scholarly journals PORTFOLIO INSURANCE UNDER ROUGH VOLATILITY AND VOLTERRA PROCESSES

2021 ◽  
Author(s):  
JEAN-LOUP DUPRET ◽  
DONATIEN HAINAUT
Keyword(s):  
Characteristic Function ◽  
Estimation Procedure ◽  
Heston Model ◽  
Portfolio Insurance ◽  
Portfolio Strategies ◽  
Simulation Techniques ◽  
Simulation Based ◽  
Rough Volatility ◽  
Past Data ◽  
Constant Proportion Portfolio Insurance

Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model and the more recent rough Heston model. The aim of this work is hence to revisit and generalize the constant proportion portfolio insurance (CPPI) under affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily to this class of processes. We instead propose an approach based on the characteristic function of the log-cushion which appears to be more consistent, stable and particularly efficient in the case of saffine Volterra processes compared with the existing simulation techniques. Using such approach, we describe in this paper several properties of CPPI which naturally result from the form of the log-cushion’s characteristic function under affine Volterra processes. This allows to consider more realistic dynamics for the underlying risky asset in the context of CPPI and hence build portfolio strategies that are more consistent with financial data. In particular, we address the case of the rough Heston model, known to be extremely consistent with past data of volatility. By providing a new estimation procedure for its parameters based on the PMCMC algorithm, we manage to study more accurately the true properties of such CPPI strategy and to better handle the risk associated with it.

scholarly journals Fractional Riccati Equation and Its Applications to Rough Heston Model

2020 ◽  
Author(s):  
Siow W. Jeng ◽  
Adem Kilicman
Keyword(s):  
Numerical Methods ◽  
Characteristic Function ◽  
Riccati Equation ◽  
Financial Market ◽  
Heston Model ◽  
Short Introduction ◽  
Volatility Models ◽  
Rough Volatility ◽  
Pricing Theory ◽  
Option Pricing Theory

Rough volatility models are popularized by \cite{gatheral2018volatility}, where they have shown that the empirical volatility in the financial market is extremely consistent with rough volatility. Fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form as of now and therefore, we must rely on numerical methods to obtain a solution. In this paper, we give a short introduction to option pricing theory and an overview of the current advancements on the rough Heston model.

scholarly journals Fractional Riccati Equation and Its Applications to Rough Heston Model Using Numerical Methods

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 959 ◽  
Author(s):  
Siow W. Jeng ◽  
Adem Kilicman
Keyword(s):  
Numerical Methods ◽  
Characteristic Function ◽  
Riccati Equation ◽  
Financial Market ◽  
Approximation Method ◽  
Padé Approximation ◽  
Heston Model ◽  
Pade Approximation ◽  
Multipoint Padé Approximation ◽  
Rough Volatility

Rough volatility models are recently popularized by the need of a consistent model for the observed empirical volatility in the financial market. In this case, it has been shown that the empirical volatility in the financial market is extremely consistent with the rough volatility. Currently, fractional Riccati equation as a part of computation for the characteristic function of rough Heston model is not known in explicit form and therefore, we must rely on numerical methods to obtain a solution. In this paper, we will be giving a short introduction to option pricing theory (Black–Scholes model, classical Heston model and its characteristic function), an overview of the current advancements on the rough Heston model and numerical methods (fractional Adams–Bashforth–Moulton method and multipoint Padé approximation method) for solving the fractional Riccati equation. In addition, we will investigate on the performance of multipoint Padé approximation method for the small u values in D α h ( u − i / 2 , x ) as it plays a huge role in the computation for the option prices. We further confirm that the solution generated by multipoint Padé (3,3) method for the fractional Riccati equation is incredibly consistent with the solution generated by fractional Adams–Bashforth–Moulton method.

scholarly journals VARIANCE AND VOLATILITY SWAPS UNDER A TWO-FACTOR STOCHASTIC VOLATILITY MODEL WITH REGIME SWITCHING

2019 ◽  
Vol 22 (04) ◽  
pp. 1950009
Author(s):  
XIN-JIANG HE ◽  
SONG-PING ZHU
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Significant Difference ◽  
Cir Process

In this paper, the pricing problem of variance and volatility swaps is discussed under a two-factor stochastic volatility model. This model can be treated as a two-factor Heston model with one factor following the CIR process and another characterized by a Markov chain, with the motivation originating from the popularity of the Heston model and the strong evidence of the existence of regime switching in real markets. Based on the derived forward characteristic function of the underlying price, analytical pricing formulae for variance and volatility swaps are presented, and numerical experiments are also conducted to compare swap prices calculated through our formulae and those obtained under the Heston model to show whether the introduction of the regime switching factor would lead to any significant difference.

