Interest Rate Models - Notes
Key Concepts
Interest rates
Simple
Compound
Short rate
Term structure dynamics
LIBOR
Yiel curve
Cupon Bond
Cash Flow
Borrower time
Pricing interest rate derivatives
Money Market Account
Zero-Cupon Bonds (dicount bond)
Discount curve
Term strcuture and yield curve
Modeling and term struture dynamics
Money Market Account
# Forward rate function under continuous compounding - ZERO Cupon
forward_rate <- function(y1, T1, y2, T2) {
P1 <- exp(-y1 * T1) # Price of zero-coupon bond maturing at T1
P2 <- exp(-y2 * T2) # Price of zero-coupon bond maturing at T2
F <- (P1 / P2)^(1 / (T2 - T1)) - 1
return(F)
}
# Example: yields and maturities
y1 <- 0.04 # 4% for 1 year
T1 <- 1
y2 <- 0.06 # 6% for 2 years
T2 <- 2
F_0_1_2 <- forward_rate(y1, T1, y2, T2)
cat("Forward rate F(0,1,2):", round(F_0_1_2 * 100, 2), "%\n")
Coupon Bonds and Interest Rate Swaps
Sintetic create long term invesments.
