is increasing in vs increases with

English translation: see discussion

09:53 Nov 7, 2016

English language (monolingual) [PRO]
Bus/Financial - Mathematics & Statistics

English term or phrase: is increasing in vs increases with

For example: "The value of an option is increasing in the volatility of the underlying asset."

Meaning the higher the volatility of the underlying asset, the higher the value of the option.

"In" seems a very strange preposition to use here. To a non-statistician like me, it seems almost to reverse the relationship.

Is this usage of "is increasing in" OK? What is the logic behind it?

I get loads of hits but it just sounds weird to me...

I would want to say: The value of an option "increases with" the volatility of the underlying asset.

Christopher Schröder
United Kingdom

Selected answer:see discussion

Explanation:
"y is increasing in x" is correct and means that y=f(x) in a way that when x increases then y does also e.g. y = x^2 + 5.

Increases with wouldn't be wrong but might be read as something slightly different e.g. the two are correlated so y generally (but not always) increases when x increases.

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Note added at 22 mins (2016-11-07 10:16:17 GMT)
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The specific situation given is commonly modelled by Black-Scholes
https://en.wikipedia.org/w/index.php?title=Black–Scholes_mod...

The volatility is the sigma term (and is positive). That occurs in the d_2 and d_1 terms effectively in an additive way (trust me on this) so bigger sigmas give bigger values of P (the call price).

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Note added at 29 mins (2016-11-07 10:23:28 GMT)
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Actually, think of it like this - underlying assets with higher volatility will sometimes reach higher prices than underlying assets with lower volatility. So a person with a call option (which is what's being priced here) will sometimes have the option of buying a higher-valued asset (and there's no downside since they don't have to buy if the price doesn't suit them). Hence, they need to pay more to buy the more volatile asset.

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Note added at 49 mins (2016-11-07 10:43:35 GMT)
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I don't quite know the rationale but it's been around "forever" e.g. "Wherefore, since that Force, in approaching the Earth, increases in the reciprocal duplicate Proportion of the Distance" from "Astronomia accurata: or The royal astronomer and navigator." Heath, R. 1760.

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Note added at 53 mins (2016-11-07 10:47:36 GMT)
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Even earlier - Edmond Halley, 1715.

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Note added at 1 hr (2016-11-07 11:19:44 GMT)
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Obviously goes back to the Latin in which scientific works were written
"ut per quamcunque addírionem nequear crescere in ea ratione". Re the appropriate use of the pronoun in Latin, there I leave you :-)

Selected response from:

DLyons
Ireland
Local time: 19:46

Grading comment

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4 KudoZ points were awarded for this answer

SUMMARY OF ALL EXPLANATIONS PROVIDED

4 +3

see discussion

DLyons

4 +1

increases with

airmailrpl

Discussion entries: 1

Answers

3 mins confidence:

peer agreement (net): +1

increases with

Explanation:
"increases with" sounds better

airmailrpl
Brazil
Local time: 15:46
Native speaker of:

English,

Portuguese

4 mins confidence:

peer agreement (net): +3

see discussion

DLyons
Ireland
Local time: 19:46
Specializes in field
Native speaker of: English
PRO pts in category: 24

Grading comment

Thanks

Notes to answerer

Asker: Thanks! I should've said that the example I've given here was taken randomly from Google. It's the use of "in" that seems bizarre to me, I just can't see how it works logically/semantically. Even a bacon sarnie isn't helping.

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