Option Positions Research Articles

Martingale optimal transport and robust hedging in continuous time

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge–Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

Attention on Options

This paper investigates the impact of retail investor attention, measured by Google search frequency, on option trading and option pricing as well as stock return volatility. We document a significant positive relation between Google search volume and future option trading activity of retail investors. Moreover, retail investors tend to take more bullish option positions following increased attention. Although option implied volatilities initially rise, the long run impact of Google search volume on option prices is negative, albeit small in magnitude. In contrast, we find a significantly positive and persistent relation between Google search volume and future realized stock return volatility. An option trading strategy of buying high attention delta-hedged straddles and selling low attention delta-hedged straddles generates an annual return of 6.44%, which is uncorrelated with standard risk factors. Our findings suggest that retail investor attention not only affects trading activity but also is a source of noise trader risk.

The Impact of Volatility and Net Buying Pressure on the Trading Demand of Speculators and Hedgers

We investigate the ways in which the net buying pressure of options and the volatility of the underlying asset affect the trading demand for speculation and hedging in TAIEX options. We place particular focus on an examination of whether any changes were discernible in the volatility effects after the 2007 subprime mortgage crisis, and find that volatility seems to have had little significant impact on the trading demand of either speculators or hedgers; however, the net buying pressure of OTM calls and ATM puts are found to provide significant explanatory power on the trading demand of both types of investors. Furthermore, a significant change is found after the subprime crisis in the trading activities of speculators, who are generally found to have become more risk-averse, resulting in a reduction in their option positions when there is any sharp increase in risk in the underlying asset.

Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?

AbstractWe investigate the pricing of risk-neutral skewness in the stock options market by creating skewness assets comprised of two option positions (one long and one short) and a position in the underlying stock. The assets are created such that exposure to changes in the underlying stock price (delta), and exposure to changes in implied volatility (vega) are removed, isolating the effect of skewness. We find a strong negative relation between risk-neutral skewness and the skewness asset returns, consistent with a positive skewness preference. The returns are not explained by well-known market, size, book-to-market, momentum, short-term reversal, volatility, or option market factors.

A Generalization of Gray and Whaley's Option

Options markets display interesting features. Most options are executed when they are near the money. However, the underlying asset price varies significantly during the life-time option. It is therefore difficult to predict the future option position. In order to make options' markets more liquid, the paper proposes to replace all options into At-the-Money (ATM) ones by resetting the strike price X to the asset price at pre-specified time point t, before maturity time T. Strike price is locked in at the then underlying asset price S_{t} regardless whether it is above or below S_{t}.The reset condition is in exchange for deposit in the Clearing House. The idea is to provide a general valuation of reset option of Gray and Whaley (1999) in which reset condition does not depend on the relation between the strike price and the underlying asset price. The contribution of this paper is double. First, it shows that our general model option, under specific conditions, can be generalized to the most common ones like for example Black-Scholes-Merton, forward-start and strike reset pricing formulae etc... Second, in line with Haug and Haug (2001), we use the CRR binominal approach (Cox et al., 1979) and an estimation program of the cumulative bivariate normal distribution to provide closed-form solution for the pricing of the generalized European reset option.

Sensitivity of Option Contracts

There are plenty of reasons why investors use option contracts in their portfolios. The main reason for using such contracts or their strategies is to hedge against risk concerned with the uncertainty of underlying asset price movements. The identification of risk factors and their management is essential for all kinds of business. However, the process of risk assessment and management is especially important in the case of using complex activities such as option contracts. Options have characteristics that may make them less attractive for some investors. Options can be risky but provide opportunities to profit for those who properly use this flexible instrument. Before the investor can explore the application of strategies for various options, first, he must be able to analyze and understand the degree of risk they impose. The purpose of the article is to analyze the basic measures of option risk, sensitivity factors and their meaning to the investor. When understanding, calculating and using such measures as delta, gamma, theta and vega, the investor can manage the riskiness of the option and the whole portfolio. Each Greek letter measures a different dimension of risk in an option position.

