# Questions tagged [lognormal]

A continuous probability distribution of a random variable whose logarithm is normally distributed.

72 questions
Filter by
Sorted by
Tagged with
59 views

### Summary of Pricing Options of Log-Normal Claims Using Black's Formula

Cross posted from here. Let $B$ be a $Q$-Brownian motion and $X^{s,x}$ given by $$dX_t = X_t(\mu_t dt + \sigma_t dB_t),\quad X_s = x$$ for $\mu, \sigma$ deterministic. Let $\mu_{s,t}=\int_s^t \mu_u du$...
94 views

### Probability of a stock price using implied volatility

I have attempted to use the fact of having implied volatility, but have not been able to come up with a viable way to calculate the probability, any ideas? Suppose that a stock $S_t$ follows a ...
57 views

### What is the industry standard model for pricing Swaptions during this time of negative interest rates, normal model or shifted log-normal model?

I have referred to the some of the well known papers but none of them has a clear answer for my question. I know that both of these models have some disadvantages but, what is the industry standard ...
60 views

### Geometric brownian motion and probabilities

A stock's price movement is described by the equations $dS_t=0.02S_tdt+0.25S_tdW_t$ and $S_0=100$. An investor buys a call option on said stock with a strike price $K=95$ which expires in $T=2$ years. ...
19 views

### Lognormal correlation bounds for Monte Carlo

As the lognormal distribution imposes bounds of attainable correlations as discussed in https://stats.stackexchange.com/questions/41734/attainable-correlations-for-lognormal-random-variables my ...
22 views

### Minimal bounds to enclose most sample paths of a GBM (Geometric Brownian Motion)

For a (generalized) Brownian motion $Y = F(t,W)$, starting at $InitialValue$ and running for a total of $T$ time, if I want to "enclose" (in a visual way) "most" of the possible sample paths, I could ...
57 views

### Generate Monte Carlo simulation of multivariate lognormal or weibull distributions in R

I intend to perform a Monte Carlo simulation of asset returns in R. I am currently using the rmvnorm function in the mvtnorm R ...
60 views

### lognormal assumption of Black Scholes

I have recently started learning about option pricing and the Black Scholes formula, where stock prices are assumed to be lognormally distributed and returns normally distributed. While trying to do ...
867 views

### Stock Prices are Lognormal - Formal Definition

I'm struggling with what the exact meaning of "stock prices are lognormal" (and its use to show normality of returns). My assumption was that given ${S_t}$ are stock prices and returns are ...
127 views

### How to Understand Lognormal Distribution in the Following Case

I got a question and corresponding solution, but have some difficulties in understand the lognormal distribution part of it, so I really appreciate your advice: Question: assume zero interest rate ...
78 views

6k views

### Black Scholes and the Log Normal Distribution

Why does the Black Scholes Equation imply the returns are log-normally distributed?? How can we tell that the returns of the underlying asset wouldnt be normally distributed??
474 views

142 views

### Price is Log-normal distributed, yet the return is non-normal

I have a price series. The natural logarithm of the price shows good normality. As shown in the standardized normal probability plot below: However, by viewing the standardized normal probability ...