Payoff Structures Research Articles

Effective Stochastic Volatility: Applications to ZABR-type Models

There are numerous models for specifying the uncertainty of future instantaneous volatility or variance, including the Heston, SABR and ZABR models. Often it is observed that a specific stochastic volatility model is chosen not for particular dynamical features, relevant for exotic payoff structures, but instead for convenience and ease of implementation. The SABR model, with its semi-closed form approximate solution for the prices of vanilla options, is a well-known example. In this article, we consider a general approach that includes all practically relevant stochastic volatility models and introduces new variants of the ZABR model. In particular, we consider the mean-reverting ZABR and free ZABR models. We use the method of deriving an effective partial differential equation for the density. This approach leads to the known approximation formula for the SABR model, but also provides expressions for arbitrage-free models. Numerical experiments illustrate our approach.

Optimal Volatility Position Construction and Risk Management: A Linear Discrete Ill-Posed Problem With Box Constraints

This paper examines how volatility positions can be optimally constructed by modeling the selection process as a linear discrete ill-posed problem with box constraints. We show how this framework allows for a priori investor expectations and risk parameters to be applied in the optimization process for robust position risk management. We use implied volatility decreases following significant changes in firm fundamentals proxied by U.S. Food and Drug Administration (FDA) New Drug Application (NDA) events to construct a linear system where feasible solutions represent an investor’s optimal volatility position. Significant implied volatility drops from these events occur due to changes in the information environment surrounding a firm’s real growth options. It provides a natural laboratory to demonstrate how practitioners can use interior-point solvers to construct optimal positions under a priori constraints. The feasible solutions to these linear systems represent optimal volatility positions that provide better payoff structures than traditional option spread trading around these NDA events. Further, we show that this model can be applied dynamically to manage portfolio risk for positions with multiple options and an underlying stock hedge.

Generalized Graph k-Coloring Games

We investigate pure Nash equilibria in generalized graphk-coloring games where we are given an edge-weighted undirected graph together with a set of k colors. Nodes represent players and edges capture their mutual interests. The strategy set of each player consists of k colors. The utility of a player v in a given state or coloring is given by the sum of the weights of edges {v, u} incident to v such that the color chosen by v is different than the one chosen by u, plus the profit gained by using the chosen color. Such games form some of the basic payoff structures in game theory, model lots of real-world scenarios with selfish players and extend or are related to several fundamental class of games. We first show that generalized graph k-coloring games are potential games. In particular, they are convergent and thus Nash Equilibria always exist. We then evaluate their performance by means of the widely used notions of price of anarchy and price of stability and provide tight bounds for two natural and widely used social welfare, i.e., utilitarian and egalitarian social welfare.

Tacit knowledge sharing in IT R&D teams: Nonlinear evolutionary theoretical perspective

Tacit knowledge sharing influences the performance of IT R&D teams. However, information regarding the mechanism of tacit knowledge sharing is limited. Accordingly, we develop a nonlinear dynamic model to explore the influence of structural changes on tacit knowledge sharing behavior in an IT R&D team, particularly in response to gradual changes in payoff structures. The following results were observed：(1) Certain situations and a traditional correlation analysis confirmed that the current contradictions in the influence of reward systems on knowledge sharing behavior are unified. (2) Under special conditions, the influences of several critical factors (e.g., reciprocity, penalty of social reputation, and supervising mechanism) lose efficacy. As an alternative, managers can only enhance the reward system or reduce sharing cost. The effectiveness of knowledge sharing substantially improves only once it reaches certain critical thresholds. (3) During a catastrophe, a team’s behavior may become immune to the deterioration of payoff structures. However, sudden jumps (i.e., from sharing to hiding knowledge) may occur when another threshold is reached. In summary, once team members experience a sudden jump, retrieving the previous cooperative status becomes difficult.

Culture and Child Attachment Patterns: a Behavioral Systems Synthesis.

We propose that the two dominant culture institutions (individualist and collectivist) are neither learned nor cognitively represented by the people who practice them. Instead, they exist as group-level payoff structures that reflect differential distributions of child attachment patterns within a society. Individualist societies reflect an overrepresentation of insecure-avoidant attachments and collectivist societies reflect an overrepresentation of insecure-anxious attachments. Moreover, attachment patterns are embodied rather than representational-schedule-induced rather than incrementally shaped or verbally learned. If attachment patterns are schedule-induced, the prospects are poorer for effecting cultural change through economic incentives or informational campaigns (top-down). Rather, cultural practices will be responsive to changes in family practices-to the extent they affect attachment patterns (bottom-up). For example, if breastfeeding rates decline or the workforce participation of women increases, a society will become more individualist and less collectivist. That is because those practices increase avoidant as compared to anxious attachments. Moreover, because insecurely attached children are behaviorally less flexible than are securely attached children, the former have a greater impact on cultural practices than do the latter.

