Rafael De Santiago

Derivatives Markets with Stochastic Volatility: Interest-rate Derivatives and Value-at-risk Rafael De Santiago

Although the assumption of constant volatility is a reasonable approximation for some markets, in the last two decades the need for more general non-constant volatility models has been the driving force behind numerous works in Financial Mathematics. In this book we study systems that arise in interest-rate markets when the volatility of the short rate is modeled as a function of two mean-reverting diffusions that vary on different scales. This allows us to capture a rich variety of volatility patterns. In the last part of the book the analysis is extended to other areas, like Value-at-Risk, in which similar systems arise when the volatility is modeled as a stochastic process. The book is oriented to researchers who work in the field of Mathematical Finance, as well as to practitioners who would like to gain a better understanding of how to include stochastic volatility in their models.