Modeling Volatility and Valuing Derivatives Under Anchoring

Valuing Credit Derivatives

Credit derivatives are potentially one of the most important new types of financial products introduced during the past decade. Many investors have portfolios with values that ar higWy sensitive to shifts in the spread between risky and riskless yields, and credit derivatives offer these investors an important new tool for managing and hedging their exposure to this type of risk. In this articl...

Volatility Derivatives

Volatility derivatives are a class of derivative securities where the payoff explicitly depends on some measure of the volatility of an underlying asset. Prominent examples of these derivatives include variance swaps and VIX futures and options. We provide an overview of the current market for these derivatives. We also survey the early literature on the subject. Finally, we provide relatively ...

New Methodologies for Valuing Derivatives

High-dimensional integrals are usually solved with Monte Carlo algorithms although theory suggests that low discrepancy algorithms are sometimes superior. We report on numerical testing which compares low discrepancy and Monte Carlo algorithms on the evaluation of nancial derivatives. The testing is performed on a Collateralized Mortgage Obligation (CMO) which is formulated as the computation o...

Exotic derivatives under stochastic volatility models with jumps

In equity and foreign exchange markets the risk-neutral dynamics of the underlying asset are commonly represented by stochastic volatility models with jumps. In this paper we consider a dense subclass of such models and develop analytically tractable formulae for the prices of a range of first-generation exotic derivatives. We provide closed form formulae for the Fourier transforms of vanilla a...

Finite Difference Methods in Derivatives Pricing under Stochastic Volatility Models