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Covered Interest rate parity with Bid Offer quotes

November 8th, 2020, 11:12 pm

Hi All,
The usual covered interest rate parity equation is
FWD = SPOT *( 1 + R_F*T)/(1+R_D*T)
and If I want to find out the value for foreign rate R_F
R_F* T = (FWD/SPOT ) * (1+R_D*T) - 1

where R_F is the foreign or the quote currency and R_D is domestic or the base currency.
How do I change it so that it takes in to account the bid/offer spread of FX Quotes and Yield curves.

Is this the correct equation if want to get the R_F_Ask side?
R_F_ASK* T = (FWD_BID/SPOT_BID ) * (1+R_D_ASK*T) - 1

As an example, if I am given USD YC bid/offer quotes and GBPUSD Spot bid/offer quotes and GBPUSD Forward rate bid/offer quotes, how can I imply the GBP Offer and bid side of the Interest rate.

Thanks in advance