Explicit Implied Volatilities for Multifactor Local‐stochastic Volatility Models

Lorig, Matthew; Pagliarani, Stefano; Pascucci, Andrea

doi:10.1111/mafi.12105

Cited by 83 publications

(129 citation statements)

References 50 publications

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“…Watanabe (1987), An and Li (2015) provide closed-form expansions for evaluating a general conditional expectation that involves marginal distributions which are generated by stochastic differential equations. In Lorig et al (2015) for a general class of SLV models a family of asymptotic expansions for European-style option prices and implied volatilities are derived. Further, in Pascucci and Mazzon (2015) the authors derive an asymptotic expansion for forward-starting options in a multi-factor local-stochastic volatility model, which results in explicit approximation formulas for the forward implied volatility.…”

Section: Slv Modelsmentioning

confidence: 99%

A Novel Monte Carlo Approach to Hybrid Local Volatility Models

Stoep¹,

Grzelak

Oosterlee

2016

SSRN Journal

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We present in a Monte Carlo simulation framework, a novel approach for the evaluation of hybrid local volatility [Risk, 1994, 7, 18-20] [Risk, 2007, 20, 138-143]. For both model classes a particular (conditional) expectation needs to be evaluated which cannot be extracted from the market and is expensive to compute. We establish accurate and 'cheap to evaluate' approximations for the expectations by means of the stochastic collocation method [SIAM

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Section: Slv Modelsmentioning

confidence: 99%

A Novel Monte Carlo Approach to Hybrid Local Volatility Models

Stoep¹,

Grzelak

Oosterlee

2016

SSRN Journal

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“…Instead, studies find that volatility is strongly mean-reverting [15] and show the presence of multiple time scales (or dimensions) of volatility variation [7,16]. More recently, Lorig et al [14] adopted a general class of multifactor Local-Stochastic Volatility (LSV) models with hybrid dynamics. For an extensive review of local-stochastic modelling see [12].…”

mentioning

confidence: 99%

“…Both model classes provide successive option price expansions which are translated into successive approximating calibration formulas to the implied volatility surface. We present the theoretical results from [9] and [14] needed in each model class for practical calibration of market parameters within a second order expansion and discuss the calibration challenges of existing approaches and motivate our proposed solution.…”

mentioning

confidence: 99%

“…[14] derive implied volatility expressions based on time-independent Taylor expansions within the more general framework of LocalStochastic Volatility (LSV) models of the type (one volatility factor case),…”

mentioning

confidence: 99%

“…For an extensive review of local-stochastic modelling see [12]. Both multiscale SV and LSV models are based on explicit asymptotic approximations of implied volatility in successive orders of perturbation [9] and Taylor [14] expansions, respectively.…”

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confidence: 99%

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Robust Numerical Calibration for Implied Volatility Expansion Models

Baltean-Lugojan¹,

Parpas²

2016

SIAM J. Finan. Math.

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Abstract. Implied volatility expansions allow calibration of sophisticated volatility models. They provide an accurate fit and parametrization of implied volatility surfaces that is consistent with empirical observations. Fine-grained higher order expansions offer a better fit but pose the challenge of finding a robust, stable and computationally tractable calibration procedure due to a large number of market parameters and nonlinearities. We propose calibration schemes for second order expansions that take advantage of the model's structure via exact parameter reductions and recoveries, reuse and scaling between expansion orders where permitted by the model asymptotic regime and numerical iteration over bounded significant parameters. We perform a numerical analysis over 12 years of real S&P 500 index options data for both multiscale stochastic and general local-stochastic volatility models. Our methods are validated empirically by obtaining stable market parameters that meet the qualitative and numerical constraints imposed by their functional forms and model asymptotic assumptions.Key words. implied volatility expansions, numerical calibration, parameter reductions, nonlinear least squares AMS subject classifications. 91G20, 91G60, 90C30, 60-081. Introduction. Research into implied volatility modelling both in academia and industry is focused on addressing the unrealistic assumption of constant asset volatility in the well-known Black-Scholes framework for pricing financial options (see [13] for an overview). A robust model parametrization of implied volatility needs to capture both characteristics and dynamics of the implied volatility surface along different strikes and maturities (or expiries). In addition, volatility models need to balance parameter stability with quality of fit over market data. Practitioners often prioritize tight fits and re-calibrate daily due to overfits that are not stable over multiple days. Meanwhile, existing literature focuses more on consistency. The downside of models that focus on consistency is that they can be computationally expensive to calibrate or are narrowly applicable in pricing a range of derivative contracts. The literature around volatility models is substantial, and we refer the reader to [10] for an extensive overview and comparison of volatility model classes.Models that consistently capture detailed volatility dynamics typically require calibration via numerical-based approaches that are often computationally expensive or lead to numerical instabilities. In order to address these issues, theoretical results have been proposed that translate model formulations into explicit implied volatility expansions for an alternative faster parameter calibration. Fouque et al [8,9] studied Stochastic Volatility (SV) models with multiple factors driving volatility on different time scales. These multifactor models have been validated by empirical studies that show that the deterministic volatility assumption is inconsistent with real data [2]. Instead, studies find that vol...

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Stochastic Volatility

Lorig

Sircar

2016

Financial Signal Processing and Machine Learning

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Explicit Implied Volatilities for Multifactor Local‐stochastic Volatility Models

Cited by 83 publications

References 50 publications

A Novel Monte Carlo Approach to Hybrid Local Volatility Models

A Novel Monte Carlo Approach to Hybrid Local Volatility Models

Robust Numerical Calibration for Implied Volatility Expansion Models

Stochastic Volatility

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