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FX rate evolution

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  • Casey
    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
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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:
      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.
    • Nitish
      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
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        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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      • Casey
        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
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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 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.
          >
          >
          >
          > Yahoo! Groups Sponsor
          > ADVERTISEMENT
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          >
          > a.. To visit your group on the web, go to:
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          > probability-unsubscribe@yahoogroups.com
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          >
          >
          > [Non-text portions of this message have been removed]
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