AN APPROXIMATION METHOD FOR PRICING CONTINUOUS BARRIER OPTIONS UNDER MULTI-ASSET LOCAL STOCHASTIC VOLATILITY MODELS

This paper presents a new approximation method for pricing multi-asset continuous single-barrier options. Barrier options are frequently traded, and it is necessary for practitioners to evaluate these precisely and quickly, both for competitiveness, and for risk management. However, it is a difficult task under local stochastic volatility models. To the best of our knowledge, this paper is the first to provide an analytical approximation for continuous barrier options prices in a multi-asset environment. In numerical experiments, we examine the validity of the formula by using parameters calibrated to EURUSD European options.

An analytical approximation for single barrier options under stochastic volatility models

Annals of Operations Research ◽

10.1007/s10479-017-2559-3 ◽

2017 ◽

Vol 266 (1-2) ◽

pp. 129-157 ◽

Cited By ~ 5

Author(s):

Hideharu Funahashi ◽

Tomohide Higuchi

Keyword(s):

Stochastic Volatility ◽

Analytical Approximation ◽

Barrier Options ◽

A unified approach to Bermudan and barrier options under stochastic volatility models with jumps

Journal of Economic Dynamics and Control ◽

10.1016/j.jedc.2017.05.001 ◽

2017 ◽

Vol 80 ◽

pp. 75-100 ◽

Cited By ~ 38

Author(s):

J. Lars Kirkby ◽

Duy Nguyen ◽

Zhenyu Cui

Keyword(s):

Stochastic Volatility ◽

Barrier Options ◽

Unified Approach ◽

PRICING AND HEDGING OF VIX OPTIONS FOR BARNDORFF-NIELSEN AND SHEPHARD MODELS

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024919500432 ◽

2019 ◽

Vol 22 (08) ◽

pp. 1950043 ◽

Cited By ~ 1

Author(s):

TAKUJI ARAI

Keyword(s):

Fourier Transform ◽

Stochastic Volatility ◽

Numerical Experiments ◽

Option Price ◽

Call Option ◽

Risky Assets ◽

Volatility Models ◽

Vix Options ◽

Non Gaussian

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.

Market Risk Management with Stochastic Volatility Models

Risk Management in Environment, Production and Economy ◽

10.5772/16584 ◽

2011 ◽

Author(s):

Per Solibakke

Keyword(s):

Risk Management ◽

Stochastic Volatility ◽

Market Risk ◽

Robust static hedging of barrier options in stochastic volatility models

Mathematical Methods of Operations Research ◽

10.1007/s00186-008-0273-2 ◽

2008 ◽

Vol 70 (3) ◽

pp. 405-433 ◽

Cited By ~ 11

Author(s):

J. H. Maruhn ◽

E. W. Sachs

Keyword(s):

Stochastic Volatility ◽

Barrier Options ◽

Static Hedging ◽

Computation of the Delta of European options under stochastic volatility models

Computational Management Science ◽

10.1007/s10287-018-0316-y ◽

2018 ◽

Vol 15 (2) ◽

pp. 213-237

Author(s):

Yeliz Yolcu-Okur ◽

Tilman Sayer ◽

Bilgi Yilmaz ◽

B. Alper Inkaya

Keyword(s):

Stochastic Volatility ◽

European Options ◽

Computation of the Delta of European Options Under Stochastic Volatility Models

SSRN Electronic Journal ◽

10.2139/ssrn.2877709 ◽

2016 ◽

Author(s):

Yeliz Yolcu-Okur ◽

Tilman Sayer ◽

Bilgi Yilmaz ◽

B. Alper Inkaya

Keyword(s):

Stochastic Volatility ◽

European Options ◽

Capturing implied correlation skew from options prices via multiscale stochastic volatility models

International Journal of Financial Engineering ◽

10.1142/s2424786320500425 ◽

2020 ◽

Vol 07 (04) ◽

pp. 2050042

Author(s):

T. Pellegrino

Keyword(s):

Stochastic Volatility ◽

Calibration Procedure ◽

Second Order ◽

Model Parameters ◽

Option Prices ◽

European Options ◽

Volatility Models ◽

Order Expansion ◽

Implied Correlation

The aim of this paper is to derive a second-order asymptotic expansion for the price of European options written on two underlying assets, whose dynamics are described by multiscale stochastic volatility models. In particular, the second-order expansion of option prices can be translated into a corresponding expansion in implied correlation units. The resulting approximation for the implied correlation curve turns out to be quadratic in the log-moneyness, capturing the convexity of the implied correlation skew. Finally, we describe a calibration procedure where the model parameters can be estimated using option prices on individual underlying assets.

DG framework for pricing European options under one-factor stochastic volatility models

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2018.05.064 ◽

2018 ◽

Vol 344 ◽

pp. 585-600 ◽

Cited By ~ 5

Author(s):

Jiří Hozman ◽

Tomáš Tichý

Keyword(s):

Stochastic Volatility ◽

European Options ◽

PRICING EUROPEAN OPTIONS IN SELECTED STOCHASTIC VOLATILITY MODELS

Metody Ilościowe w Badaniach Ekonomicznych ◽

10.22630/mibe.2020.21.3.14 ◽

2020 ◽

Vol 21 (3) ◽

pp. 145-156

Author(s):

Arkadiusz Orzechowski

Keyword(s):

Stochastic Volatility ◽

Computational Efficiency ◽

Characteristic Functions ◽

European Options ◽

In this paper four methods of calculating characteristic functions and their application to selected stochastic volatility models are considered. The methods applied are based on the assumption that the prices of European calls are evaluated numerically by means of the Gauss-Kronrod quadrature. Such approach is used to investigate computational efficiency of pricing European calls. Particular attention in this matter is paid to the speed of generating theoretical prices of the analyzed contracts.