Week 2 Flashcards
Continuously Compounded Interest Rate
e^(rT)
Conversion Between Continuously Compounded Rate and Rate Compounded n Times/Year
r(c) = n ln (1 + r(n)/n)
Bond Prices
Mark as red, look at examples to understand
Bond Yield Definition
The discount rate that makes the PV(all cash flows on the bond) = market price of the bond
Forward Rate Definition
The future zero rate implied by today’s term structure of interest rates
Continuously Compounded Forward Rate Formula
r(T1, T2) = [r(0,T2)T2 - r(0,T1)T1] / [T2 - T1]
Discrete Forward Rate
[1 + r(T1,T2)]^(T2-T1) = [1 + r(0,T2)^T2]/[1 + r(0,T1)^T1]
When do we have an upward sloping yield curve?
Forward rate > zero rate
Times of economic growth
When do we have a downward sloping yield curve?
Forward rate < zero rate
Times of economic recession
Price of Prepaid Forward if No Dividends
S(0)
Price of Prepaid Forward if Dividends
S(0) - PV(all dividends from t=0 to t=T)
Discrete dividends: S(0) - ΣPV(D)
Continuous dividends: S(0)*e^(-δT)
*To do PV you do *e^(-rT)
Price of Forward If No Dividends
F = FV(Prepaid Forward) = FV(S(0)) = S(0)*e^(rT)
*To get FV, multiple by e^(rT)
Price of Forward if Continuous Dividends
F = FV(Prepaid Forward) = FV(S(0)e^(-δT)) = S(0)e^[(r-δ)T]
Synthetic Forward
A way to offset the risk of a forward
Buy e^(-δT) units of the index Borrow S(0)*e^(-δT)
Cash-and-Carry Arbitrage
Buy the index, short the forward
Short forward (0) Buy tailed position in stock, paying S(0)*e^(-δT) Borrow S(0)*e^(-δT)
