FORMULA SHEET
Interest Rates:
R 

Rc = m ln 1 + m 
m 

Rc / m
Rm = m e
−1
(
Forward Rates:
)
R2T2 − R1T1
T2 − T1
Forwards and Futures:
Optimal Hedge Ratio:
h* = 
N* =
Optimal Number of Contracts:
Stock Index Futures: N * =

S
F
P
F
h * QA
QF
Futures Prices:
Futures Prices with known Income: 𝐹0
= (𝑆0 − 𝐼)𝑒 𝑟𝑇
Value of a long forward contract: ƒ = (F0 – K )e–rT
Value of a short forward contract: (K – F0 )e–rT
Value of a forward contract on an investment that provides a fixed income: ƒ = S0 – I – Ke–rT
Options:
Lower bounds for European options on non-dividend paying shares:
c ≥ S0 – Ke-rT
and
p ≥ Ke-rT – S0
Put- Call Parity: c + Ke -rT = p + S0
Put-Call Parity with Dividends: c + D + Ke -rT = p + S0
For American options: S0 – K ≤ C – P ≤ S0 – Ke-rT