[R-SIG-Finance] Modeling FX rates

[Dominykas Grigonis]

In theory FX rates are expected to grow at rate equal to interest rate differential.
In practise it is never true. Though you have 2 ways to calc your expected growth:  
1. empirical
2. int rate differential

Code I included is simple daily simulation, adjust parameters as you wish. However, quantiles can be obtained empirically, so simulation is not really needed. Also, what I did is daily simulation, which is useful for path dependent applications, in your case distribution at final time T is enough and this would make code faster.

Calibrating:
1. Volatility
lnS = lng(S_t/S_t-1)
muS = mean(lnS)
volS = sqrt(sum(lnS - muS))

or simply sd(lnS)

2. expected rate of return
a) empirical would just be mean(lnS)
b) interest rate differential: careful with compounding. Online will be simple compounding, need to convert it to continuous.

If you need any other further help/advice let me know. I would gladly support you if I understood what you are trying to achieve. Provide me with some data/workings so I can help you more.

Kind regards,--  
Dominykas Grigonis


On Friday, 17 January 2014 at 06:39, Jaimie wrote:

> Hi dominykas
>  
> First of all, thanks for Your help.
>  
> I'm trying to model try/eur exchange rate.  
> I would like to find out whether spot rate as of december 31st 2013 is normal (is as expected)  or is not due to some external factors like political inestability that could have affected its expected evolution.
> Therefore, i would like to calibrate the model based on data up to december 31st 2012 and make forecasts 1 yr ahead to get its expected evolution  and also to simulate and get what the quantile of spot rate as of december 31st 2013 is, based on simulated values. Is It in the tail of the distribution? , is It nearest to the expected value....?
>  
> If You have some code that would help me to get these goals, i would be strongly grateful if you could share It.
>  
> Bests
>  
> Jaimie
>  
> Pd: forgive any spelling mistakes.
> Enviado desde mi iPhone
>  
> El 16/01/2014, a las 10:36, Dominykas Grigonis <dominykasgrigonis at gmail.com (mailto:dominykasgrigonis at gmail.com)> escribió:
>  
> > BS means black scholes model. Simply: S_1 = S_0 exp((mu - vol^2/2)t + vol dW), where dW ~ N(0,t)
> >  
> > Do not know about packages, if you want I can provide you some code. It is pretty simple if you know what you are doing. What are you trying to achieve? Do you want to get a view for the future? Price options? Or building some kind of strategy testing?  
> >  
> >  
> > Kind regards,--  
> > Dominykas Grigonis
> >  
> >  
> > On Thursday, 16 January 2014 at 04:14, Jaimie Villanueva wrote:
> >  
> > > Hi,  
> > >  
> > > I'm not experienced on this so, Could you tell me a bit more on this?
> > >  
> > > What BS stands for and what are the package/s i should go to?
> > > I would need to calibrate the parameter of the model as well as simulate values.
> > >  
> > > Bests
> > >  
> > > Jaimie
> > >  
> > >  
> > > On Wed, Jan 15, 2014 at 8:34 PM, Dominykas Grigonis <dominykasgrigonis at gmail.com (mailto:dominykasgrigonis at gmail.com)> wrote:
> > > > Exchange rates are not mean reverting. Simple BS with interest rate differential is usually applied.  
> > > >  
> > > >  
> > > > Kind regards,--  
> > > > Dominykas Grigonis
> > > >  
> > > >  
> > > > On Wednesday, 15 January 2014 at 19:30, Jaimie wrote:
> > > >  
> > > >  
> > > >  
> > > > > Hi R users
> > > > >  
> > > > > I'm trying to model fx rates with one-factor models like CIR, Vasicek, hull-white etc. Those usually used in the context of interest rate modeling.  
> > > > > I was wondering:
> > > > >  
> > > > > 1- Would It make sense? I mean, applying short rate models to exchange rates.  
> > > > >  
> > > > > 2- What would be the best r package i should go to? Is there one specially recomended?  
> > > > >  
> > > > > Thanks a lot in advanced.
> > > > >  
> > > > > Jaimie
> > > > >  
> > > > > Enviado desde mi iPhone
> > > > > _______________________________________________
> > > > > R-SIG-Finance at r-project.org (mailto:R-SIG-Finance at r-project.org) mailing list
> > > > > https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> > > > > -- Subscriber-posting only. If you want to post, subscribe first.
> > > > > -- Also note that this is not the r-help list where general R questions should go.
> > > > >  
> > > > >  
> > > > >  
> > > >  
> > > >  
> > >  
> > >  
> > >  
> > > --  
> > > Jaimie.  
> >  

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