Local risk-minimization for Lévy markets

Int. J. Theor. Appl. Finan.

2019

Self Cite

The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein-Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.

“…This theorem is shown by Theorem A.1 of [2] (see also Theorem 3.7 of [3]). Thus, we confirm if all the conditions of Theorem A.1 of [2] are satisfied in our setting.…”

Section: Proofmentioning

confidence: 96%

Pricing and Hedging of Vix Options for Barndorff-Nielsen and Shephard Models

Int. J. Theor. Appl. Finan.

2019

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“…Next, we introduce integral representations of I 1 and I 2 given in [2] in order to show we can adopt Carr and…”

Section: Proposition 2 ([2 Proposition 46]) For Any K > 0 and T ∈ [mentioning

confidence: 99%

“…LRM is closely related to the equivalent martingale measure which is well known as the minimal martingale measure (MMM). For more details on LRM, see [1,2]. Delta hedging strategies, which are also well-known and often used by practitioners, are given by differentiating the option price under a certain martingale measure with respect to the underlying asset price.…”

Section: Introductionmentioning

confidence: 99%

“…The paper [2] showed explicit representations of LRM for call options by using Malliavin calculus for Lévy processes based on the canonical Lévy space. Carr and Madan introduced a numerical method for valuing options based on the fast Fourier transform (FFT) in [3].…”

Section: Introductionmentioning

confidence: 99%

“…This paper aims to illustrate, based on [2], how different is LRM from delta hedging strategies for call options in exponential Lévy models. Furthermore, we show that delta hedging strategies are easily calculated by using the numerical scheme developed in [1].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Comparison of local risk minimization and delta hedging strategy for exponential Lévy models

Imai

2015

JSIAM Letters

Self Cite

We discuss the differences of local risk minimization (LRM) and delta hedging strategies, in exponential Lévy models, where delta hedging strategies in this paper are defined under the minimal martingale measures (MMM). First of all we give inequality estimations for the differences of LRM and delta hedging strategies, and then show numerical examples for the two typical exponential Lévy models, Merton models and variance Gamma (VG) models.

Numerical Analysis on Quadratic Hedging Strategies for Normal Inverse Gaussian Models

Advances in Mathematical Economics

Imai

Nakashima

2018

Self Cite

The authors aim to develop numerical schemes of the two representative quadratic hedging strategies: locally risk minimizing and mean-variance hedging strategies, for models whose asset price process is given by the exponential of a normal inverse Gaussian process, using the results of Arai et al. [2], and Arai and Imai [1]. Here normal inverse Gaussian process is a framework of Lévy processes frequently appeared in financial literature. In addition, some numerical results are also introduced.