Robustness and Informativeness of Systemic Risk Measures

Recent literature has proposed new methods for measuring the systemic risk of financial institutions based on observed stock returns. In this paper we examine the reliability and robustness of such risk measures, focusing on CoVaR, marginal expected shortfall, and option-based tail risk estimates. We show that CoVaR exhibits undesired characteristics in the way it responds to idiosyncratic risk. In the presence of contagion, the risk measures provide conflicting signals on the systemic risk of infectious and infected banks. Finally, we explore how limited data availability typical of practical applications may limit the measures’ performance. We generate systemic tail risk through positions in standard index options and describe situations in which systemic risk is misestimated by the three measures. The observations raise doubts about the informativeness of the proposed measures. In particular, a direct application to regulatory capital surcharges for systemic risk could create wrong incentives for banks.

A margin requirement based return calculation for portfolios of short option positions

PurposeShort option positions carry significant risk of losses well in excess of 100 per cent of the initial option price. Margin requirements associated with such positions are therefore considerable. The purpose of this paper is to develop a methodology for calculating margin requirement‐based option portfolio returns that realistically represent the returns realized by investors, and to demonstrate the effects of this methodology on analyses of option returns.Design/methodology/approachA methodology is developed for calculating margin requirement‐based short option portfolio returns.FindingsAccounting for margin requirements reduces the returns of simple short option strategies by up to 92 per cent compared to the price return. In long/short portfolio analyses, use of margin requirement returns necessitates additional methodological adjustments to ensure that unwanted volatility risk is properly hedged.Originality/valueThe result is a portfolio return that more accurately represents the return realized by investors, and increased power to detect cross‐sectional patterns in option returns.

Design of Cylinder Positioning System Based on Proportional Valve

Proportional valve-cylinder buffering positioning system was designed based on PID control method, which has simple structure, strong anti-pollution ability, convenient use and maintenance, and high precision. The system is endowed with high engineering value owing to its ability to achieve buffering positioning of cylinder in optional position of the whole cylinder stroke with positioning precision within ±0.2mm enough to meet the positioning requirement of manipulator.

International Assets Allocation with Risk Management via Multi-Stage Stochastic Programming

In this paper, we develop a multi-stage stochastic programming model for dynamic international portfolio risk management with options in an integrated view. Upon scenario trees, the model can automatically compute the optimal hedging strategies, which provides rolling and dynamic decisions for how much option positions should be established and how much should be liquidated, while simultaneously allocating the corresponding underlying assets. Extensive numerical analyses strongly verify the effectiveness of the model, especially in market downturns, and support the computational feasibility and performance of the model.

Investment, firm value, and risk for a system operator balancing energy grids

With the liberalization of energy markets integrated energy companies have separated into entities that specialize in production and/or transmission of energy. Transmission of energy requires balancing the grid to guarantee system security, which is performed by the (independent) system operator (SO). When the SO faces stochastic demand, grid balancing has sizeable consequences on current and future profits, and hence, on firm value and firm risk. We explore these value and risk consequences with and without an investment option to expand transmission capacity. We show that firm value consists of the value of the transmission capacity in place plus the value of a short put and a short call option that are the result of the SO's balancing actions. Firm risk without investment option is non-linear and determined by the short option positions. It is decreasing with increasing energy demand. The existence of an option to expand transmission capacity increases firm value and firm risk.

Worst-Case Value at Risk of Nonlinear Portfolios

Portfolio optimization problems involving value at risk (VaR) are often computationally intractable and require complete information about the return distribution of the portfolio constituents, which is rarely available in practice. These difficulties are compounded when the portfolio contains derivatives. We develop two tractable conservative approximations for the VaR of a derivative portfolio by evaluating the worst-case VaR over all return distributions of the derivative underliers with given first- and second-order moments. The derivative returns are modelled as convex piecewise linear or—by using a delta–gamma approximation—as (possibly nonconvex) quadratic functions of the returns of the derivative underliers. These models lead to new worst-case polyhedral VaR (WPVaR) and worst-case quadratic VaR (WQVaR) approximations, respectively. WPVaR serves as a VaR approximation for portfolios containing long positions in European options expiring at the end of the investment horizon, whereas WQVaR is suitable for portfolios containing long and/or short positions in European and/or exotic options expiring beyond the investment horizon. We prove that—unlike VaR that may discourage diversification—WPVaR and WQVaR are in fact coherent risk measures. We also reveal connections to robust portfolio optimization. This paper was accepted by Dimitris Bertsimas, optimization.

