We’re rewarding the question askers & reputations are being recalculated! Read more.

# Questions tagged [lognormal]

The tag has no usage guidance.

61 questions
Filter by
Sorted by
Tagged with
9k views

### Annualzing the log of daily returns riddle

Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
30 views

### Realized vol/var log-normal approximation

It is not clear to me what is a better approximation (based on empirical evidence or otherwise), a log-normal approximation for realized volatility or log-normal approximation for realized variance? ...
32 views

### Asset return distribution

What is the basis for assumption that asset prices follow a log normal distribution? Then how is it transformed to say that asset return follows a normal distribution? How this relationship between ...
43 views

### Displaced diffusion LMM

In the standard LMM a rate $L_i(t)=L(t,T_{i-1},T_i)$ has under the $T_n$-forward measure ($n>i$) the dynamics \begin{equation} d{L_i}(t) = - {\sigma _i}(t){L_i}(t)\sum\limits_{j = i + 1}^n {\frac{{...
154 views

127 views

### Log Differences vs Percentage returns [closed]

When working with a single TimeSeries of Foreign Exchange price data (EUR/USD : OHLC) on a minute by minute level, is it better to use the % difference of the close vs the lognormal difference of the ...
200 views

### Does the Ito correction term in GBM result in 'real money', or is it illusory?

There are two ways to think about investment returns and randomness. First is sort of like 'bank interest', with randomness. Suppose we invest 100 units of currency. Suppose each year there is a ...
30 views

114 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 ...
153 views

438 views

### How to compute the stochastic integral of log-normal process?

How do you compute the following integral: $$\int_0^t e^{\mu s + \sigma W_s} ds$$ or $$\int_0^t e^{\mu s + \sigma W_s} dW_s$$ ? Are those integrals stochastic processes of some well-know type (...
1k views

### Bloomberg implied volatility smile for equities

I was wondering if someone knows how Bloomberg does their computations for the implied volatility smile for equities. As far as I understand, they use a lognormal mixture to model the stock prices. ...