Calculation and formula reference for Forward Price, Spot Rates & Forward Rates, Yield to Maturity, Forward Rate Agreement (FRA), Forward Contract and Forward Exchange Rates.
Where S0 is the spot price of the asset today
T is the time to maturity (in years)
r is the annual risk free rateof interest
(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.
(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.
Where st is the t-period spot rate and
ft-1,t is the forward rate applicable for the period (t-1,t)
To solve for YTM we are solving for the interest rate (r) in the bond valuation formula:
Where CPt is the coupon payment at time t and MV is the maturity value at time n (i.e. at maturity).
The value of the FRA at time 0, VFRA, 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
RK is the fixed interest rate
Where S0is 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
I is the present value at time 0 of the known income on the investment assets
q is the know yield rate provided by the investment asset
Where rf is the value of the foreign risk free interest rate when the money is invested for time T.
Where r and rf are compounded continuously
if the interest rates were compounded on a discrete basis.
r is the risk free rate of the domestic currency
rf is the risk free rate of the foreign currency
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