Volatility Uncertainty Research Articles

Volatility Uncertainty, Time Decay, and Option Bid-Ask Spreads

This paper documents the fact that in option markets, the percentage implied volatility bid-ask spread increases at an increasing rate as the option’s maturity date approaches. We construct an equilibrium model to explain this phenomena. The equilibrium model has risk averse and competitive option market makers quoting bid and ask prices to minimize their inventory risk in an incomplete market with both directional and volatility risk. Two additional testable implications of the model are generated. These are that: (1) an increase in the level of the underlying’s volatility decreases an option’s percentage implied volatility bid-ask spread, and (2) holding the level of the volatility constant, an increase in the volatility’s variance also increases an option’s percentage implied volatility bid-ask spread. These additional implications are empirically tested using index options on the Taiwan stock price index over the time period 2007-2010. The empirical results confirm the model’s validity.

Volatility Uncertainty, Time Decay, and Option Bid-Ask Spreads

This paper documents the fact that in option markets, the percentage implied volatility bid-ask spread increases at an increasing rate as the option's maturity date approaches. We construct an equilibrium model to explain this phenomena. The equilibrium model has risk averse and competitive option market makers quoting bid and asking prices to minimize their inventory risk in an incomplete market with both directional and volatility risk. Two additional testable implications of the model are generated. These are that: (1) an increase in the level of the underlying volatility decreases an option's percentage implied volatility bid-ask spread, and (2) holding the level of the volatility constant, an increase in the volatility's variance also increases an option's percentage implied volatility bid-ask spread. These additional implications are empirically tested using index options on the Taiwan stock price index over the time period 2007-2010. The empirical results confirm the model's validity.

Superreplication under volatility uncertainty for measurable claims

We establish the duality-formula for the superreplication price in a setting of volatility uncertainty which includes the example of random $G$-expectation. In contrast to previous results, the contingent claim is not assumed to be quasi-continuous.

Inverse Optimization: A New Perspective on the Black-Litterman Model.

The Black-Litterman (BL) model is a widely used asset allocation model in the financial industry. In this paper, we provide a new perspective. The key insight is to replace the statistical framework in the original approach with ideas from inverse optimization. This insight allows us to significantly expand the scope and applicability of the BL model. We provide a richer formulation that, unlike the original model, is flexible enough to incorporate investor information on volatility and market dynamics. Equally importantly, our approach allows us to move beyond the traditional mean-variance paradigm of the original model and construct "BL"-type estimators for more general notions of risk such as coherent risk measures. Computationally, we introduce and study two new "BL"-type estimators and their corresponding portfolios: a Mean Variance Inverse Optimization (MV-IO) portfolio and a Robust Mean Variance Inverse Optimization (RMV-IO) portfolio. These two approaches are motivated by ideas from arbitrage pricing theory and volatility uncertainty. Using numerical simulation and historical backtesting, we show that both methods often demonstrate a better risk-reward tradeoff than their BL counterparts and are more robust to incorrect investor views.

Research on Fuzzy-PID Compound Control in Inverter-Driven Energy-Saving Technology for Injection Molding Machine

the modern Inverter-driven technology has been applied in energy-saving control for injection molding machine. Aimming at the complex control of system because of its multiple input multiple output, strongly nonlinearity, some volatility parameters and uncertainty factor , the adaptive fuzzy PID compound control is put forward from the viewpoint of energy-conditioning. Using the above method, the control system have better dynamic characteristics and stability, strong robustness and adaptability. Experiment results show that the method can effectively improve energy-saving technology for the injection molding machine.

Computation of the effects of uncertainty in volatility on option pricing and hedging

We quantify the effect of uncertainty in the volatility parameter σ on the Black–Scholes price of the European and American put. We apply probabilistic uncertainty analysis to the Black–Scholes model and compare the results with those of the Uncertain Volatility model. From historical data, we calibrate a probability distribution for the volatility. We then use Monte Carlo (MC) and a surrogate Polynomial Chaos (PC)/MC method to compute uncertainty bounds. The calibrated probability distribution is not one related to a standard orthogonal basis, so a basis is constructed numerically for the PC approximation. We show how to construct one stably from the probability distribution. We show that both methods give the same results, and quantify the relative speedup of the surrogate method. Finally, we investigate the effect of the parametric uncertainty, and show, for example, that the presence of uncertainty smoothes out the optimal exercise boundary of the American put.

