A Collective Investment Problem in a Stochastic Volatility Environment: The Impact of Sharing Rules

2019 ◽  
Author(s):  
An Chen ◽  
Thai Nguyen ◽  
Manuel Rach
Keyword(s):  
Stochastic Volatility ◽  
Investment Problem ◽  
Sharing Rules ◽  
The Impact

scholarly journals A collective investment problem in a stochastic volatility environment: The impact of sharing rules

2021 ◽  
Author(s):  
An Chen ◽  
Thai Nguyen ◽  
Manuel Rach
Keyword(s):  
Stochastic Volatility ◽  
Well Being ◽  
Pension Funds ◽  
Individual Investors ◽  
Sharing Rule ◽  
Fund Managers ◽  
Investment Problem ◽  
Sharing Rules ◽  
State Dependent ◽  
The Impact

AbstractIt is typical in collectively administered pension funds that employees delegate fund managers to invest their contributions. In addition, many pension funds still need to sustain guarantees (prescribed by law) in spite of the current low interest environment. In this paper, we consider an optimal collective investment problem for a pool of investors who (implicitly) demand minimum guarantees by deriving utility from the wealth exceeding their guarantees in two financial market settings, one with a stochastic and one with a constant volatility. We find that individual investors’ well-being will not be worsened through the collective investment in both financial markets, as individual optimal solutions are attainable if a financially fair state-dependent sharing rule is applied. When more prevailing sharing rules like linear rules are applied, this holds no longer. Furthermore, the degree of sub-optimality imposed by linear sharing rules is more pronounced in the stochastic volatility market than in the constant volatility market.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

scholarly journals Time-Consistent Investment and Reinsurance Strategies for Mean-Variance Insurers under Stochastic Interest Rate and Stochastic Volatility

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2183
Author(s):  
Jiaqi Zhu ◽  
Shenghong Li
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Financial Market ◽  
Equilibrium Strategy ◽  
Stochastic Interest Rate ◽  
Programming Approach ◽  
Model Parameters ◽  
Stochastic Interest ◽  
The Impact ◽  
Mean Variance

This paper studies the time-consistent optimal investment and reinsurance problem for mean-variance insurers when considering both stochastic interest rate and stochastic volatility in the financial market. The insurers are allowed to transfer insurance risk by proportional reinsurance or acquiring new business, and the jump-diffusion process models the surplus process. The financial market consists of a risk-free asset, a bond, and a stock modelled by Heston’s stochastic volatility model. Interest rate in the market is modelled by the Vasicek model. By using extended dynamic programming approach, we explicitly derive equilibrium reinsurance-investment strategies and value functions. In addition, we provide and prove a verification theorem and then prove the solution we get satisfies it. Moreover, sensitive analysis is given to show the impact of several model parameters on equilibrium strategy and the efficient frontier.

VALUATION OF VULNERABLE OPTIONS UNDER THE DOUBLE EXPONENTIAL JUMP MODEL WITH STOCHASTIC VOLATILITY

2018 ◽  
Vol 33 (1) ◽  
pp. 81-104 ◽  
Author(s):  
Xingyu Han
Keyword(s):  
Stochastic Volatility ◽  
Numerical Solutions ◽  
Characteristic Functions ◽  
Transform Method ◽  
Put Options ◽  
Fourier Cosine ◽  
Jump Model ◽  
Double Exponential ◽  
Vulnerable Options ◽  
The Impact

In this paper, we extend the framework of Klein [15] [Journal of Banking & Finance 20: 1211–1229] to a general model under the double exponential jump model with stochastic volatility on the underlying asset and the assets of the counterparty. Firstly, we derive the closed-form characteristic functions for this dynamic. Using the Fourier-cosine expansion technique, we get numerical solutions for vulnerable European put options based on the characteristic functions. The inverse fast Fourier transform method provides a fast numerical algorithm for the twice-exercisable vulnerable Bermuda put options. By virtue of the modified Geske and Johnson method, we obtain an approximate pricing formula of vulnerable American put options. Numerical simulations are made for investigating the impact of stochastic volatility on vulnerable options.

