Question

The fixed strike (also known as an average rate) Asian call option with the strike K has the payoff defined as max(A - K, 0), where A is the average observed price of the underlying asset from the time the option is issued up to the time of exercise. Use the 3-step binomial tree to price the fixed strike Asian call option of the American exercise type. Assume that the spot price is $50. The time to maturity T is 3 months. Risk-free rate is 0.1 with continuous compounding, u = 1.2, d = 0.9. USE STRIKE PRICE OF 52

Answer 1

r = e^(0.1*1/12))

r = e^0.008333

r = 1.00836

p = r-d / u-d = 1.00836 - 0.9 / 1.2 - 0.9

p = 0.36

A	50
K	52
u	1.2
d	0.9
p	0.36
(1-p)	0.64
r	1.0084

	Period 0			Period 1			Period 2			Period 3
									uuuS	86.40
									C+++	34.4
						uuS	72.00
						C++	20.43
			uS	60					uudS	64.80
			C+	10.22					C++-	12.8
S	50					uds	54.00
C	4.70					C+-	4.59
			dS	45					uddS	48.60
			C-	1.64					C+--	0
						ddS	40.50
						C--	0.00
									dddS	36.45
									C---	0

Value of Call at "node uuS" can be calculated using the formulae
C++ = (p * C+++) + ((1-p) * C++-))/(1+r)

C++ = (0.36*34.4) + (0.64*12.8)/1.000836

C++ = 20.43

Similarly all the nodes can be calculated

Value of call = C = 4.7