LECTURE 1 — FIXED INCOME, BOND & LOAN PRICING, DURATION

Discount Factor

DFₜ = 1 / (1+R)ᵗ

Bond Price

P = Σ CFₜ / (1+R)ᵗ

Present Value of Cash Flow

PVₜ = CFₜ × DFₜ

DF with m payments

DFₜ = 1 / (1 + R/m)^(m·t)

Bond Price with m payments

P = Σ CFₜ / (1 + R/m)^(m·t)

French Loan Instalment

x = 1 / Σ DFₜ

Interest Payment (Loan)

Interestₜ = ResidualDebtₜ₋₁ × R

Principal Repayment (Loan)

Principalₜ = Instalment − Interestₜ

Macaulay Duration (annual)

D = Σ[ t·CFₜ/(1+R)ᵗ ] / P

Macaulay Duration (m payments)

D = Σ[ t·CFₜ/(1+R/m)^(m·t) ] / P

Modified Duration

MD = D / (1+R)

Dollar Duration

ΔP/ΔR = MD × P

Duration Approximation

ΔP/P = − MD × ΔR