第五章 汇率的决定与预测 Exchange rate determination and Forcasting exchange rate

• The law of one price: P_d = S_d/f * P_f
• Absolute PPP: S_d/f = P_d / P_f
• overvalue/undervalue: (Actual exchange rate - Implied exchange rate) / Implied exchange rate
• Relative PPP: S₁ = S₀ * [ ( P₁^d / P₀^d ) / ( P₁^f / P₀^f ) ]

The relationship of Forward rate and Interest rate

• ( 1 + i^d ) = ( 1 + i^f ) * F^d/f / S^d/f
• i^d - i^f ~= ( F^d/f - S^d/f ) / S^d/f

Covered Interest Arbitrage

i^d - i^f > ( F^d/f - S^d/f ) / S^d/f
Move funds from f to d

Uncovered Interest Arbitrage

E [ P_t^d/f ] = F^d/f

1. > buy foreign currency forward
2. < sell foreign currency forward

• i^d - i^f ~= ( E [ P_t^d/f ] - S^d/f ) / S^d/f
• i^d - i^f +~= ( E [ P_t^d/f ] - S^d/f ) / S^d/f + rp

Real Interests Rates and Real Interest Parity

The Fisher Equation

• ( 1 + i ) = ( 1+ r )( 1 + pi )
• i ~= r + pi

The International Fisher Equation

• ( 1 + i^d ) / ( 1 + i^f ) = [ (1 + r^d) (1 + E[ pi^d ]) ] / [ (1 + r^f) (1 + E[ pi^d ]) ]
• ( 1 + i^d ) / ( 1 + i^f ) = (1 + E[ pi^d ]) / (1 + E[ pi^d ])