Let T = {0, 1, . . . , 10}. Consider a binomial model for the price S of a share of stock.
That is: • Ω = {0, 1} 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .sample space.
• P(ω) = p k (1 − p) 10−k , where p ∈ (0, 1) and k is the number of 1’s in the sequence ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . probability distribution.
• 0 < D < 1 < U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . price ratios.
• S(t)(ω) = 100 · U kDt−k , where k is the number of 1’s among the first t entries of ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the price process.
That is: • Ω = {0, 1} 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .sample space.
• P(ω) = p k (1 − p) 10−k , where p ∈ (0, 1) and k is the number of 1’s in the sequence ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . probability distribution.
• 0 < D < 1 < U . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . price ratios.
• S(t)(ω) = 100 · U kDt−k , where k is the number of 1’s among the first t entries of ω . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . the price process.