Research on Simulation Techniques of Space Information Confrontation Based on Agent and HLA

2011 ◽  
Vol 121-126 ◽  
pp. 4112-4116
Author(s):  
Wei Kui Wang ◽  
Xin Hui Zhang ◽  
Shi Liang Yang ◽  
Yun Liu
Keyword(s):  
Development Trend ◽  
Effect Evaluation ◽  
Simulation Technology ◽  
Modeling Framework ◽  
Agent Modeling ◽  
Simulation Techniques ◽  
Simulation Based ◽  
Key Technologies ◽  
The Development Trend ◽  
Simulation Systems

This paper analyzes the shortcomings of the present applications of the space information confrontation simulation technology in the light of the development trend of the technology and points out establishing simulation platforms based on the HLA and Agent technologies is an effective method to carry out the demonstration and effect evaluation of space information confrontation systems. this paper also proposes an information confrontation Agent modeling framework and an architecture of space information confrontation simulation systems and describes several key technologies needing to be noted in the simulation based on the Agent and HLA technologies.

Categorized Application Technology of Numerical Simulation on Electronic Equipment Thermal Design

2009 ◽  
Author(s):  
Yasuyuki Yokono ◽  
Katsumi Hisano ◽  
Kenji Hirohata
Keyword(s):  
Numerical Simulation ◽  
Product Development ◽  
Statistical Approach ◽  
Thermal Design ◽  
Electronic Equipment ◽  
Product Development Process ◽  
Design Stage ◽  
Application Technology ◽  
Simulation Techniques ◽  
Simulation Based

In order to utilize a numerical simulation on a product development for electronic equipment, not only the simulation techniques themselves, but the application technologies of the simulation in the product design, were examined. The design process of electronic equipment was categorized into four stages, which were a concept, a function, a layout and a parameter design. Each design stage consists of a specifying that a human decide the specification for the next stage and a verification whether the specification satisfy the previous stage requirements. The specifying and the verification are conducted over and over again. Numerical simulation is corresponded to the verification and is used to accelerate this iteration instead of experiments. The examples of numerical simulation corresponding to these four verifications were shown in the present paper. There are few examples in last two type of simulation. The progress of the numerical technology for function and concept verification is expected. The product development process requires not only numerical simulation based on physics but also statistical approach.

Option Based Portfolio Insurance Revisited

2007 ◽  
Vol 2 (2) ◽  
pp. 195-215
Author(s):  
R. Bouchaib
Keyword(s):  
Transaction Costs ◽  
Asset Allocation ◽  
Investment Strategy ◽  
Theoretical Framework ◽  
Market Impact ◽  
Dynamic Allocation ◽  
Portfolio Insurance ◽  
Dynamic Investment ◽  
Constant Proportion Portfolio Insurance

ABSTRACTIn recent years, Constant Proportion Portfolio Insurance (CPPI) has been the most widely recognised form of portfolio insurance among market practitioners, despite a lack of theoretical framework to support it. This paper presents a revised formulation of Option Based Portfolio Insurance (OBPI) and shows, through a case study, how it can be used as a structured product and applied in practice as a dynamic investment strategy for insurance and pensions funds such as with-profits funds. CPPI and the Revised Option Based Portfolio Insurance (ROBPI) technique adopted in this paper are similar in the sense that they rely on dynamic allocation between risky and risk-free assets to provide downside protection. Comparison between the two methods shows that ROPBI is more efficient and forward looking, giving more information about downside risk and producing less volatile asset allocation, which reduces transaction costs and any market impact.

scholarly journals Simulation-Based Computation of the Workload Correlation Function in a Lévy-Driven Queue

2011 ◽  
Vol 48 (1) ◽  
pp. 114-130 ◽  
Author(s):  
Peter W. Glynn ◽  
Michel Mandjes
Keyword(s):  
Correlation Function ◽  
Variance Reduction ◽  
Single Server ◽  
Monotone Functions ◽  
Single Server Queue ◽  
Completely Monotone Functions ◽  
Simulation Techniques ◽  
Completely Monotone ◽  
Simulation Based ◽  
Server Queue

In this paper we consider a single-server queue with Lévy input, and, in particular, its workload process (Qt)t≥0, focusing on its correlation structure. With the correlation function defined asr(t):= cov(Q0,Qt) / varQ0(assuming that the workload process is in stationarity at time 0), we first study its transform ∫0∞r(t)e-ϑtdt, both for when the Lévy process has positive jumps and when it has negative jumps. These expressions allow us to prove thatr(·) is positive, decreasing, and convex, relying on the machinery of completely monotone functions. For the light-tailed case, we estimate the behavior ofr(t) for larget. We then focus on techniques to estimater(t) by simulation. Naive simulation techniques require roughly (r(t))-2runs to obtain an estimate of a given precision, but we develop a coupling technique that leads to substantial variance reduction (the required number of runs being roughly (r(t))-1). If this is augmented with importance sampling, it even leads to a logarithmically efficient algorithm.

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