Management Insights

Management Insights

Martingale Optimal Transport and Robust Hedging in Continuous Time

The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fi xed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that has the given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

Robust Hedging with Proportional Transaction Costs

Duality for robust hedging with proportional transaction costs of path dependent European options is obtained in a discrete time financial market with one risky asset. Investor’s portfolio consists of a dynamically traded stock and a static position in vanilla options which can be exercised at maturity. Only stock trading is subject to proportional transaction costs. The main theorem is duality between hedging and a Monge-Kantorovich type optimization problem. In this dual transport problem the optimization is over all the probability measures which satisfy an approximate martingale condition related to consistent price systems in addition to the usual marginal constraints.

Robustness and Informativeness of Systemic Risk Measures

Recent literature has proposed new methods for measuring the systemic risk of financial institutions based on observed stock returns. In this paper we examine the reliability and robustness of such risk measures, focusing on CoVaR, marginal expected shortfall, and option-based tail risk estimates. We show that CoVaR exhibits undesired characteristics in the way it responds to idiosyncratic risk. In the presence of contagion, the risk measures provide conflicting signals on the systemic risk of infectious and infected banks. Finally, we explore how limited data availability typical of practical applications may limit the measures' performance. We generate systemic tail risk through positions in standard index options and describe situations in which systemic risk is misestimated by the three measures. The observations raise doubts about the informativeness of the proposed measures. In particular, a direct application to regulatory capital surcharges for systemic risk could create wrong incentives for banks.

On Hedging American Options Under Model Uncertainty

We consider as given a discrete time financial market with a risky asset and options written on that asset and determine both the sub- and super-hedging prices of an American option in the model independent framework of ArXiv:1305.6008. We obtain the duality of results for the sub- and super-hedging prices. For the sub-hedging prices we discuss whether the sup and inf in the dual representation can be exchanged (a counter example shows that this is not true in general). For the super-hedging prices we discuss several alternative definitions and argue why our choice is more reasonable. Then assuming that the path space is compact, we construct a discretization of the path space and demonstrate the convergence of the hedging prices at the optimal rate. The latter result would be useful for numerical computation of the hedging prices. Our results generalize those of ArXiv:1304.3574 to the case when static positions in (finitely many) European options can be used in the hedging portfolio.

What happens with Eastern and Central Europe in the Globalising World Today? / Ce se ȋntâmplă cu Europa de Est şi Centrală ȋn contextul globalizării actuale?

Abstract The author of this paper searches for insights concerning Eastern Europe as a region in the making in a global context. New systems of governance and new economic set-ups, which challenge current powers, are emerging uninterruptedly coined by various global dynamics. The evolving divergences, choices and dynamics of governments on a global scale generate new players, coalitions and ways of engagement into multifaceted actions, which are in urgent need of study. The discrepancies on the line lead to geopolitical struggle, security threats, and political turmoil and water and food shortages. The world is going through a multiple crisis of finance, investment/growth and ecosystem. These channels seem to be unrelated, but are interconnected with each other in various ways. They reflect large structural discrepancies between different regional unions and local alliances; between actors on local and national levels; between the developed world and nations that are less developed; between finance and the real economy; and between the earth's ecological units, on one side and economic systems and political decisions on the other side. Author argues that Eastern and Central Europe's situation in the globalising world today is somehow still an open end option position as it is not clear which eastern alliance will lead within the EU as alternative to a powerful Franco-German coalition.

Active Hedging Greeks of an Options Portfolio integrating churning and minimization of cost of hedging using Quadratic & Linear Programing

This paper proposes a methodology for active hedgingGreeks of an option portfolio integrating churning and minimization of cost of hedging. In the first section, hedging strategy is implemented by taking positions in other available options, while simultaneously minimizing the net premium paid for the hedging and then churning the portfolio to take into account the changed value of Greeks in the new portfolio. In the second section, the paper extends the model to incorporate the transaction cost while hedging the portfolio and churning it in Indian Scenario. Both constant and nonlinear shape of transaction cost has been considered as per the Security Transaction Tax and Brokerage charges in India. A quadratic programming has been presented which has been approximated by a linear programming solution. The prototype software has been developed in MS Excel using Visual Basic.

HEDGING GREEKS FOR A PORTFOLIO OF OPTIONS USING LINEAR AND QUADRATIC PROGRAMMING

The aim of this paper is to develop a hedging methodology for making a portfolio of options delta, vega and gamma neutral by taking positions in other available options, and simultaneously minimizing the net premium to be paid for the hedging. A quadratic programming solution for the problem is formulated, and then it is approximated to a linear programming solution. A prototype for the linear programming solution has been developed in MS Excel using VBA.