Quantitative finance: problems and solutions

This book is a collection of exercises in quantitative finance for graduate students in financial markets. After the notations have been introduced and the relevant continuous-time models have been discussed, four main topics are addressed. The first section proposes problems based on one-period mar- kets, where the focus is on the determination of no-arbitrage prices for claims that provide given payoff profiles in complete or incomplete markets. Within the same discrete-time framework, the second section aims at fostering the understanding of optimal mean-variance portfolio choices and the related un- constrained or constrained optimization techniques. The third section relies instead on the continuous-time Black-Scholes representation of financial mar- kets in the presence of market risk. The exercises concern the determination of the equilibrium return and the no-arbitrage price of instruments exposed to such a risk via their payoffs. The fourth section deals with the continuous- time Vasicek model of interest rate risk. The exercises focus on the financial features of the no-arbitrage pricing formula of zero-coupon bonds and on the equilibrium term structure of interest rates.