scholarly journals Calibration of local-stochastic and path-dependent volatility models to vanilla and no-touch options

2021 ◽  
Author(s):  
Alan Bain ◽  
Matthieu Mariapragassam ◽  
Christoph Reisinger
Keyword(s):  
Volatility Models ◽  
Path Dependent

scholarly journals Robustness of Delta Hedging for Path-Dependent Options in Local Volatility Models

2007 ◽  
Vol 44 (04) ◽  
pp. 865-879 ◽  
Author(s):  
Alexander Schied ◽  
Mitja Stadje
Keyword(s):  
Payoff Function ◽  
Hedging Strategy ◽  
Local Volatility ◽  
Directional Convexity ◽  
Volatility Models ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Delta Hedging ◽  
Path Dependent

We consider the performance of the delta hedging strategy obtained from a local volatility model when using as input the physical prices instead of the model price process. This hedging strategy is called robust if it yields a superhedge as soon as the local volatility model overestimates the market volatility. We show that robustness holds for a standard Black-Scholes model whenever we hedge a path-dependent derivative with a convex payoff function. In a genuine local volatility model the situation is shown to be less stable: robustness can break down for many relevant convex payoffs including average-strike Asian options, lookback puts, floating-strike forward starts, and their aggregated cliquets. Furthermore, we prove that a sufficient condition for the robustness in every local volatility model is the directional convexity of the payoff function.

scholarly journals A General Multidimensional Monte Carlo Approach for Dynamic Hedging under Stochastic Volatility

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Daniel Bonetti ◽  
Dorival Leão ◽  
Alberto Ohashi ◽  
Vinícius Siqueira
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
A Priori ◽  
Monte Carlo Study ◽  
Full Generality ◽  
Hedging Strategies ◽  
Volatility Models ◽  
Discontinuous Payoffs ◽  
Quadratic Hedging ◽  
Path Dependent

We propose a feasible and constructive methodology which allows us to compute pure hedging strategies with respect to arbitrary square-integrable claims in incomplete markets. In contrast to previous works based on PDE and BSDE methods, the main merit of our approach is the flexibility of quadratic hedging in full generality without a priori smoothness assumptions on the payoff. In particular, the methodology can be applied to multidimensional quadratic hedging-type strategies for fully path-dependent options with stochastic volatility and discontinuous payoffs. In order to demonstrate that our methodology is indeed applicable, we provide a Monte Carlo study on generalized Föllmer-Schweizer decompositions, locally risk minimizing, and mean variance hedging strategies for vanilla and path-dependent options written on local volatility and stochastic volatility models.

Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

2021 ◽  
Vol 53 (1) ◽  
pp. 220-250
Author(s):  
Zorana Grbac ◽  
David Krief ◽  
Peter Tankov
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Variance Reduction ◽  
Large Deviation ◽  
Heston Model ◽  
Stochastic Volatility Models ◽  
Monte Carlo Computation ◽  
Volatility Models ◽  
Long Time ◽  
Path Dependent

AbstractWe establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

PRICING PATH-DEPENDENT OPTIONS ON STATE DEPENDENT VOLATILITY MODELS WITH A BESSEL BRIDGE

2007 ◽  
Vol 10 (01) ◽  
pp. 51-88 ◽  
Author(s):  
GIUSEPPE CAMPOLIETI ◽  
ROMAN MAKAROV
Keyword(s):  
Monte Carlo ◽  
Diffusion Model ◽  
Path Integral ◽  
Bridge Sampling ◽  
State Dependent ◽  
Volatility Models ◽  
Squared Bessel Process ◽  
Bessel Bridge ◽  
Pricing Kernels ◽  
Path Dependent

This paper develops bridge sampling path integral algorithms for pricing path-dependent options under a new class of nonlinear state dependent volatility models. Path-dependent option pricing is considered within a new (dual) Bessel family of semimartingale diffusion models, as well as the constant elasticity of variance (CEV) diffusion model, arising as a particular case of these models. The transition p.d.f.s or pricing kernels are mapped onto an underlying simpler squared Bessel process and are expressed analytically in terms of modified Bessel functions. We establish precise links between pricing kernels of such models and the randomized gamma distributions, and thereby demonstrate how a squared Bessel bridge process can be used for exact sampling of the Bessel family of paths. A Bessel bridge algorithm is presented which is based on explicit conditional distributions for the Bessel family of volatility models and is similar in spirit to the Brownian bridge algorithm. A special rearrangement and splitting of the path integral variables allows us to combine the Bessel bridge sampling algorithm with either adaptive Monte Carlo algorithms, or quasi-Monte Carlo techniques for significant numerical efficiency improvement. The algorithms are illustrated by pricing Asian-style and lookback options under the Bessel family of volatility models as well as the CEV diffusion model.

scholarly journals Robustness of Delta Hedging for Path-Dependent Options in Local Volatility Models

2007 ◽  
Vol 44 (4) ◽  
pp. 865-879 ◽  
Author(s):  
Alexander Schied ◽  
Mitja Stadje
Keyword(s):  
Payoff Function ◽  
Hedging Strategy ◽  
Local Volatility ◽  
Directional Convexity ◽  
Volatility Models ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Delta Hedging ◽  
Path Dependent

We consider the performance of the delta hedging strategy obtained from a local volatility model when using as input the physical prices instead of the model price process. This hedging strategy is called robust if it yields a superhedge as soon as the local volatility model overestimates the market volatility. We show that robustness holds for a standard Black-Scholes model whenever we hedge a path-dependent derivative with a convex payoff function. In a genuine local volatility model the situation is shown to be less stable: robustness can break down for many relevant convex payoffs including average-strike Asian options, lookback puts, floating-strike forward starts, and their aggregated cliquets. Furthermore, we prove that a sufficient condition for the robustness in every local volatility model is the directional convexity of the payoff function.

Robustness for path-dependent volatility models

2012 ◽  
Vol 36 (2) ◽  
pp. 137-167
Author(s):  
Mauro Rosestolato ◽  
Tiziano Vargiolu ◽  
Giovanna Villani
Keyword(s):  
Volatility Models ◽  
Path Dependent

Moral reasoning is the process of asking moral questions and answering them

2019 ◽  
Vol 42 ◽  
Author(s):  
Mark Alfano
Keyword(s):  
Moral Reasoning ◽  
Dependent Process ◽  
Asking Questions ◽  
Path Dependent ◽  
Path Dependent Process ◽  
Moral Questions

Abstract Reasoning is the iterative, path-dependent process of asking questions and answering them. Moral reasoning is a species of such reasoning, so it is a matter of asking and answering moral questions, which requires both creativity and curiosity. As such, interventions and practices that help people ask more and better moral questions promise to improve moral reasoning.

Intrinsic Liquidity in Conditional Volatility Models

2016 ◽  
pp. 225
Author(s):  
Serge Darolles ◽  
Gaëlle Le Fol ◽  
Christian Francq ◽  
Jean-Michel Zakoïan
Keyword(s):  
Conditional Volatility ◽  
Volatility Models
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