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Multiscale stochastic volatility for variance swaps with constant elasticity of variance

SOFT COMPUTING 2023年第8期27卷 4879-4890页

作者： Yu, Ji-Su Kim, Jeong-Hoon Yonsei Univ Dept Math Seoul 03722 South Korea

The variance swap is one of volatility derivatives popularly used for the risk management of financial instruments traded in volatile market. An appropriate choice of a volatility model is an important part of the risk management. One of desirable considerations should be given to the fact that the volatility varies on several characteristic time scales. Stochastic volatility models can reflect this feature by introducing multiscale volatility factors. However, pure stochastic volatility models cannot capture the whole volatility surface accurately although the model parameters have been calibrated to replicate the market implied volatility data for near at-the-money strikes. So, we choose a hybrid model of constant elasticity of variance type of local volatility and fast and slow scale stochastic volatility for evaluating the fair strikes of variance swaps. We obtain a closed-form solution formula for the approximate fair strike values of continuously sampled variance swaps and compute the solution. The theoretical formula is validated through Monte Carlo simulation. The predictability of the strike price movements is discussed in terms of the sensitive effects of the stochastic volatility and the elasticity of variance parameters for a given partial information about the underlying asset and volatility.

关键词： Multiscale Stochastic volatility constant elasticity of variance variance swap Monte Carlo simulation

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ROBUST OPTIMAL INVESTMENT STRATEGY FOR A DC PENSION PLAN IN THE MARKET WITH MISPRICING AND constant elasticity of variance

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JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2023年第10期19卷 7540-7564页

作者： Sun, Jingyun Yao, Haixiang LI, Zhongfei Lanzhou Univ Finance & Econ Sch Stat Lanzhou 730020 Peoples R China Ctr Quantitat Anal Gansu Econ Dev Lanzhou 730020 Peoples R China Guangdong Univ Foreign Studies Sch Finance Guangzhou 510006 Peoples R China Southern China Inst Fortune Management Res IFMR Guangzhou 510006 Peoples R China Southern Univ Sci & Technol Dept Finance Shenzhen 518055 Peoples R China Guizhou Univ Finance & Econ Coll Big Data Stat Guiyang 550025 Peoples R China

This paper considers an optimal asset allocation problem for a de -fined contribution pension fund in a continuous time setting, and the manager is concerned about potential model misspecification. We suppose that the fi-nancial market consists of one risk-free asset, one market index fund whose price satisfies the constant elasticity of variance model, and a pair of risky as-sets with mispricing. Under the objective of maximizing the expected utility of the pension fund wealth at the retirement, the closed form expressions of the robust optimal investment strategy and the corresponding value function are obtained by using the stochastic control theory. Finally, some numerical examples are given to compare the difference between the ambiguity averse and the ambiguity neutral strategies, and to investigate the effect of relevant parameters on the strategy. We find that the optimal investment strategy is not a long-short symmetric strategy when the mispricing assets have different mispricing correct capability, and it will lead to significant utility loss for the manager if the model uncertainty risk is ignored.

关键词： Ambiguity-averse investor robust optimal control constant elasticity of variance power utility

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Finite-maturity stock loans under the constant elasticity of variance model

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APPLIED ECONOMICS LETTERS 2019年第4期26卷 316-320页

作者： Yan, Li Qin, Xiaoer Li, Haoqi Chongqing Normal Univ Sch Math Sci Chongqing Peoples R China Yangtze Normal Univ Sch Math & Stat Chongqing Peoples R China

This article expresses the constant elasticity of variance stock loans pricing formula in terms of the noncentral chi-square distribution. By using the numerical solutions of the integral equation for the early exit boundary, we calculated the valuation of the stock loans. Numerical analysis is carried out to establish explicitly the value of such a loan, as well as the loan amount and the fee for providing such a service.

关键词： Stock loans constant elasticity of variance noncentral Chi-Squared distribution integral equation

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Mean-variance asset-liability management under constant elasticity of variance process

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INSURANCE MATHEMATICS & ECONOMICS 2016年第0期70卷 11-18页

作者： Zhang, Miao Chen, Ping Univ Melbourne Ctr Actuarial Studies Dept Econ Melbourne Vic 3010 Australia

This paper investigates a mean variance asset liability management (ALM) problem under the constant elasticity of variance (CEV) process. The company can invest in n + 1 assets: one risk-free bond and n risky stocks. The uncontrollable liability process is modelled by a geometric Brownian motion. The feasibility is studied and potential optimal portfolio is proven to be admissible. We derive the efficient frontier and efficient feedback portfolio in terms of the solutions of two backward stochastic differential equations (BSDEs), which do not admit analytical solutions in general. The closed form solutions are obtained under some special cases. Applying the Monte Carlo simulation, we provide several numerical examples to demonstrate how the efficient frontier is influenced by the relevant parameters. Crown Copyright (C) 2016 Published by Elsevier B.V. All rights reserved.

关键词： Mean-variance Asset-liability management constant elasticity of variance Multiple assets BSDE

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OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A constant elasticity of variance MODEL UNDER variance PRINCIPLE

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Acta Mathematica Scientia 2015年第2期35卷 303-312页

作者：周杰明邓迎春黄娅杨向群 School of Mathematical Sciences Nankai University College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing Ministry of Education of ChinaHunan Normal University College of Business Administration Hunan University

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance （CEV） model. Assume that the insurer＇s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model. The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims. The objective of the insurer is to maximize the expected exponential utility of terminal wealth. This optimization problem is studied in two cases depending on the diffusion term＇s explanation. In all cases, by using techniques of stochastic control theory, closed-form expressions for the value functions and optimal strategies are obtained.