The Impact of Self-Relevance on Preschool Children's Sharing.

This study was designed to investigate the impact of self-relevance between preschool children and recipients on children’s sharing behavior in dictator games using a forced-choice resource distribution paradigm. Experiment 1: A total of 75 children aged 3–6 years were evaluated in a first-party situation in which they were distributed as recipients and dictators and shared resources with distracting recipients with different extents of self-relevance under three different payoff structures, including non-costly, costly, and envy structures. Children could choose between a sharing option and a non-sharing option. The results showed that, in a first-party situation, children aged 3–6 years old typically share more resources with highly self-relevant recipients (friends) than with moderately self-relevant recipients (acquaintances) and lowly self-relevant recipients (strangers) and that they share more resources with moderately self-relevant recipients (acquaintances) than lowly self-relevant recipients (strangers). Experiment 2: A total of 62 children aged 3–6 years old were evaluated in a third-party situation in which they were distributed not as recipients but only dictators, making decisions between the options of sharing more or sharing less with distracting recipients who had different extents of self-relevance under three different payoff structures, such as non-bias, high self-bias, and low self-bias. The results showed that, in a third-party situation, children typically share in a similar manner to that of Experiment 1, meaning that children display selective generosity and that the self-relevance between the children and recipients played a key role. Across age groups, this study of preschool children (total N = 137) demonstrates a degree of effect of self-relevance on preschool children’s sharing in first-party and third-party situations, with highly self-relevant recipients receiving a more preferential share in the dictator game than those with low self-relevance, although this effect was stronger in the older preschool children.

On the optimal hedge ratio in index-based longevity risk hedging

In an index-based longevity hedge, the so-called longevity basis risk arises from the potential mismatch between the hedging instrument and the annuity portfolio being hedged, due to the differences in the underlying populations and payoff structures. To reduce the impact of this longevity basis risk and increase the hedge effectiveness, an optimal position in the hedging instrument should be determined appropriately with regard to the nature of the two populations and also the timing of the payments. In this paper, we examine some analytical results on the optimal hedge ratio in hedging the longevity exposure of an annuity portfolio with index-based longevity- or mortality-linked securities. This optimal hedge ratio may serve as a convenient starting point for constructing an index-based hedge. We also conduct a cost–benefit analysis using different financial objectives. Our results are based on data of Australian public sector pensioners.

Managing Systematic Mortality Risk in Life Annuities: An Application of Longevity Derivatives

This paper assesses the hedge effectiveness of an index-based longevity swap and a longevity cap for a life annuity portfolio. Although longevity swaps are a natural instrument for hedging longevity risk, derivatives with non-linear pay-offs, such as longevity caps, provide more effective downside protection. A tractable stochastic mortality model with age dependent drift and volatility is developed and analytical formulae for prices of longevity derivatives are derived. The model is calibrated using Australian mortality data. The hedging of the life annuity portfolio is comprehensively assessed for a range of assumptions for the longevity risk premium, the term to maturity of the hedging instruments, as well as the size of the underlying annuity portfolio. The results compare the risk management benefits and costs of longevity derivatives with linear and nonlinear payoff structures.

Static and Semi-Static Hedging as Contrarian or Conformist Bets

In this paper, we argue that, once the costs of maintaining the hedging portfolio are properly taken into account, semi-static portfolios should more properly be thought of as separate classes of derivatives, with non-trivial, model-dependent payoff structures. We derive new integral representations for payoffs of exotic European options in terms of payoffs of vanillas, different from Carr-Madan representation, and suggest approximations of the idealized static hedging/replicating portfolio using vanillas available in the market. We study the dependence of the hedging error on a model used for pricing and show that the variance of the hedging errors of static hedging portfolios can be sizeably larger than the errors of variance-minimizing portfolios. We explain why the exact semi-static hedging of barrier options is impossible for processes with jumps, and derive general formulas for variance-minimizing semi-static portfolio. We show that hedging using vanillas only leads to larger errors than hedging using vanillas and first touch digitals. In all cases, efficient calculations of the weights of the hedging portfolios are in the dual space using new efficient numerical methods for calculation of the Wiener-Hopf factors and Laplace-Fourier inversion.

