Exam Marco–finance Januari 2019
Question 1: Utility theory
• Give the expected utility theorem and explain.
• Explain and illustrate the certainty equivalent and risk premium
• Show that risk premium only depends on the volatility of shocks in wealth by using
second order Taylor expansions (not 100% sure)
Question 2:
• Give the optimal saving condition and explain its components.
• Give the important determinants of saving and the corresponding effects on savings
(CRRA of 2).
• Explain the wealth and precautionary savings effect.
• Why did savings during the financial crisis increase while interests were very low?
Question 4: Risk–neutral pricing (max. 2 pages)
• Risk–neutral pricing has become one of the most important techniques for pricing
derivatives. The approach allows to obtain no–arbitrage prices for derivatives
contracts on the basis of simple assumptions for the price dynamics of the underlying
asset and the risk–free rate. The approach is extremely flexible and allows to price
any type of derivative. Answer the following questions:
a. Explain briefly what is meant by risk–neutral pricing. Specifically, give the risk–
neutral pricing equation and explain (briefly its meaning).
b. Illustrate the concept of risk–neutral pricing by valuing the following exotic derivative.
The derivative is “European”, i.e. it only pays out at the end of the contract (1 year from
now). The payoff¤ of the derivative equals max(Smax – K; 0); where Smax denotes the
maximum observed price between now (t) and the end of the contract (T = t + 1) and K is the
strike price. The derivative hence locks in the maximum price gain above K: Consider the
following situation: the current price of the asset St = 110; K = 100: Price the derivative (i.e.