关键词： constant elasticity of variance Hami!ton-Jacobi-Bellman equation jump-diffusion process exponential utility reinsurance

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A recursive pricing formula for a path-dependent option under the constant elasticity of variance diffusion

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STATISTICS & PROBABILITY LETTERS 2014年 94卷 39-47页

作者： Kim, Jeong-Hoon Park, Sang-Hyeon Yonsei Univ Dept Math Seoul 120749 South Korea Univ Louisville Dept Math Louisville KY 40292 USA

In this paper, we consider a path-dependent option in finance under the constant elasticity of variance diffusion. We use a perturbation argument and the probabilistic representation (the Feynman-Kac theorem) of a partial differential equation to obtain a complete asymptotic expansion of the option price in a recursive manner based on the Black-Scholes formula and prove rigorously the existence of the expansion with a convergence error. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Stochastic differential equation constant elasticity of variance Asymptotic expansion Lookback option

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European Option Pricing Under Fuzzy CEV Model

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2023年第2期196卷 415-432页

作者： Wei, Xinyue You, Cuilian Zhang, Yujie Hebei Univ Coll Math & Informat Sci Baoding 071002 Peoples R China Hebei Univ Hebei Key Lab Machine Learning & Computat Intelli Baoding 071002 Peoples R China

In modern financial market, option is a very effective tool to hedge the risks brought by various uncertainties in real society. Therefore, it is of great significance to select an appropriate stock model to price options. To this aim, the paper presents a general stock model with fuzzy volatility for fuzzy financial market, that is, fuzzy constant elasticity of variance model. The advantage is that the fuzzy volatility of underlying stock is related to its price and can explain volatility smile. In addition, we consider the impact of elasticity coefficient on stock price and then limit the elasticity coefficient to a reasonable range. Subsequently, the European call and European put option pricing formulas are given, separately. Finally, some figures and tables are given to illustrate the impact of parameter changes on option prices.

关键词： Credibility measure Fuzzy differential equation Liu process Option pricing constant elasticity of variance

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A martingale method for option pricing under a CEV-based fast-varying fractional stochastic volatility model

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第6期42卷 1-22页

作者： Kim, Hyun-Gyoon Cho, So-Yoon Kim, Jeong-Hoon Ajou Univ Dept Financial Engn Suwon 443749 South Korea Yonsei Univ Dept Math Seoul 03722 South Korea Financial Supervisory Serv Seoul 07321 South Korea

Modeling the volatility smile and skew has been an active area of research in mathematical finance. This article proposes a hybrid stochastic-local volatility model which is built on the local volatility term of the CEV model multiplied by a stochastic volatility term driven by a fast-varying fractional Ornstein-Uhlenbeck process. We find that the Hurst exponent of the implied volatility is less than 1/2 usually but it is larger than 1/2 during an immediate period of recovery from the COVID-19 pandemic. We use a martingale method to obtain option price and implied volatility formulas in the both short- and long-memory volatility cases. As a result, the existing CEV implied volatility can be complemented to reflect implied volatility patterns (skewed smiles) that arise in pricing short time-to-maturity options in equity markets by incorporating convexity into it and controlling the downward slope of it at-the-money. We verify that one additional parameter of the CEV-based fractional stochastic volatility model contributes to a better qualitative agreement with market data than the Black-Scholes-based fractional stochastic volatility model or the CEV-based non-fractional stochastic volatility model.

关键词： Fractional volatility Ornstein-Uhlenbeck process constant elasticity of variance Martingale method Option pricing

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Optimal investment strategy for a family with a random household expenditure under the CEV model

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2022年第17期51卷 5993-6007页

作者： Li, Danping Liu, Xiaotao Liu, Hailong East China Normal Univ Fac Econ & Management Sch Stat Key Lab Adv Theory & Applicat Stat & Data Sci MOE Shanghai 200062 Peoples R China Shanghai Jiao Tong Univ Antai Coll Econ & Management Shanghai Peoples R China

This paper considers an optimal investment strategy to maximize the expected constant absolute risk averse (CARA) utility of the terminal wealth for a family in the presence of stochastic household expenditure under the constant elasticity of variance (CEV) model. Since the corresponding Hamilton-Jacobi-Bellman (HJB) equation is difficult to solve for the high dimensionality and nonlinearity, previous work only gives an approximate numerical solution for some special model parameters under the slow-fluctuating regime assumption. In this paper, by directly conjecturing the functional form of the value function, we transform the HJB equation into two one-dimensional parabolic partial differential equations (pdes) and further find their explicit solutions via the Feynman-Kac formula. We prove that the exact and explicit solution for the value function as well as the optimal investment strategy can be expressed as integral of confluent hyper-geometric function. Finally, numerical examples are provided to illustrate the effects of parameters on the optimal strategies.

关键词： Optimal investment strategy stochastic household expenditure constant elasticity of variance Feynman-Kac formula

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THE PRICING OF EUROPEAN OPTIONS UNDER THE constant elasticity of variance WITH STOCHASTIC VOLATILITY

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FLUCTUATION AND NOISE LETTERS 2013年第1期12卷 1-1页

作者： Bock, Bounghun Choi, Sun-Yong Kim, Jeong-Hoon Yonsei Univ Dept Math Seoul 120749 South Korea

This paper considers a hybrid risky asset price model given by a constant elasticity of variance multiplied by a stochastic volatility factor. A multiscale analysis leads to an asymptotic pricing formula for both European vanilla option and a Barrier option near the zero elasticity of variance. The accuracy of the approximation is provided in a rigorous manner. A numerical experiment for implied volatilities shows that the hybrid model improves some of the well-known models in view of fitting the data for different maturities.

关键词： Multiscale option pricing stochastic volatility constant elasticity of variance

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