Valuing step barrier options and their icicled variations

This paper intends to investigate an interesting class of barrier options, called step barrier options, whose barrier levels are a piecewise constant function of time. These options, while having transparent, simple, and flexible payoff structures, allow for explicit pricing formulas under the Black-Scholes model, and thus can be easily embedded into equity-linked products to enhance the yield or reduce the downside risk. Moreover, the class can be further generalized by attaching vertical branches of barriers to the horizontal one as in Lee and Ko (2018). Using the actuarial method of Esscher transform and the factorization formula, we derive the option pricing formulas under a more general framework with vertical branches attached to horizontal barriers. We explore the formulas through numerical examples, demonstrating their applicability to equity-linked investment with the step barrier option embedded.

Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem

The paper reports on market-entry experiments that manipulate both payoff structures and payoff levels to assess two stationary models of behaviour: Exploration vs Exploitation (EvE, which is equivalent to Quantal Response Equilibrium) and Impulse Balance Equilibrium (IBE). These models explain the data equally well in terms of goodness-of-fit whenever the observed probability of entry is less than the symmetric Nash equilibrium prediction; otherwise IBE marginally outperforms EvE. When assuming agents playing symmetric strategies, and estimating the models with session data, IBE yields more theory-consistent estimates than EvE, no matter the payoff structure or level. However, the opposite occurs when the symmetry assumption is relaxed. The conduct of a specification test rejects the validity of the restrictions on entry probabilities imposed by EvE for agents with symmetric strategies, in 50 to 75% of sessions and it always rejects it in the case of IBE, which indicates that the symmetric variant of these models has little empirical support.

Collective Strategizing : The UK Government’s Polycentric Approach to Plan HS2

This inductive study investigates an organization’s collective strategy to endogenize nominally-independent stakeholders with heterogeneous interests and payoff structures. We ground our research o...

Multiple-Event Catastrophe Bond Pricing Based on CIR-Copula-POT Model

Catastrophe events are attracting increased attention because of their devastating consequences. Aimed at the nonlinear dependency and tail characteristics of different triggered indexes of multiple-event catastrophe bonds, this paper applies Copula function and the extreme value theory to multiple-event catastrophe bond pricing. At the same time, floating coupon and principal payoff structures are adopted instead of fixed coupon and principal payoff structures, to reduce moral hazard and improve bond attractiveness. Furthermore, we develop a CIR-Copula-POT bond pricing model with CIR stochastic rate and estimate flood multiple-event triggered catastrophe bond price using Monte Carlo simulation method. Finally, we implement the sensitivity analysis to show how catastrophe intensity, maturity date, and the dependence affect the prices of catastrophe bonds.

Equilibrium existence in global games with general payoff structures

We consider global games with general payoff structures and prove existence of equilibrium. This shows that the global games’ method is well defined with arbitrary strategic interaction among players, thus providing a foundation for the study of more general equilibrium behavior, especially as research in global games moves beyond the case of strategic complements. We also show that, in every global game, even though the information of each player is correlated, the joint information measure is absolutely continuous with respect to the product of its marginals. As one application, the result here can be used to show the existence of equilibrium in global games with both complementarity and congestion. This proves existence of equilibrium in a finite-player version of the model in Karp et al. (Games Econ Behav 60:155–175, 2007), thus addressing a gap in the proof of equilibrium existence documented in Hoffmann and Sabarwal (Games Econ Behav 94:188–190, 2015).

Farmers’ Adoption of Irrigation Technologies: Experimental Evidence from a Coordination Game with Positive Network Externalities in India

Abstract Electric irrigation contributes to food security in rural India, but deteriorating electrical infrastructures threaten the functioning of farmers’ pump sets. This problem could be solved through investments in energy-efficient technologies. However, network externalities create a coordination problem for farmers. We develop a framed field experiment to study the effects of group size, leading by example, and payoff structures on the ability to coordinate technology adoption investments. The experiment is based on a game that combines features of a step-level public goods game and a critical mass game. Our findings show that smaller groups more frequently coordinate on payoff- superior equilibria and that higher payoffs lead to more investments. Contrary to previous studies, leading by example reduces investments but has no effect on efficiency. Building on this analysis, we discuss possible bottom-up solutions to the energy crisis in rural India.