scholarly journals The Impact of Stock Prices on Consumption and Interest Rate in Turkey: Evidence from a Time Varying Vector Autoregressive Model

2014 ◽  
Author(s):  
Evrim Tören
Keyword(s):  
Interest Rate ◽  
Stochastic Volatility ◽  
Open Economy ◽  
Stock Prices ◽  
Autoregressive Model ◽  
Time Varying ◽  
Vector Autoregressive Model ◽  
Macroeconomic Dynamics ◽  
Vector Autoregressive ◽  
The Impact

This paper aims to examine the spillovers from stock prices onto consumption and interest rate for Turkey by using a time-varying vector autoregressive model with stochastic volatility. A three-variable time-varying vector autoregressive model is estimated to capture the time-varying nature of the macroeconomic dynamics in the Turkish economy between real consumption, nominal interest rate and real stock prices. In order to obtain the macroeconomic dynamics in a small open economy, the data covers the period 1987:Q1 until 2013:Q3 in Turkey. The sample data is gathered from the official website of Central Bank of the Republic of Turkey. Overall, this study provides the evidence of significant time-varying spillovers on consumption and interest rate coming from the stock market during financial crises and implications of monetary policy in Turkey. In addition, a time-varying vector autoregressive model with stochastic volatility offers remarkable results about the impact of price shock on consumption levels in Turkey.

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

2021 ◽  
pp. 1-20
Author(s):  
Y. HAN ◽  
Z. LI ◽  
C. LIU
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

Abstract We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT PROBLEM WITH CONSTRAINTS ON RISK CONTROL IN A GENERAL JUMP-DIFFUSION FINANCIAL MARKET

2016 ◽  
Vol 57 (3) ◽  
pp. 352-368
Author(s):  
HUIMING ZHU ◽  
YA HUANG ◽  
JIEMING ZHOU ◽  
XIANGQUN YANG ◽  
CHAO DENG
Keyword(s):  
Diffusion Process ◽  
Closed Form ◽  
Financial Market ◽  
Optimal Strategies ◽  
Jump Diffusion ◽  
Model Parameters ◽  
Proportional Reinsurance ◽  
Investment Problem ◽  
Jump Diffusion Process ◽  
The Impact

We study the optimal proportional reinsurance and investment problem in a general jump-diffusion financial market. Assuming that the insurer’s surplus process follows a jump-diffusion process, the insurer can purchase proportional reinsurance from the reinsurer and invest in a risk-free asset and a risky asset, whose price is modelled by a general jump-diffusion process. The insurance company wishes to maximize the expected exponential utility of the terminal wealth. By using techniques of stochastic control theory, closed-form expressions for the value function and optimal strategy are obtained. A Monte Carlo simulation is conducted to illustrate that the closed-form expressions we derived are indeed the optimal strategies, and some numerical examples are presented to analyse the impact of model parameters on the optimal strategies.

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 Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Ying Chang ◽  
Yiming Wang ◽  
Sumei Zhang
Keyword(s):  
Brownian Motion ◽  
Stochastic Volatility ◽  
Stock Price ◽  
Heston Model ◽  
Characteristic Functions ◽  
Option Prices ◽  
Approximation Factor ◽  
Numerical Result ◽  
The Impact

We establish double Heston model with approximative fractional stochastic volatility in this article. Since approximative fractional Brownian motion is a better choice compared with Brownian motion in financial studies, we introduce it to double Heston model by modeling the dynamics of the stock price and one factor of the variance with approximative fractional process and it is our contribution to the article. We use the technique of Radon–Nikodym derivative to obtain the semianalytical pricing formula for the call options and derive the characteristic functions. We do the calibration to estimate the parameters. The calibration demonstrates that the model provides the best performance among the three models. The numerical result demonstrates that the model has better performance than the double Heston model in fitting with the market implied volatilities for different maturities. The model has a better fit to the market implied volatilities for long-term options than for short-term options. We also examine the impact of the positive approximation factor and the long-memory parameter on the call option prices.

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