Maximum Maximum of Martingales Given Marginals

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset and statically trade European call options for all possible strikes and finitely-many maturities. We present a general duality result which converts this problem into a min-max calculus of variations problem where the Lagrange multipliers correspond to the static part of the hedge. Following Galichon, Henry-Labord\`ere and Touzi, we apply stochastic control methods to solve it explicitly for Lookback options with a non-decreasing payoff function. The first step of our solution recovers the extended optimal properties of the Az\'ema-Yor solution of the Skorokhod embedding problem obtained by Hobson and Klimmek (under slightly different conditions). The two marginal case corresponds to the work of Brown, Hobson and Rogers.The robust superhedging cost is complemented by (simple) dynamic trading and leads to a class of semi-static trading strategies. The superhedging property then reduces to a functional inequality which we verify independently. The optimality follows from existence of a model which achieves equality which is obtained in Ob\l\'oj and Spoida.

Coherent Price Systems and Uncertainty-Neutral Valuation

We consider fundamental questions of arbitrage pricing arising when the uncertainty model incorporates volatility uncertainty. The resulting ambiguity motivates a new principle of preference-free valuation. By establishing a microeconomic foundation of sublinear price systems, the principle of ambiguity-neutral valuation imposes the novel concept of equivalent symmetric martingale measures. Such measures exist when the asset price with uncertain volatility is driven by Peng's G-Brownian motion.

An Empirical Study of US Corporate Credit Spreads

This paper presents an analysis of the factors that affect US corporate credit spreads. Using data from Bloomberg we investigate the various determinants that cause changes in credit spreads of US corporate firms. As previous research has shown, the variables that should be based on theory determine credit spread changes have limited explanatory power. Our study breaks apart a range of variables into three different sections and analyzes them individual in the groups and together using multiple regressions. We investigate the spot rate, interest rate volatility and slope for the interest rate effects and find strong relationships between spot rate and slope with credit spreads. For the effects of volatility and market uncertainty we find strong relationships between credit spreads and market volatility proxied by VIX and firm volatility proxied by an average of Call and Put implied volatility. TED spreads, SPX and RTY returns show strong relationships between macro-economic variables and credit spreads. Implied default correlations in the Investment Grade and High Yield market also show a strong positive relationship with credit spreads. Our research investigates certain macro-economic variables that have not been researched before and re-establishes previous findings for other variables post-2007 crisis.

Superhedging and Dynamic Risk Measures under Volatility Uncertainty

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a càdlàg nonlinear martingale which is also the value process of a superhedging problem. The superhedging strategy is obtained from a representation similar to the optional decomposition. Furthermore, we prove an optional sampling theorem for the nonlinear martingale and characterize it as the solution of a second order backward SDE. The uniqueness of dynamic extensions of static sublinear expectations is also studied.

Stock Return and Cash Flow Predictability: The Role of Volatility Risk

We examine the joint predictability of return and cash flow within a present value framework, by imposing the implications from a long-run risk model incorporating both time varying volatility and volatility uncertainty. We provide new evidence that the expected return variation and the variance risk premium positively forecast both short-horizon returns and dividend growth rates. Our equilibrium-based “structural” factor GARCH model permits much more accurate inference than the reduced form VAR and univariate regression procedures traditionally employed in the literature. The model also allows for the direct estimation of the underlying “structural” shocks and economic transmission mechanisms, including a new volatility leverage effect.

Volatility (Model) Uncertainty, Derivatives Time Decay and Options Bid-Ask Spread Pattern

Volatility (Model) Uncertainty, Derivatives Time Decay and Options Bid-Ask Spread Pattern

Weak approximation of [formula omitted]-expectations

We introduce a notion of volatility uncertainty in discrete time and define the corresponding analogue of Peng’s G -expectation. In the continuous-time limit, the resulting sublinear expectation converges weakly to the G -expectation. This can be seen as a Donsker-type result for the G -Brownian motion.

A Stochastic Control Approach to No-Arbitrage Bounds Given Marginals, with an Application to Lookback Options

We consider the problem of superhedging under volatility uncertainty for an investor allowed to dynamically trade the underlying asset, and statically trade European call options for all possible strikes with some given maturity. This problem is classically approached by means of the Skorohod Embedding Problem (SEP). Instead, we provide a dual formulation which converts the superhedging problem into a continuous martingale optimal transportation problem. We then show that this formulation allows to recover previously known results about Lookback options. In particular, our methodology induces a new presentation of the Azema-Yor solution of the SEP.

