Quant - Simulation Methods Flashcards
What is a lognormal distribution?
A lognormal distribution is a probability distribution of a random variable whose logarithm is normally distributed. This means that if you take the natural logarithm of the variable, the resulting values form a normal distribution. The lognormal distribution is skewed to the right, unlike the symmetric bell shape of a normal distribution, and is used to model a variety of natural phenomena and financial variables.
Why is the lognormal distribution used in finance?
the lognormal distribution is widely used for modeling the probability distribution of financial asset prices because the distribution is bounded from below by 0 as asset prices and usually describes accurately the statistical distribution properties of financial assets prices.
What is a Monte Carlo simulation?
A Monte Carlo simulation generates a large number of random samples from a specified probability distribution or a series of distributions to obtain the likelihood of a range of results.
What are Monte Carlo simulations used for in investments?
Monte Carlo simulation is widely used to estimate risk and return in investment applications. Specifically, it is commonly used to value securities with complex features, such as embedded options, where no analytic pricing formula is available.
What is “Bootstrapping”?
Bootstrapping mimics the process of performing random sampling from a population to construct the sampling distribution by treating the randomly drawn sample as if it were the population.
Bootstrap, one of the most popular resampling methods, uses computer simulation for statistical inference without using an analytical formula such as a z-statistic or t-statistic.
What base is used for the lognormal distribution?
In the context of a lognormal distribution, the logarithmic base typically used is the natural logarithm, or base 𝑒 e (where 𝑒 e approximately equals 2.71828). This is the most common base for logarithms in continuous growth processes and many areas of finance and natural sciences, primarily because the derivative and integration involving 𝑒 e are simpler and more elegant mathematically.
What is “Resampling”?
A statistical method that repeatedly draws samples from the original observed data sample for the statistical inference of population parameters.
Does “Bootstrapping” have replacement?
yes, samples are “put back” into the population.
