Asset Pricing
Assignment 1
Asset Pricing (Leopold So?gner) ,
Quantitative Finance Program
WU Vienna
November 5, 2020 due on November 20, 2020 (upload pdf via Learn WU)
Problem max. points points
Problem 1 25
Problem 2 25
Problem 3 25
Problem 4 25
Points 100
1: Consider an economy where bid-ask spreads show up. A long spot position in asset D is the contract
(?Sa,D), Sa is called the ask price. A short spot position in asset D corresponds to (?Sb,D), Sb
is called the bid price. Sa ? Sb. In addition a risk-free discount bond is traded, where we get
(??b,1K) and (??a,1K). The lending rate is rl = 1?a ?1 while the borrowing rate is rb = 1 ?b ?1. For
forward contracts the forward-ask and forward-bid prices are Fa and Fb, respectively The payoffs are
(0,D ?Fa1K) for long forward position and (0,?D + Fb1K) for a short forward position; Fa ? Fb.
Show that in an arbitrage-free market,
rl ? rb, ?b ? ?a,Sb ? ?aFa and ?bFb ? Sa have to hold.
2: Construct your own example with J = 3 assets and K = 3 states, where the market is incomplete.
One of the three assets is a risk-free discount bond. Provide an argument or proof that the market
is incomplete in your example.
Derive the set of the state-prices and state price densities.
1
3: We defined a pricing cash flow as a cash-flow x? ? X where there exist constants ? and q such that
q 6= 0 and
x(0) + ?E(x(1)) + qCov(x?(1),x(1)) = 0 for all x ? X .
Consider the case where a risk-free asset is traded.
Suppose that somebody claims that the pricing cash-flow x? is equal to the cash-flow xE. What hap-
pens (or what can go wrong), what are the implications? [Consider a case where xE is proportional
to x? and the case where this is not the case.]
4: Consider an economy where two risky assets are traded and a risk-free asset is traded. I.e. J = 3,
the number of states is finite.
Construct your own example: Obtain x?, xE, R?, a beta pricing returns R? and the highest attain-
able Share-ratio. Choose your own numbers and obtain these objects. Describe how the cash-flows
and returns are obtained (at least the formulas). Provide a figure where you also include/describe
the efficiency frontier.