The Salient Implications of Geo-Strategic Policies on Stablizing the Oil Market in the MENA (Middle East and North Africa) Region

Oil as a Geo-strategic economic commodity will continue to play at least for the next 100 years a prominent worldly role in shaping Energy Security strategies and policies. This is why the Geo-strategic implications relating to the degree of stabilizing the oil market has increasingly started to gain more attention, concern, interest and momentum by multivariate parties. Another serious dimension that needs to be analyzed further in the foreseeable future in a cautious and calculating manner is the question of the implications of the ‘Arab Spring Revolutions or Uprising’ as fit to be categorized. Thus, according to the recent EIU Study under the title: “Spring Tide: Will the Arab Risings yield democracy, dictatorship or disorder?” Popular uprisings in the Arab world have produced the most dramatic changes in the region since the end of the colonial era in the middle of the 20th century. Admittedly, the fate of these popular uprisings remains in the balance. Building on this dramatic development, Frank A. Verrastro in his article entitled “Security implications of the changing energy landscape” asserted that there is a new energy landscape characterized by five prominent trends or dynamics as follows: shifting demand patterns; the changing resource base; price volatility and investment uncertainty; new players, alignments, and evolving rules; and the threat of climate change and efforts to impose carbon constraints on a fossil fuel – dependent world”. From a wider perspective, the Geo-strategic dimensions will continue to be determined not just by new players, but increasingly by multivariate areas of specific interests or concerns: security, politics, economics, social, status, and the ever changing technologies whereby innovative projects or solutions are constantly surprising the markets particularly with regards to the question of “renewable non-fossil energy options” such as the American Green Project (best known as Obama’s dream for energy security). It seems perceptive to note, that David L. Goldwyn is realistic in stating that “Energy insecurity is greater today than it has been in nearly 30 years. The global oil market is more fragile, more competitive, and more volatile.”

Variations in emerging-market equity premia: impact of financial architecture

This article examines a topic of much interest, the association of financial architecture and national equity premia for recent eight-year period from 15 emerging-market countries. Modeling simultaneously our estimate of the ex-ante equity premium as a dependent variable and our measure of financial architecture as an instrumental variable, we document that equity premia are larger in countries that have a more bank-oriented financial architecture, as well as greater control of corruption, more foreign access to capital, and higher spending on education. Smaller equity premia are associated with greater political stability, greater measures against self-dealing, higher market volatility and greater uncertainty avoidance. Given the importance of the ex-ante equity premium in long-term investment decisions, the anticipated demographic challenges and financial reform in most countries and recent increases in cross-border investment, there is much interest among bankers, managers and policy-makers in these results, documenting the determinants of cross-national variations in equity premia.

Aggregate Volatility and Threshold CAPM

We propose a volatility-based capital asset pricing model (V-CAPM) in which asset betas change discretely with respect to changes in investors’ expectations regarding near-term aggregate volatility. Using a novel measure to proxy uncertainty about expected changes in aggregate volatility, i.e. monthly range of the VIX index (RVIX), we find that portfolio betas change significantly when uncertainty about aggregate volatility expectations is beyond a certain threshold level. Due to changes in their market betas, small and value stocks are perceived as riskier than their big and growth counterparts in bad times, when uncertainty about aggregate volatility expectations is high. The proposed model yields a positive and significant market risk premium during periods when investors do not expect significant uncertainty in near-term aggregate volatility. Our findings support a volatility-based time-varying risk explanation.

Superhedging and Dynamic Risk Measures Under Volatility Uncertainty

We consider dynamic sublinear expectations (i.e., time-consistent coherent risk measures) whose scenario sets consist of singular measures corresponding to a general form of volatility uncertainty. We derive a cadlag nonlinear martingale which is also the value process of a superhedging problem. The superhedging strategy is obtained from a representation similar to the optional decomposition. Furthermore, we prove an optional sampling theorem for the nonlinear martingale and characterize it as the solution of a second order backward SDE. The uniqueness of dynamic extensions of static sublinear expectations is also studied.

Numerical Methods for Non-Linear Black–Scholes Equations

In recent years non-linear Black–Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black–Scholes concept. In this article we discuss the applicability of implicit numerical schemes for the valuation of contingent claims in these models. It is possible to derive sufficient conditions, which are required to ensure the convergence of the backward differentiation formula (BDF) and Crank–Nicolson scheme (CN) scheme to the unique viscosity solution. These stability conditions can be checked a priori and convergent schemes can be constructed for a large class of non-linear models and payoff profiles. However, if these conditions are not satisfied we show that the schemes are not convergent or produce spurious solutions. We study the practical implications of the derived stability criterions on relevant numerical examples.

DYNAMIC HEDGING OF INFLATION RISK

National and international investors are exposed to risk, stemming from volatile asset prices and inflation uncertainty. However investors can enter futures markets to hedge against these risks. The paper develops a dynamic hedging model, where the evolution of asset price, price level and futures price and hence real wealth is stochastic. For a risk averse investor, optimal dynamic consumption and hedging strategy are derived and discussed.