forward_fx#

rateslib.fx.forward_fx(date, curve_domestic, curve_foreign, fx_rate, fx_settlement=None)#

Return a forward FX rate based on interest rate parity.

Parameters:

  • date (datetime) – The target date to determine the adjusted FX rate for.

  • curve_domestic (Curve) – The discount curve for the domestic currency. Should be collateral adjusted.

  • curve_foreign (Curve) – The discount curve for the foreign currency. Should be collateral consistent with domestic curve.

  • fx_rate (float or Dual) – The known FX rate, typically spot FX given with a spot settlement date.

  • fx_settlement (datetime, optional) – The date the given fx_rate will settle, i.e. spot T+2. If None is assumed to be immediate settlement, i.e. date upon which both curves have a DF of precisely 1.0. Method is more efficient if fx_rate is given for immediate settlement.

Return type:

float, Dual, Dual2

Notes

We use the formula,

\[(EURUSD) f_i = \frac{(EUR:USD-CSA) w^*_i}{(USD:USD-CSA) v_i} F_0 = \frac{(EUR:EUR-CSA) v^*_i}{(USD:EUR-CSA) w_i} F_0\]

where \(w\) is a collateral adjusted discount curve and \(v\) is the locally derived discount curve in a given currency, and * denotes the domestic currency. \(F_0\) is the immediate FX rate, i.e. aligning with the initial date on curves such that discounts factors are precisely 1.0.

This implies that given the dates and rates supplied,

\[f_i = \frac{w^*_iv_j}{v_iw_j^*} f_j = \frac{v^*_iw_j}{w_iv_j^*} f_j\]

where j denotes the settlement date provided.

Examples

Using this function directly.

In [1]: domestic_curve = Curve({dt(2022, 1, 1): 1.0, dt(2023, 1, 1): 0.96})

In [2]: foreign_curve = Curve({dt(2022, 1, 1): 1.0, dt(2023, 1, 1): 0.99})

In [3]: forward_fx(
   ...:     date=dt(2022, 7, 1),
   ...:     curve_domestic=domestic_curve,
   ...:     curve_foreign=foreign_curve,
   ...:     fx_rate=2.0,
   ...:     fx_settlement=dt(2022, 1, 3)
   ...: )
   ...: 
Out[3]: 1.9700450724927536

Best practice is to use FXForwards classes but this method provides an efficient alternative and is occasionally used internally in the library.

In [4]: fxr = FXRates({"usdgbp": 2.0}, settlement=dt(2022, 1, 3))

In [5]: fxf = FXForwards(fxr, {
   ...:     "usdusd": domestic_curve,
   ...:     "gbpgbp": foreign_curve,
   ...:     "gbpusd": foreign_curve,
   ...: })
   ...: 

In [6]: fxf.rate("usdgbp", dt(2022, 7, 1))
Out[6]: <Dual: 1.970045, (fx_usdgbp), [1.0]>