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Lattice Distribution

TL;DR

Section titled “TL;DR”
  • A probability distribution that lists possible outcomes and their probabilities.
  • Commonly used in finance and economics to model asset behavior and the risk of returns.
  • Examples include the binomial and trinomial distributions.

Definition

Section titled “Definition”

A lattice distribution is a type of probability distribution that represents the possible outcomes and their corresponding probabilities of a random variable. It is often used in finance and economics to model the behavior of financial assets and the risk associated with their returns.

Explanation

Section titled “Explanation”

A lattice distribution provides a way to enumerate outcomes of a random variable together with probabilities for each outcome. In applied settings such as finance and economics, lattice distributions are used to model how financial assets may evolve and to quantify the risk of their returns. They also enable calculation of probabilities for different outcomes and support decision-making for investment strategies and risk management.

Examples

Section titled “Examples”

Binomial distribution

Section titled “Binomial distribution”

The binomial distribution is an example of a lattice distribution. It models the probability of a certain number of successes or failures in a series of independent events where each event has a fixed probability of success or failure. For example, if a coin is flipped 10 times, the binomial distribution can be used to model the probability of getting exactly 5 heads or exactly 6 heads.

Trinomial distribution

Section titled “Trinomial distribution”

The trinomial distribution is another example; it allows for three possible outcomes instead of just two. It is often used in finance to model the possible outcomes of an option at expiration, where the option can expire in the money, at the money, or out of the money. For example, if a call option has a strike price of 50andtheunderlyingstockiscurrentlytradingat50 and the underlying stock is currently trading at 55, the trinomial distribution can be used to model the probability of the option expiring in the money, at the money, or out of the money.

Use cases

Section titled “Use cases”
  • Modeling the behavior of financial assets in finance and economics.
  • Calculating probabilities of different outcomes for asset returns.
  • Supporting investment strategy decisions and risk management.
Section titled “Related terms”
  • Binomial distribution
  • Trinomial distribution
  • Option (financial derivative)