Derivatives E5.5 Asian Option

Stock Price ($)S100

Strike Price ($)K100

Volatilityσ0.3

Time to expiration (year)T1

continuous compounding rate r0.1

the number of periods n3dt = T/n =0.3333

upward movement u 1.1891exp(σ*dt^0.5)

downward movement d0.84101/u

risk-neutral probability p0.5542(exp(rdt)-d)/(u-d) Outputs

68.1381

44.676618.9110

28.317510.13630.0000

American call option17.5210 5.43300.00000.0000

time period0123

Interim Calculations

168.1381

141.3982118.9110

118.9110100.000084.0965 Stock lattice100.000084.096570.722259.4749 time period0123