Question: What is the maximum that the investor should be willing to pay for the option? P(L) = 0.49 P(s1 | L) = 0.85 P(s2 | L) = 0.15
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A real estate investor has the opportunity to purchase land currently zoned as residential. If the county board approves a request to rezone the property as commercial within the next year, the investor will be able to lease the land to a large discount firm that wants to open a new store on the property. However, if the zoning change is not approved, the investor will have to sell the property at a loss. Profits (in thousands of dollars) are shown in the following payoff table:
| s1 | s2 | |
| Purchase d1 | 640 | -200 |
| Do not purchase d2 | 0 | 0 |
probability that the rezoning will be approved is 0.5
The investor can purchase an option to buy the land. Under the option, the investor maintains the rights to purchase the land anytime during the next three months while learning more about possible resistance to the rezoning proposal from area residents. Probabilities are as follows:
Let H = High resistance to rezoning
L = Low resistance to rezoning
P(H) = 0.51 P(s1 | H) = 0.16 P(s2 | H) = 0.84
Question:
What is the maximum that the investor should be willing to pay for the option?
P(L) = 0.49 P(s1 | L) = 0.85 P(s2 | L) = 0.15
Given,
Let H = High resistance to rezoning
L = Low resistance to rezoning
P (Rezoning will be approved) = 0.5=P(s1)
P(Rezoning will not be approved) = 0.5=P(s2)
P(H) = 0.51
P(s1 | H) = 0.16
P(s2 | H) = 0.84
P(L) = 0.49
P(s1 | L) = 0.85
P(s2 | L) = 0.15
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