Stochastic volatility
Stochastic volatility’s orderly smiles
Stochastic volatility’s orderly smiles
Sponsored statement: Ito33
Which model for equity derivatives?
Perturbed Gaussian copula: introducing the skew effect in co-dependence
Gaussian copula models are often used in the industry when single-asset information is quoted but little is known about their joint relation. These models may arise from correlated stochastic Brownian processes with deterministic volatility and…
Being particular about calibration
Following previous work on the calibration of multi-factor local stochastic volatility models to market smiles, Julien Guyon and Pierre Henry-Labordère show how to calibrate exactly any such model. Their approach, based on McKean’s particle method,…
Right Laplace, right time
Right Laplace, right time
Lifetime achievement award: John Hull
Risk awards 2011
A Libor market model with a stochastic basis
A Libor market model with a stochastic basis
Sponsored statement: Controlling volatility to reduce uncertainty
Controlling volatility to reduce uncertainty
The value of a variance swap – a question of interest
Pricing equity variance swaps is well understood in the case of deterministic interest rates, but particularly for longer-dated swaps the stochastic nature of the rate cannot be ignored. Here, Per Hörfelt and Olaf Torné derive the fair strike when both…
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