Notation can be divided naturally into three parts: lower case (generally deterministic), upper case (generally random), and Greek.

Lower case

a a (real) parameter

c a constant; coupon rate

Radon—Nikodym derivative of ℚ with respect to ℙ

dt infinitesimal time increment

dWt infinitesimal Brownian increment

f a function

fℙ(x) probability density function of the law ℙ

f(t, T) bond forward rates

g a function

g(x, t, T) the function (− log P(t, T) ∣ rt = x)

i an integer

j an integer

k contract strike/exercise price; an integer; an offset

n an integer

n[t] number of dividend payments made by time t

p, pj a probability

q, Qj a probability

r constant interest rate

rt variable interest rate process; instantaneous rate

s initial stock price, alternative time variable

Sj possible value for the discrete stock process

t time

u foreign currency interest rate; real variable

x a real variable; horizontal axis variable

Xi(t) time-dependent factor of volatility surface

yi(T) maturity-dependent factor of volatility surface

Upper case

A an event; a constant

At HJM volatility matrix

Bi, Bt bond price process

B(t, T) solution of a Riccati equation

Ct foreign exchange rate; coupon bond price; numeraire

Di financing gap

Dt foreign currency cash bond

D(t, T) solution of a Riccati equation

E expectation operator

Eℙ expectation under the measure ℙ

Et discounted portfolio value process

F forward price

Fs(t, T) forward price at time s for P(t, T)

Fq quanto forward price

Fi history of discrete stock-price process up to tick-time i