Calculation references for Forward Price, Spot Rates & Forward Rates, Yield to Maturity, Forward Rate Agreement (FRA), Forward Contract and Forward Exchange Rates.

Short and sweet Lessons in Forward Pricing

Valuing a forward contract in Excel – Lesson Zero

Calculating Forward Prices in Excel – Lesson 1

Calculating Forward Prices and YTMS in Excel – Lesson 2

Calculating Forward Foreign Exchange Rates in Excel – Lesson 3

Defining the Par Interest Rate Term Structure

Calculating the Zero interest rate curve

Calculating the Forward interest rate curve

Calculating the MTM of the Interest Rate Swaps – IRS

Pricing Basis swap

Projecting Foreign Exchange Currency Rates for Cross Currency Swap Valuation (from CCS)

CCS – Cross Currency Swap Valuation & Pricing

Forward Price

• Forward price of a security with no income
• Forward price of a security with known cash income
• Forward price of a security with known dividend yield
  

Spot Rates and Forward Rates

• Relationship between spot rates and forward rates-1
• Relationship between spot rates and forward rates-2

Yield to Maturity (YTM)

Forward Rate Agreement (FRA)

Forward Contract

• Value of a long forward contract (continuous)
• Value of a long forward contract (discrete)
• Value of a long forward contract (continuous) which provides a known income
• Value of a long forward contract (continuous) which provides a known yield
• Value of a forward foreign current contract (continuous)

Forward Exchange Rates

1. Forward Price

Forward price of a security with no income

Where S₀ is the spot price of the asset today
T is the time to maturity (in years)

r is the annual risk free rate of interest

Forward price of a security with known cash income

(Securities such as stocks paying known dividends or coupon bearing bonds)

Where I is the present value of the cash income during the tenor of the contract discounted at the risk free rate.

Forward price of a security with known dividend yield:

(Securities such as currencies and stock indices)

Where q is the dividend yield rate. For a foreign currency q will be the foreign risk free rate.

2. Spot Rates and Forward Rates

Relationship between spot rates and forward rates-1

Relationship between spot rates and forward rates-1

Where s_t is the t-period spot rate and

f_t-1,t is the forward rate applicable for the period (t-1,t)

3. Yield to Maturity (YTM)

To solve for YTM we are solving for the interest rate (r) in the bond valuation formula:

Where CP_t is the coupon payment at time t and MV is the maturity value at time n (i.e. at maturity).

4. Forward Rate Agreement (FRA)

The value of the FRA at time 0, V_FRA, for someone receiving fixed and paying floating will be

if R₂ (the zero coupon rate for a maturity of T₂) is calculated on a discrete basis or

if R₂ is calculated on a continuous basis.
Where, L is the principal amount

R_K is the fixed interest rate

R_F is the forward interest rate assuming that it will equal the realized benchmark or floating rate for the period between times T₁ and T₂

5. Forward Contract

Value of a long forward contract (continuous)

Where S₀ is the spot price
T is the remaining time to maturity

r is the risk free rate

K is the delivery price which is set in the contract

Value of a long forward contract (discrete)

Value of a long forward contract (continuous) which provides a known income

I is the present value at time 0 of the known income on the investment assets

Value of a long forward contract (continuous) which provides a known yield

q is the know yield rate provided by the investment asset

Value of a forward foreign current contract (continuous)

Where r_f is the value of the foreign risk free interest rate when the money is invested for time T.

Forward exchange rates

Where r and r_f are compounded continuously

or

if the interest rates were compounded on a discrete basis.
r is the risk free rate of the domestic currency

r_f is the risk free rate of the foreign currency

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