Fixed Income

Price of a T-Period Zero-Coupon Bond

= 1 ÷ (1 + Sₜ)ᵗ

Forward Price (at t = j) of a Zero-Coupon Bond Maturing at (j + k)

= 1 ÷ [1 + f(j,k)]ᵏ

Forward Pricing Model

= P(j+k) = Pⱼ × F(j,k)

Forward Rate Model

= [1 + f(j,k)]ᵏ = [1 + S(j+k)]^(j+k) ÷ (1 + Sⱼ)ʲ

Swap Spread

= Swap Rateₜ − Treasury Yieldₜ

TED Spread

= 3-Month MRR − 3-Month T-Bill Rate

MRR-OIS Spread

= MRR − Overnight Indexed Swap Rate

Portfolio Value Change Due to Level, Steepness, and Curvature Movements

= −DᴸΔxᴸ − DˢΔxˢ − DᶜΔxᶜ

Callable Bond Value

= Vₛₜᵣₐᵢgₕₜ − Vcₐₗₗₐbₗₑ

Putable Bond Value

= Vₛₜᵣₐᵢgₕₜ + Vₚᵤₜ

Value of Put Option on Bond

= Vₚᵤₜₐbₗₑ − Vₛₜᵣₐᵢgₕₜ

Effective Duration

= (BV₋Δy − BV₊Δy) ÷ (2 × BV₀ × Δy)

Effective Convexity

= (BV₋Δy + BV₊Δy − 2 × BV₀) ÷ (BV₀ × Δy²)

Minimum Value of Convertible Bond

= Greater of Conversion Value or Straight Value

Market Conversion Price

= Market Price of Convertible Bond ÷ Conversion Ratio

Market Conversion Premium per Share

= Market Conversion Price − Stock’s Market Price

Market Conversion Premium Ratio

= Market Conversion Premium per Share ÷ Market Price of Common Stock

Premium Over Straight Value

= (Market Price of Convertible Bond ÷ Straight Value) − 1

Callable and Putable Convertible Bond Value

= Straight Value + Value of Call Option on Stock − Value of Call Option on Bond + Value of Put Option on Bond

Recovery Rate

= % of Money Received Upon Default

Loss Given Default (%)

= 100 − Recovery Rate

Expected Loss

= Probability of Default × Loss Given Default

Present Value of Expected Loss

= Value of Risk-Free Bond − Value of Credit-Risky Bond

Upfront Premium % (CDS)

≈ (CDS Spread − CDS Coupon) × Duration

Price of CDS (per $100 Notional)

≈ $100 − Upfront Premium (%)

Profit for Protection Buyer

≈ Change in Spread × Duration × Notional Principal