Risk Latte - Brownian Motion Quiz

The principle behind the arbitrage derivation method in modern option pricing theory is:

a) Brownian motion without a memory;
b) Brownian motion with a memory;
c) Both of the above;
d) None of the above

The distribution of the extrema of any Brownian motion will be such that:

a) It will be maximal very early on or very late in the
       game;
b) It will be minimal very early on or very late in the
       game;
c) The maximas and minimas cannot be determined with
       accuracy;
d) None of the above;

A process where the market maintains constant expected dollar moves, regardless of its level is a example of :

a) Geometric Brownian motion;
b) Arithmetic Brownian motion;
c) Exponential Brownian motion;
d) Not a random walk

Money market instruments can sometimes exhibit:

a) Arithmetic Brownian motion;
b) Geometric Brownian motion;
c) Over-geometric Brownian motion;
d) Both Arithmetic and Over-geometric Brownian motion;

An over-geometric process is where:

a) The volatility of the assets increases at higher levels
       and decreases at lower levels;
b) The volatility of the assets decreases at higher levels
       and increases at lower levels;
c) The volatility is a very high at both higher and lower
       levels;
d) None of the above;

Bond prices can be modeled by a "Brownian Bridge" process. This is sometimes referred as:

a) "Extreme Brownian motion";
b) "Tied-down Brownian motion";
c) "memory-less Brownian motion";
d) "non-Markovian Brownian motion";

"Brownian Bridge" process (for modeling bond prices) defines:

a) Random motion when both the beginning and the
       ending points are fixed ex-ante;
b) Random motion when only the ending points are fixed
       ex-ante;
c) Random motion when only the beginning points are
       fixed ex-ante;
d) A quasi-random process where the ending price is an
       exponential function of the beginning prices;

Brownian motion is an example of :

a) a Markovian diffusion process;
b) a Poisson diffusion process;
c) a Levy diffusion process;
d) None of the above;

A Wiener process implies that :

a) A continuously compound rate of return R obtained by
       holding an asset for a given interval of time is
       normally distributed with a variance that is
       proportional to holding period;
b) A continuously compound rate of return R obtained by
       holding an asset for a given interval of time is
       normally distributed with a variance that is
       proportional to the square root of holding period
c) A continuously compound rate of return R obtained by
       holding an asset for a given interval of time is
       normally distributed with a variance that is
       proportional to the square root of the average level
       of the asset during the holding period;
d) None of the above;