Stochastic volatility
Expanded smiles
Implementing models with stochastic as well as deterministic local volatility can be challenging. Here, Jesper Andreasen and Brian Huge describe an expansion approach for such models that avoids the high-dimensional partial differential equations usually…
Smile dynamics IV
Lorenzo Bergomi addresses the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. He introduces a new quantity, the skew stickiness ratio (SSR), and shows how, at order one in…
Calibration of local stochastic volatility models to market smiles
Pierre Henry-Labordère introduces a new technique for calibrating local volatility extensions of arbitrary multi-factor stochastic volatility models to market smiles. Although approximate, this technique is both fast and accurate. The procedure is…
Quant of the Year - Dilip Madan
Risk Awards 2008
Lifetime Achievement Award - Bruno Dupire
Risk Awards 2008
Calibrating and pricing with local volatility models
Cutting edge - Option pricing
Calibrating and pricing with embedded local volatility models
Consistently fitting vanilla option surfaces when pricing volatility derivatives such as Vix options or interest rate/equity hybrids is an important issue. Here, Yong Ren, Dilip Madan and Michael Qian Qian show how this can be accomplished, using a…
Markovian projection for volatility calibration
Vladimir Piterbarg looks at the Markovian projection method, a way of obtaining closed-form approximations of European-style option prices on various underlyings that, in principle, is applicable to any (diffusive) model. The aim is to distil the essence…
Markovian projection for volatility calibration
Vladimir Piterbarg looks at the 'Markovian projection method', a way of obtaining closed-form approximations of European-style option prices on various underlyings that, in principle, is applicable to any (diffusive) model. The aim is to distil the…
Variance swaps under no conditions
Conditional variance swaps are claims on realised variance that is accumulated when the underlying asset price stays within a certain range. Being highly sensitive to movements in both asset price and its variance, they require a very reliable model for…
Inflation-indexed securities - Inflation with a smile
In the current inflation-indexed markets, most traded options have zero or even negative strikes. This highlights the need for a smile-consistent valuation of caps and floors on inflation rates. To this end, Fabio Mercurio and Nicola Moreni propose a…
Smile dynamics II
In an article published in Risk in September 2004, Lorenzo Bergomi highlighted how traditionalstochastic volatility and jump/Lévy models impose structural constraints on the relationshipbetween the forward skew, the spot/volatility correlation and the…
Back to the future
Current developments in exotic interest rate products push the demand for more sophisticatedinterest rate models. Here, Jesper Andreasen presents a new class of stochastic volatility multifactoryield curve models enabling quick calibration and efficient…
Time to smile
Cutting edge: Option pricing
Smile at the uncertainty
Smile-consistent alternatives to the Black-Scholes model are often too cumbersome to be used for large portfolios of exotic options. Damiano Brigo, Fabio Mercurio and Francesco Rapisarda propose an intuitive stochastic volatility model that is easy to…
Unifying volatility models
This article introduces a method for building analytically tractable option pricing models that combine state-dependent volatility, stochastic volatility and jumps. The eigenfunction expansion method is used to add jumps and stochastic volatility to…
Black smirks
Fei Zhou presents a simple stochastic volatility extension of the Black interest rate option pricing model widely used by traders. Using a perturbative expansion in volatility of volatility, he derives modified Black formulas that correctly fit the…
Risk management based on stochastic volatility
Risk management approaches that do not incorporate randomly changing volatility tend to under- or overestimate the risk, depending on current market conditions. We show how some popular stochastic volatility models in combination with the hyperbolic…
Volatile volatilities
When pricing exotic interest rate derivatives, calibration of model parameters to vanilla cap or swaption prices can be especially time-consuming, especially if stochastic volatility is incorporated into the standard Libor market models or low…
Testing assumptions
In calculating value-at-risk forecasts for trading portfolios, distributional assumptions are asimportant as the choice of risk factors, but it is not easy to determine the source of errorwhen rejected forecasts occur. Here, Jeremy Berkowitz develops a…
Behind the mirror
Barrier options
The stochastic volatility Libor market model
Interest rates