) the black scholes pricing formula

Answer 1

Fomulas Used :-

u	=EXP(C5*SQRT(C6))
d	=EXP(-C5*SQRT(C6))
p	=(EXP(C6*C7)-F4)/(F3-F4)
1-p	=1-F6

			=D14*$F$3
			=MAX($C$4-E12,0)
		=C16*$F$3
		=EXP(-$C$6*$C$7)*((E13*$F$6)+($F$7*E17))
STOCK	20		=D14*$F$4
OPTION	=EXP(-$C$6*$C$7)*((D15*$F$6)+($F$7*D19))		=MAX($C$4-E16,0)
		=C16*$F$4
		=EXP(-$C$6*$C$7)*((E17*$F$6)+($F$7*E21))
			=D18*$F$4
			=MAX($C$4-E20,0)

Black and Scholes Model:-

Formulas Used :-

ln(S0/K)	=IFERROR(LN(C5/C6),"na")
(r+σ2/2)t	=(C8+(C9^2)/2)*C7
σ√t	=C9*SQRT(C7)
d1	=IFERROR((C13+C14)/C15,"na")
d2	=IFERROR(C16-C15,"na")
N(d1)	=IFERROR(NORM.S.DIST(C16,TRUE),"na")
N(d2)	=IFERROR(NORM.S.DIST(C17,TRUE),"na")
N(-d1)	=IFERROR(NORM.S.DIST(-C16,TRUE),"na")
N(-d2)	=IFERROR(NORM.S.DIST(-C17,TRUE),"na")
e-rt	=EXP(-C8*C7)

I hope my efforts will be fruitful to you