Question

Suppose you are attempting to value a 1-year expiration option on a stock with volatility (i.e., annualized standard deviation) of σ = 0.50. a. 1 period of 1 year. b. 4 subperiods, each 3 months. c. 12 subperiods, each 1 month. What would be the appropriate values for u and d if your binomial model is set up using: (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Answer 1

Binomial option is one of the option valuation model which depict that price of stock can move only to two direction upward and downward. therefore, in binomial model we have to find the value of u and d which are calculated as follows

Here standard deviation is 0.5

u = exp (σ√Δt)

d= exp (-σ√Δt)

a) 1 period of 1 year

u = exp (σ√Δt)

  = exp (0.5√1)

=1.648

d= exp (-σ√Δt)

= exp (-0.5√1)

=0.606

b) 4 subperiods , each 3 months

u = exp (σ√Δt)

= exp (0.5√1/4)

=1.284

d= exp (-σ√Δt)

= exp (-0.5√1/4)

=0.778

c. 12 subperiods, each 1 month

u = exp (σ√Δt)

= exp (0.5√1/12)

= 1.155

d= exp (-σ√Δt)

= exp (-0.5√1/12)

= 0.866

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