Definitions

Question 1

Arrow-Debreu security (state contract)

Answer 1

a financial contract for a certain state j, bought at time 0, that pays one unit of income at time 1 if state j realizes

Question 2

State price

Answer 2

π_j, the price of a state contract at time 0 that pays off one unit of income at time 1 if state j realizes and zero otherwise. (i.e. the price of a state contract)

Question 3

Discount factor

Answer 3

π(1) = 1/(1+r), where r is the interest rate. This factor shows the amount that one unit of income at time 1 is worth at time 0

Question 4

Interest compounding (discrete)

Answer 4

d_i = 1/(1+r_i)^i

Question 5

Interest compounding (continuous)

Answer 5

d_i = exp(-r_i*i)

Question 6

Implied probabilities/normalized prices/risk-neutral probabilities

Answer 6

denoted by q_j = π_j/(sum(π_i)), where π_j is the state price for state j

Question 7

Normalized pricing kernel

Answer 7

θ_j=q_j/p_j, where q_j is the normalized price of state j and p_j is the objective probability that state j realizes

Question 8

Pricing kernel/Stochastic discount factor (SDF)

Answer 8

M_j=π(1)q_j/p_j, where π(1)=1/(1+r) represents the price of a contract that pays one unit of income for certain, no matter what state realizes and q_j/p_j is the normalized pricing kernel

Question 9

Aggregate income

Answer 9

Total income of all agents (i=1,…,k) together in state j

Question 10

Market clearing condition

Answer 10

the condition that for each traded asset, total demand equals total supply. If this is the case, we speak of a general equilibrium

Question 11

Dynamic strategies

Answer 11

a kind of trading strategy. This may involve trading at periods different from the current one.

Question 12

Liquidity

Answer 12

A liquid asset is easy to buy or sell, for example stocks of large companies and government bonds. Illiquid assets are privately owned companies, large real estate objects and collector items in art.

Question 13

Liquid market

Answer 13

a market in which all contracts are liquid; all contracts can be easily bought and sold at any time for a fixed price

Question 14

Efficient market

Answer 14

a market is said to be efficient if all relevant information is available and adequately processed by all market participants. In an inefficient market, some traders have an information advantage

Question 15

Utility function

Answer 15

u(x), a function of an agent that describes the value associated to hold a certain commodity or money by this agent

Question 16

Coefficient of absolute risk aversion

Answer 16

this coefficient tells the degree of risk aversion for an agent at some wealth level x: R(x) = -(u’‘(x)/u’(x))

Question 17

Rationality

Answer 17

agents take their decisions on the basis of a principle that can be expressed in terms of optimization of the utility function

Question 18

Complete market

Answer 18

A market is complete if every possible cash flow sequence can be generated by the cash flows of the basic assets. This happens when there is a unique solution to the vector-matrix equation Fd=π

Question 19

Replication

Answer 19

Given a collection of series of future cash flows, we say that a series of cash flows is replicable if there exist numbers x_1,…,x_m, such that sum(x_j*f_ji)=f^_i for all i=1,…,n

Question 20

Hedging

Answer 20

a trading strategy that is aimed to reduce the risk that is associated with a given contractual obligation. For perfect hedging there must be a complete market and exact model

Question 21

Arbitrage

Answer 21

a trading strategy that, with a positive probability, generates a positive cash flow either immediately or at some point in the future, and that does not generate any negative cashlows

Question 22

Strict arbitrage

Answer 22

a trading strategy that, with a positive probability, generates a positive cash flow immediately and that does not generate any negative cashlows

Question 23

Call option

Answer 23

gives the holder the right, but not an obligation, to buy an underlying asset for a pre-specified price K (strike price). Let S_gamma be the stock price at a certain possible state in time gamma and K be the strike price. The pay-off is then Call_gamma = max(S_gamma-K,0)

Question 24

Put option

Answer 24

gives the holder the right, but not an obligation, to sell an underlying asset for a pre-specified price K (strike price). Let S_gamma be the stock price at a certain possible state in time gamma and K be the strike price. The pay-off is then Put_gamma = max(K-S_gamma,0)

Question 25

European option

Answer 25

A call or put option that can only be exercised at a pre-specified date (maturity date)

Question 26

American option

Answer 26

A call or put option that can be exercised at any period at or before the maturity date

Question 27

European Central Bank

Answer 27

ECB uses government bonds to construct discount and yield curves. It uses continuous compounding and the bonds are characterized by their market price and future cash flows as given by their contract

Question 28

Binomial tree

Answer 28

A tree, which in each possible state has two possible states in the next point in time. A binomial tree with N steps has 2^N nodes at the N-th step

Question 29

Recombining tree model

Answer 29

A tree model in which there is no difference between asset prices at nodes that have an equal amount of u's and d's with respect to each other, so nodes with equal amounts of u's and d's essentially form one state. A recombining tree has N+1 different nodes at the N-th step

Question 30

Geometric tree model

Answer 30

A multi-period uncertainty discrete-time model for evolution of asset prices. In this model, given the price of the asset at time t, the price at time t+1 can take finitely many values, obtained by multiplying the asset price at time t by one of a fixed set of positive multiplication factors. Completeness and absence of arbitrage hold under the condition that d<1+r

Question 31

Zero coupon bond

Answer 31

a special bond that does not pay any interest payments before the time of maturity. Always in a market without arbitrage opportunity and positive discount factors. If the market is complete, it is possible to determine a specific value, otherwise you need to find a price range.