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# Questions tagged [lognormal]

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### Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?

The following is an interview question. All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
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### 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? ...
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### 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 ...
55 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{{...
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### Reference for pricing geometric-mean basket option

Let $(Z_1,\ldots,Z_N)$ be an $N$-dimensional Brownian motion with correlation matrix $\rho$ and consider the multivariate Black-Scholes model \begin{align} dS_i(t) \ = \ (r-q_i)\, S_i(t) \, dt \, + \,...
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### Transforming non-normally distributed interest rates for OLS regression

I am studying the effects of short- and long-term interest rates on bank risk-taking in the Euro zone countries. To analyse the effects, I will use, amongst other, an OLS regression. However I have ...
122 views

### How does the Black Scholes Model Incorporate Log Prices Into Model?

I am still not understanding the link between log prices and how that is incorporated into the BS model. I understand why log(S) is assumed because it makes math easier and it prevents ending prices ...
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### 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??
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### 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 ...
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### 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 (...
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### How do we know if the volatility which is quoted in market is Normal (Bachelier model) or log normal (Black 76)?

In markets, many instruments are quoted in volatility, but how we can tell what kind of volatility is this? Is it normal volatility, or lognormal volatility. because it affect our hedging positions. ...