# Questions tagged [lognormal]

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

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### What exactly is the 'continuous asset price model'?

I am reading An Introduction to Financial Option Valuation by Higham. In Chapter 6, the book covers two asset price models, a discrete one and a continuous one. In Section 6.3 (Continuous asset model) ...
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### Pricing with log-normal interes rate

The annual rate of return in year $t$, denoted as $1+i_t$, where $i_0$ represents the interest rate from $t=0$ to $t=1$, has a log-normal distribution with an expected value $108\%$ and a standard ...
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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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### 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 ...
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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 ...
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### 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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### Distribution of simple returns vs logreturns

I understand that stock prices are conditionally modeled using a log normal distribution by the relationship $y_t/y_{t−1}∼logN(μ_{daily},σ^2_{daily})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{daily}))$ ...
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### Shifted Log-Normal model

I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
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### Does GBM stock price model have E[S(t)] unaffected by volatility?

Many an author claims that, if you model stock prices through GBM, $E[S(t)]=e^{\mu t}$, and the expectation is thus not related to volatility. I keep running around in circles on this one. First ...
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I am trying to price an ATMF FX (say Usdidr) straddle - the fxdelta for call and put leg are quite different with put fxdelta being higher than call delta. (Absolute values) Why would this be the case?...
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### 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 ...
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### 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 ...
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### Why does MACD not use log normalization

Today I wondered why the MACD oscillator uses the differences of two averages instead of the log of their quotient just like it's done for volatility estimation. With this kind of log normalization ...
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I am new to option pricing and following problem came up that I don't understand how to handle. A derivative will pay out dollar amount equal to $$\frac1T\ln \frac{S_T}{S_0}$$ at maturity, where \$...