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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 27th, 2011, 11:23 am

My initial statement that "Equation (1) can not be applied for a FX model" does not accurate. It might be more accurate to say that diffusion coefficien in equation (1) can be expressed in more realistic way.
 
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bearish
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 27th, 2011, 7:35 pm

I would respectfully like to resubmit my second comment in this thread.
 
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 28th, 2011, 7:58 am

I think that for example equation d S(t) = (rd (t) - rf(t)) S(t) dt + sigma (rd (t) - rf(t)) S(t) dW(t)looks more analytically realistic thand S(t) = (rd (t) - rf(t)) S(t) dt + sigma S(t) dW(t) ( 1 )because it explicitly shows that exchange rate for a currency to itself is unchanged and equal to 1 if S ( 0 ) = 1It shows that if S ( t ) approach to 1 then diffusion tends to 0 that looks natural while diffusion of eq (1) tends to sigma dWIt is strange how it can be difficult to see for smart financial professional.
 
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 28th, 2011, 5:18 pm

I notice that most of the "smart finance professionals" around here ignore your posts. I will try to follow their example from now on.
 
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manolom
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 29th, 2011, 3:37 pm

QuoteOriginally posted by: list I think that for example equation d S(t) = (rd (t) - rf(t)) S(t) dt + sigma (rd (t) - rf(t)) S(t) dW(t)looks more analytically realistic thand S(t) = (rd (t) - rf(t)) S(t) dt + sigma S(t) dW(t) ( 1 )This means that the exchange rate between 2 currencies with similar interest rates would be constant over time! One thing is the drift, a different one is the volatility.
 
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 29th, 2011, 3:58 pm

QuoteOriginally posted by: manolomQuoteOriginally posted by: list I think that for example equation d S(t) = (rd (t) - rf(t)) S(t) dt + sigma (rd (t) - rf(t)) S(t) dW(t)looks more analytically realistic thand S(t) = (rd (t) - rf(t)) S(t) dt + sigma S(t) dW(t) ( 1 )This means that the exchange rate between 2 currencies with similar interest rates would be constant over time! One thing is the drift, a different one is the volatility.S ( t ) would be changed over the time as far as r_d and r_f are functions in t and also sigma will also change in time.
 
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 29th, 2011, 5:27 pm

QuoteOriginally posted by: listQuoteOriginally posted by: manolomQuoteOriginally posted by: list I think that for example equation d S(t) = (rd (t) - rf(t)) S(t) dt + sigma (rd (t) - rf(t)) S(t) dW(t)looks more analytically realistic thand S(t) = (rd (t) - rf(t)) S(t) dt + sigma S(t) dW(t) ( 1 )This means that the exchange rate between 2 currencies with similar interest rates would be constant over time! One thing is the drift, a different one is the volatility.S ( t ) would be changed over the time as far as r_d and r_f are functions in t and also sigma will also change in time.look, let's just define sigma_list = sigma*(r_d-r_f) ok? then we're back to dX = drift*Xdt + sigma*XdW, get my drift?
 
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Modeling Spot Exchange Rate with Stochastic Interest Rates

August 29th, 2011, 5:51 pm

Yes, you are right in general. On the other hand in the same way we can replace drift rd (t) - r f(t) by a mu and say that it sufficient model for exchange rate. The essence of the model to express explicitly as much as it possible. In this case we can be more specific. In math there exists a principle: more assume more you can prove. Actually I do not know whether the first power of the term rd (t) - r f(t) in diffusion is the best.