Stochastic process for interest rates allowing negative valuesShifted Log-Normal modelExtensions of CIRHow to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?Modelling with negative interest rates Value options when the currency’s risk free rate is negative?Deriving Interest RatesThe effect of negative interest rates on derivative pricingModels crumbling down due to negative (nominal) interest ratesNegative Interest Rate & Basis ModelsHow to price a stock under Q and stochastic interest rates?Valuing derivatives under stochastic interest ratesTransforming non-normally distributed interest rates for OLS regression
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Stochastic process for interest rates allowing negative values
Shifted Log-Normal modelExtensions of CIRHow to reduce variance in a Cox-Ingersoll-Ross Monte Carlo simulation?Modelling with negative interest rates Value options when the currency’s risk free rate is negative?Deriving Interest RatesThe effect of negative interest rates on derivative pricingModels crumbling down due to negative (nominal) interest ratesNegative Interest Rate & Basis ModelsHow to price a stock under Q and stochastic interest rates?Valuing derivatives under stochastic interest ratesTransforming non-normally distributed interest rates for OLS regression
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The Cox-Ingersoll-Ross process for the short term interest rate r(t) does not allow r(t) to become negative, but short-term rates are negative in much of the developed world. To account for this, do you use a CIR process for a shadow rate r'(t) that equals r(t) + c, where c = 0.01 if you think short-term rates cannot get more negative than 1%? Has there been research on this?
interest-rates
asked 9 hours ago
FortrannerFortranner
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The Cox-Ingersoll-Ross process for the short term interest rate r(t) does not allow r(t) to become negative, but short-term rates are negative in much of the developed world. To account for this, do you use a CIR process for a shadow rate r'(t) that equals r(t) + c, where c = 0.01 if you think short-term rates cannot get more negative than 1%? Has there been research on this?
interest-rates
asked 9 hours ago
FortrannerFortranner
3831 silver badge8 bronze badges
$endgroup$
add a comment |
$begingroup$
The Cox-Ingersoll-Ross process for the short term interest rate r(t) does not allow r(t) to become negative, but short-term rates are negative in much of the developed world. To account for this, do you use a CIR process for a shadow rate r'(t) that equals r(t) + c, where c = 0.01 if you think short-term rates cannot get more negative than 1%? Has there been research on this?
interest-rates
asked 9 hours ago
FortrannerFortranner
3831 silver badge8 bronze badges
$endgroup$
The Cox-Ingersoll-Ross process for the short term interest rate r(t) does not allow r(t) to become negative, but short-term rates are negative in much of the developed world. To account for this, do you use a CIR process for a shadow rate r'(t) that equals r(t) + c, where c = 0.01 if you think short-term rates cannot get more negative than 1%? Has there been research on this?
interest-rates
interest-rates
asked 9 hours ago
FortrannerFortranner
3831 silver badge8 bronze badges
asked 9 hours ago
FortrannerFortranner
3831 silver badge8 bronze badges
asked 9 hours ago
FortrannerFortranner
3831 silver badge8 bronze badges
asked 9 hours ago
FortrannerFortranner
3831 silver badge8 bronze badges
asked 9 hours ago
FortrannerFortranner
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Yes, people have looked into that alreaday, for instance here and here (for lognormal models). Brigo and Mercurio took the CIR short rate $(x_t)$ and added a deterministic shift $vartheta(t)$ to it in order to obtain the short rate process $(r_t)$ via $r_t=x_t+vartheta(t)$. The function $vartheta$ serves to guarantee a perfect fit with observed discount factors and hence, can lead to negative short rate. In their book, you can read about their CIR extension (named CIR++) in Section 3.9 which addresses the issue of positivity explicitly in 3.9.3.
Note that normally distributed short rate models like the models from Vasicek, Ho-Lee and Hull-White allow directly for negative short rates.
answered 9 hours ago
KeSchnKeSchn
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Yes, people have looked into that alreaday, for instance here and here (for lognormal models). Brigo and Mercurio took the CIR short rate $(x_t)$ and added a deterministic shift $vartheta(t)$ to it in order to obtain the short rate process $(r_t)$ via $r_t=x_t+vartheta(t)$. The function $vartheta$ serves to guarantee a perfect fit with observed discount factors and hence, can lead to negative short rate. In their book, you can read about their CIR extension (named CIR++) in Section 3.9 which addresses the issue of positivity explicitly in 3.9.3.
Note that normally distributed short rate models like the models from Vasicek, Ho-Lee and Hull-White allow directly for negative short rates.
answered 9 hours ago
KeSchnKeSchn
70810 bronze badges
$endgroup$
add a comment |
$begingroup$
Yes, people have looked into that alreaday, for instance here and here (for lognormal models). Brigo and Mercurio took the CIR short rate $(x_t)$ and added a deterministic shift $vartheta(t)$ to it in order to obtain the short rate process $(r_t)$ via $r_t=x_t+vartheta(t)$. The function $vartheta$ serves to guarantee a perfect fit with observed discount factors and hence, can lead to negative short rate. In their book, you can read about their CIR extension (named CIR++) in Section 3.9 which addresses the issue of positivity explicitly in 3.9.3.
Note that normally distributed short rate models like the models from Vasicek, Ho-Lee and Hull-White allow directly for negative short rates.
answered 9 hours ago
KeSchnKeSchn
70810 bronze badges
$endgroup$
add a comment |
$begingroup$
Yes, people have looked into that alreaday, for instance here and here (for lognormal models). Brigo and Mercurio took the CIR short rate $(x_t)$ and added a deterministic shift $vartheta(t)$ to it in order to obtain the short rate process $(r_t)$ via $r_t=x_t+vartheta(t)$. The function $vartheta$ serves to guarantee a perfect fit with observed discount factors and hence, can lead to negative short rate. In their book, you can read about their CIR extension (named CIR++) in Section 3.9 which addresses the issue of positivity explicitly in 3.9.3.
Note that normally distributed short rate models like the models from Vasicek, Ho-Lee and Hull-White allow directly for negative short rates.
answered 9 hours ago
KeSchnKeSchn
70810 bronze badges
$endgroup$
Yes, people have looked into that alreaday, for instance here and here (for lognormal models). Brigo and Mercurio took the CIR short rate $(x_t)$ and added a deterministic shift $vartheta(t)$ to it in order to obtain the short rate process $(r_t)$ via $r_t=x_t+vartheta(t)$. The function $vartheta$ serves to guarantee a perfect fit with observed discount factors and hence, can lead to negative short rate. In their book, you can read about their CIR extension (named CIR++) in Section 3.9 which addresses the issue of positivity explicitly in 3.9.3.
Note that normally distributed short rate models like the models from Vasicek, Ho-Lee and Hull-White allow directly for negative short rates.
answered 9 hours ago
KeSchnKeSchn
70810 bronze badges
answered 9 hours ago
KeSchnKeSchn
70810 bronze badges
answered 9 hours ago
KeSchnKeSchn
70810 bronze badges
answered 9 hours ago
KeSchnKeSchn
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70810 bronze badges
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