## FX rate evolution

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• Hi, I came across the FX rate evolution from one of my derivative books. It says under the assumption of lognormal model, ther FX rate process is given by:
Message 1 of 3 , Sep 8, 2004
Hi, I came across the FX rate evolution from one of my derivative
books. It says under the assumption of lognormal model, ther FX rate
process is given by:
FX(T) = FX(0)*exp{ -0.5*sigma^2*T + sigma*Z*sqrt(T)}

Where FX(0) = the spot FX rate
sigma = volatility of the FX rate
T = time to maturity
Z = std normal rv.

My question is: should the first term inside the exponential be:
(mean - 0.5*sigma^2)*T? Did the author miss the "mean" in the
formula?

Thanks.
• No, Fx series are supposed to be zero mean, due to no arbitrage equation in Fx, interest rate and inflation, also known as Fischer equation. So the author
Message 2 of 3 , Sep 8, 2004
No, Fx series are supposed to be zero mean, due to no arbitrage equation in Fx, interest rate and inflation, also known as Fischer equation. So the author hasn't miss anything.

----- Original Message -----
From: Casey
To: probability@yahoogroups.com
Sent: Thursday, September 09, 2004 2:02 AM
Subject: [probability] FX rate evolution

Hi, I came across the FX rate evolution from one of my derivative
books. It says under the assumption of lognormal model, ther FX rate
process is given by:
FX(T) = FX(0)*exp{ -0.5*sigma^2*T + sigma*Z*sqrt(T)}

Where FX(0) = the spot FX rate
sigma = volatility of the FX rate
T = time to maturity
Z = std normal rv.

My question is: should the first term inside the exponential be:
(mean - 0.5*sigma^2)*T? Did the author miss the "mean" in the
formula?

Thanks.

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• Thank you Nitish for your reply. I m new to Fischer equation(or No arbitrage in FX), can you elaborate a bit on how it leads to the conclusion that Fx series
Message 3 of 3 , Sep 9, 2004
I'm new to Fischer equation(or No arbitrage in FX), can you elaborate
a bit on how it leads to the conclusion that Fx series should have
zero mean. Is it related to interest rate parity between 2
currencies?

--- In probability@yahoogroups.com, "Nitish" <nitish@i...> wrote:
> No, Fx series are supposed to be zero mean, due to no arbitrage
equation in Fx, interest rate and inflation, also known as Fischer
equation. So the author hasn't miss anything.
>
> ----- Original Message -----
> From: Casey
> To: probability@yahoogroups.com
> Sent: Thursday, September 09, 2004 2:02 AM
> Subject: [probability] FX rate evolution
>
>
> Hi, I came across the FX rate evolution from one of my derivative
> books. It says under the assumption of lognormal model, ther FX
rate
> process is given by:
> FX(T) = FX(0)*exp{ -0.5*sigma^2*T + sigma*Z*sqrt(T)}
>
> Where FX(0) = the spot FX rate
> sigma = volatility of the FX rate
> T = time to maturity
> Z = std normal rv.
>
> My question is: should the first term inside the exponential be:
> (mean - 0.5*sigma^2)*T? Did the author miss the "mean" in the
> formula?
>
> Thanks.
>
>
>
>
>
>
>
>
> --------------------------------------------------------------------
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>
> a.. To visit your group on the web, go to:
> http://groups.yahoo.com/group/probability/
>
> b.. To unsubscribe from this group, send an email to:
> probability-unsubscribe@yahoogroups.com
>
> c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service.
>
>
>
> [Non-text portions of this message have been removed]
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