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Call put parity is : $$C(T,K) - P(T,K) = ( F_{t,T} - K ) B(t,T)$$ and with your notation : $$C(T,K) - P(T,K) = ( F_{t,T} - K ) + \text{TimeValueCall}(T,K) - \text{TimeValuePut}(T,K)$$ Reference: https://en.wikipedia.org/wiki/Put%E2%80%93call_parity

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