Question

Based on this spot price of 16 and the strike price of 18 as well as the fact that the risk-free interest rate is 6% per annum with continuous compounding, please undertake option valuations and answer related questions according to following instructions:

Binomial trees:

Additionally, assume that over each of the next two four-month periods, the share price is expected to go up by 11% or down by 10%.

a. Use a two-step binomial tree to calculate the value of an eight-month European call option using the no-arbitrage approach. [2.5 marks]

b. Use a two-step binomial tree to calculate the value of an eight-month European put option using the no-arbitrage approach. [2.5 marks]

c. Show whether the put-call-parity holds for the European call and the European put prices you calculated in a. and b. [1 mark]

Answer 1

Formulas Used:-

Strike Price	18	u	1.11
Risk Free rate	0.06	d	0.9
p	=(EXP(C4*4/12)-E4)/(E3-E4)
1-p	=1-C5
Call option Valuation		Put Option Valuation
			=D10*$E$3					=I10*$E$3
			=MAX(E8-$C$3,0)					=MAX($C$3-J8,0)
		=C12*$E$3					=H12*$E$3
		=EXP($C$4*4/12)*($C$5*E9)+($C$6*E13)					=EXP($C$4*4/12)*($C$5*J9)+($C$6*J13)
Stock	16		=D14*$E$3		Stock	16		=I14*$E$3
Option value	=EXP($C$4*4/12)*($C$5*D11)+($C$6*D15)		=MAX(E12-$C$3,0)		Option value	=EXP($C$4*4/12)*($C$5*I11)+($C$6*I15)		=MAX($C$3-J12,0)
		=C12*$E$4					=H12*$E$4
		=EXP($C$4*4/12)*($C$5*E13)+($C$6*E17)					=EXP($C$4*4/12)*($C$5*J13)+($C$6*J17)
			=D14*$E$4					=I14*$E$4
			=MAX(E16-$C$3,0)					=MAX($C$3-J16,0)

Lets Check it with Put call Parity

C + Xe^-rt = P + S₀

0.584334 + 18*e^(-6%*8/12) = 1.9284 + 16

0.584334 + 17.2942 = 1.9284+16

17.89=17.92

so, hence we can say put call parity holds, because this much error is due to round off error.