A binary call option pays $1 at expiry if the value of the underlying asset is...

A binary call option pays $1 at expiry if the value of the underlying asset is greater than the strike price, and $0 otherwise. The current interest rate is 3% pa.

(a) Calculate the return R over one month.

(b) Calculate all state prices at expiry for a ten-step binomial model where each time step is one month and the underlying asset is S=20, K=19, u=1.090, d=0.9173. That is, calculate all λ(10, j) for j = 0, 1, . . . , 10 .

Expert Solution

a)

Return over month for example for first month = (21.8-20)/20= 9%

b) Ten Step Binomial model lattice

										47.34727
									43.43787
								39.85125		39.84555
							36.56078		36.55555
						33.542		33.53721		33.53241
					30.77248		30.76808		30.76368
				28.23163		28.2276		28.22356		28.21952
			25.90058		25.89688		25.89317		25.88947
		23.762		23.7586		23.7552		23.75181		23.74841
	21.8		21.79688		21.79377		21.79065		21.78753
20		19.99714		19.99428		19.99142		19.98856		19.9857
	18.346		18.34338		18.34075		18.33813		18.33551
		16.82879		16.82638		16.82397		16.82157		16.81916
			15.43705		15.43484		15.43263		15.43042
				14.1604		14.15838		14.15635		14.15433
					12.98934		12.98748		12.98562
						11.91512		11.91341		11.91171
							10.92974		10.92818
								10.02585		10.02441
									9.196711
										8.436143
T = 0	T = 1	T = 2	T =3	T = 4	T = 5	T = 6	T = 7	T = 8	T = 9	T = 10

jeff jeffy answered 3 years ago

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