Chapter 15 - The 5-step Method In Discrete Time

Question 1

Previsible

Answer 1

φt is previsible if it is known based on information up to but not including time t

Question 2

Self-financing portfolio

Answer 2

A portfolio (φt,ψt) is self-financing if φt, ψt are previsible and 
dVt = φt dSt + ψt dBt
ie, the required change in the value of the portfolio over each instant of time is equal to the pure instantaneous investment gain.

Question 3

Replicating portfolio

Answer 3

Consider a derivative with random variable payoff X at time T. A self-financing portfolio Vt is a replicating portfolio for X if Vt = X
So for an initial investment of Vo at time 0, if we follow the self-financing portfolio strategy we will be able to reproduce the derivative payment exaclty and without risk.

Question 4

Complete investment market

Answer 4

An investment market is complete if for every derivative in that market, there exists a replicating strategy for that derivative.

Notes:
The market is complete if for any such contingent claims X there is a replicating strategy (φt,ψt)

Question 5

Q-martingale

Answer 5

Xt is a Q-martingale if

EQ[Xu|Ft] = Xt whenever t<u></u>

Question 6

Tradeable asset

Answer 6

An asset where its price at time t is equal to the total return on that investment up to time t with no dividend income payable or inputs of cash required.