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 markets, 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 unconstrained or constrained optimization techniques. The third section relies instead on the continuous-time Black-Scholes representation of financial markets 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.

Sbuelz, A., Tarelli, A., Quantitative Finance: Problems and Solutions, Giappichelli, Turin 2021: 176 [http://hdl.handle.net/10807/183627]

Quantitative Finance: Problems and Solutions

Sbuelz, Alessandro;Tarelli, Andrea
2021

Abstract

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 markets, 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 unconstrained or constrained optimization techniques. The third section relies instead on the continuous-time Black-Scholes representation of financial markets 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.
Inglese
Monografia o trattato scientifico
Giappichelli
Sbuelz, A., Tarelli, A., Quantitative Finance: Problems and Solutions, Giappichelli, Turin 2021: 176 [http://hdl.handle.net/10807/183627]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/183627
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