Pricing in stochastic-local volatility models with default

Tomassini, Monia (2014) Pricing in stochastic-local volatility models with default. [Laurea magistrale], Università di Bologna, Corso di Studio in Matematica [LM-DM270]
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In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Tipologia del documento
Tesi di laurea (Laurea magistrale)
Autore della tesi
Tomassini, Monia
Relatore della tesi
Corso di studio
Curriculum A: Generale e applicativo
Ordinamento Cds
Parole chiave
model with default Vasicek model and Cir model for the short rate
Data di discussione della Tesi
20 Giugno 2014

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