scholarly journals Dynamic Optimal Mean-Variance Investment with Mispricing in the Family of 4/2 Stochastic Volatility Models

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2293
Author(s):  
Yumo Zhang
Keyword(s):  
Stochastic Volatility ◽  
Time Inconsistency ◽  
Closed Form Expression ◽  
Optimal Time ◽  
Model Parameters ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
The Family ◽  
Mean Variance ◽  
Variance Criterion

This paper considers an optimal investment problem with mispricing in the family of 4/2 stochastic volatility models under mean–variance criterion. The financial market consists of a risk-free asset, a market index and a pair of mispriced stocks. By applying the linear–quadratic stochastic control theory and solving the corresponding Hamilton–Jacobi–Bellman equation, explicit expressions for the statically optimal (pre-commitment) strategy and the corresponding optimal value function are derived. Moreover, a necessary verification theorem was provided based on an assumption of the model parameters with the investment horizon. Due to the time-inconsistency under mean–variance criterion, we give a dynamic formulation of the problem and obtain the closed-form expression of the dynamically optimal (time-consistent) strategy. This strategy is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Results on the special case without mispricing are included. Finally, some numerical examples are given to illustrate the effects of model parameters on the efficient frontier and the difference between static and dynamic optimality.

scholarly journals Dynamic Optimal Mean-Variance Portfolio Selection with a 3/2 Stochastic Volatility

Risks ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 61
Author(s):  
Yumo Zhang
Keyword(s):  
Stochastic Volatility ◽  
Portfolio Selection ◽  
Stock Price ◽  
Backward Stochastic Differential Equation ◽  
Time Inconsistency ◽  
Optimal Time ◽  
Model Parameters ◽  
Mean Variance Portfolio ◽  
The Impact ◽  
Mean Variance

This paper considers a mean-variance portfolio selection problem when the stock price has a 3/2 stochastic volatility in a complete market. Specifically, we assume that the stock price and the volatility are perfectly negative correlated. By applying a backward stochastic differential equation (BSDE) approach, closed-form expressions for the statically optimal (time-inconsistent) strategy and the value function are derived. Due to time-inconsistency of mean variance criterion, a dynamic formulation of the problem is presented. We obtain the dynamically optimal (time-consistent) strategy explicitly, which is shown to keep the wealth process strictly below the target (expected terminal wealth) before the terminal time. Finally, we provide numerical studies to show the impact of main model parameters on the efficient frontier and illustrate the differences between the two optimal wealth processes.

scholarly journals INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS

2017 ◽  
Vol 20 (08) ◽  
pp. 1750055 ◽  
Author(s):  
ZHENYU CUI ◽  
J. LARS KIRKBY ◽  
GUANGHUA LIAN ◽  
DUY NGUYEN
Keyword(s):  
Stochastic Volatility ◽  
Probabilistic Method ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Model Parameters ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Probability Densities ◽  
Special Case

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767–785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, [Formula: see text], and a special case of the [Formula: see text]-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The [Formula: see text]-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472–1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the [Formula: see text] model and a special case of the [Formula: see text]-Hypergeometric model.

METHOD OF MOMENTS ESTIMATION FOR LÉVY-DRIVEN ORNSTEIN–UHLENBECK STOCHASTIC VOLATILITY MODELS

2020 ◽  
pp. 1-30
Author(s):  
Xiangyu Yang ◽  
Yanfeng Wu ◽  
Zeyu Zheng ◽  
Jian-Qiang Hu
Keyword(s):  
Stochastic Volatility ◽  
Method Of Moments ◽  
Model Misspecification ◽  
Analytical Framework ◽  
Model Parameters ◽  
Computationally Efficient ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Form Representation ◽  
Method Of Moments Estimation

This paper studies the parameter estimation for Ornstein–Uhlenbeck stochastic volatility models driven by Lévy processes. We propose computationally efficient estimators based on the method of moments that are robust to model misspecification. We develop an analytical framework that enables closed-form representation of model parameters in terms of the moments and autocorrelations of observed underlying processes. Under moderate assumptions, which are typically much weaker than those for likelihood methods, we prove large-sample behaviors for our proposed estimators, including strong consistency and asymptotic normality. Our estimators obtain the canonical square-root convergence rate and are shown through numerical experiments to outperform likelihood-based methods.

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

2020 ◽  
Vol 07 (04) ◽  
pp. 2050042
Author(s):  
T. Pellegrino
Keyword(s):  
Stochastic Volatility ◽  
Calibration Procedure ◽  
Second Order ◽  
Model Parameters ◽  
Option Prices ◽  
European Options ◽  
Stochastic Volatility Models ◽  
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.

scholarly journals Mean-Variance Hedging for Stochastic Volatility Models

2000 ◽  
Vol 10 (2) ◽  
pp. 109-123 ◽  
Author(s):  
Francesca Biagini ◽  
Paolo Guasoni ◽  
Maurizio Pratelli
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Mean Variance
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