Are entrepreneurial cultures stable over time? Historical evidence from China

Are entrepreneurial cultures stable over time? In this paper, we use historical measures of the outgrowth of entrepreneurial culture in China and test whether these correlate with entrepreneurial activities today. We employ provincial panel data from China documenting the regional distribution of entrepreneurial activities during the Ming Dynasty (1368–1644) and the Qing Dynasty (1644–1912) and private firm activities in post-reform China (1992–2012). Our study finds a significant association between the regional distribution of historical and current measures of entrepreneurship, supporting (1) the long-term stability of underlying regional cultural differences; and (2) the adaptability of entrepreneurial activities to changing institutional arrangements and relative payoff structures. These results are robust to numerous alternative explanations, including geography, agglomeration advantages, education, and technology. Our findings suggest that government efforts to encourage new business ventures—if they are to have more than short-term effects—will need to take into account local cultural norms.

SMOOTH UPPER BOUNDS FOR THE PRICE FUNCTION OF AMERICAN STYLE OPTIONS

We introduce a new approach for systematically obtaining smooth deterministic upper bounds for the price function of American style options. These bounding functions are characterized by sufficient conditions, under which the bounds may be infimized. In a single implementation, the proposed approach obtains explicit bounds in the form of piecewise polynomial functions, which bound the price function from above over the whole problem domain both in time and state. As a consequence, these global bounds store a continuum of information in the form of a finite number of polynomial coefficients. The proposed approach achieves these bounds, free from statistical error, without recourse to sample path simulation, without truncating the naturally unbounded domain that arises in this problem, and without discretizing the time and state variables. Throughout the paper, we demonstrate the effectiveness of the proposed method in obtaining tight upper bounds for American style option prices in a variety of market models and with various payoff structures, such as the multivariate Black Scholes and Heston stochastic volatility models and the American put and butterfly payoff structures. We also discuss extensions of the proposed methodology to perpetual American style options and frameworks in which the underlying asset contains jumps.

Exploration vs Exploitation, Impulse Balance Equilibrium, and a Specification Test for the El Farol Bar Problem

The paper reports on market-entry experiments that manipulate both payoff structures and payoff levels to assess two stationary models of behaviour: Exploration vs Exploitation (EvE, which is equivalent to Quantal Response Equilibrium) and Impulse Balance Equilibrium (IBE). These models explain the data equally well in terms of goodness-of-fit whenever the observed probability of entry is less than the symmetric Nash equilibrium prediction; otherwise IBE marginally outperforms EvE. When assuming agents playing symmetric strategies, and estimating the models with session data, IBE yields more theory-consistent estimates than EvE, no matter the payoff structure or level. However, the opposite occurs when the symmetry assumption is relaxed. The conduct of a specification test rejects the validity of the restrictions on entry probabilities imposed by EvE for agents with symmetric strategies, in 50 to 75% of sessions and it always rejects it in the case of IBE, which indicates that the symmetric variant of these models has little empirical support.

Structuring and Pricing Home Equity Release With Better Sharing of House Price Risk

We present the structure and pricing of a home-equity-release product designed for senior homeowners with a more efficient risk-sharing than traditional reverse mortgages. The homeowner borrows against their home with the protection of a nonegative-equity-guarantee (NNEG), but the repayment is based on the return on a regional house-price-index and a fixed premium to cover the NNEG. This product provides greater access to equity release for retirement-age homeowners and a wider range of investment products for investors. The rearrangement of the payoff structures described in our model allows for higher upfront loan to value ratios than have traditionally been available in the industry. We illustrate the associated payoffs with the use of 20 years of home sales data from the United Kingdom (UK), up-to-date UK mortality data, and an updated UK morbidity study.

A gaze bias with coarse spatial indexing during a gambling task.

Researchers have used eye-tracking methods to infer cognitive processes during decision making in choice tasks involving visual materials. Gaze likelihood analysis has shown a cascading effect, suggestive of a causal role for the gaze in preference formation during evaluative decision making. According to the gaze bias hypothesis, the gaze serves to build commitment gradually towards a choice. Here, we applied gaze likelihood analysis in a two-choice version of the well-known Iowa Gambling Task. This task requires active learning of the value of different choice options. As such, it does not involve visual preference formation, but choice optimization through learning. In Experiment 1 we asked subjects to choose between two decks with different payoff structures, and to give their responses using mouse clicks. Two groups of subjects were exposed to stable versus varying outcome contingencies. The analysis revealed a pronounced gaze bias towards the chosen stimuli in both groups of subjects, plateauing at more than 400ms before the choice. The early plateauing suggested that the gaze effect partially reflected eye-hand coordination. In Experiment 2 we asked subjects to give responses using a key press. The results again showed a clear gaze bias towards the chosen deck, this time without any influence from eye-hand coordination. In both experiments, there was a clear gaze bias towards the choice even though the gaze fixations did not narrowly focus on the spatial positions of choice options. Taken together, the data suggested a role for gaze in coarse spatial indexing during non-perceptual decision making.