# Research articles for the 2019-05-27

arXiv

I study optimal disclosure policies in sequential contests. A contest designer chooses at which periods to publicly disclose the efforts of previous contestants. I provide results for a wide range of possible objectives for the contest designer. While different objectives involve different trade-offs, I that show that under many circumstances the optimal contest is one of the three basic contest structures widely studied in the literature: simultaneous, first-mover, or sequential contest.

arXiv

We find various exact solutions for a new stochastic volatility (SV) model: the transition probability density, European-style option values, and (when it exists) the martingale defect. This may represent the first example of an SV model combining exact solutions, GBM-type volatility noise, and a stationary volatility density.

arXiv

This paper presents a framework of developing neural networks for predicting implied volatility surfaces. Conventional financial conditions and empirical evidence related to the implied volatility are incorporated into the neural network architecture design and model training including no static arbitrage, boundaries, asymptotic slope and volatility smile. They are also satisfied empirically by the option data on the S&P 500 index over twenty years. The developed neural network model and its simplified variations outperform the widely used surface stochastic volatility inspired (SSVI) model on the mean average percentage error in both in-sample and out-of-sample datasets. This study has two main methodological contributions. First, an accurate deep learning prediction model is developed and tailored to implied volatility surfaces. Second, a framework, which seamlessly combines data-driven models with financial theories, can be extended and applied to solve other related business problems.

arXiv

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz [2001] is widely used for pricing American options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We validate the method with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. We also obtain the convergence rates of look-ahead bias by measuring it using the LOOLSM method. The analysis and computational evidence support our findings.

arXiv

We study the problem of dynamically trading a futures contract and its underlying asset under a stochastic basis model. The basis evolution is modeled by a stopped scaled Brownian bridge to account for non-convergence of the basis at maturity. The optimal trading strategies are determined from a utility maximization problem under hyperbolic absolute risk aversion (HARA) risk preferences. By analyzing the associated Hamilton-Jacobi-Bellman equation, we derive the exact conditions under which the equation admits a solution and solve the utility maximization explicitly. A series of numerical examples are provided to illustrate the optimal strategies and examine the effects of model parameters.

arXiv

Despite the success of demand response programs in retail electricity markets in reducing average consumption, the random responsiveness of consumers to price event makes their efficiency questionable to achieve the flexibility needed for electric systems with a large share of renewable energy. The variance of consumers' responses depreciates the value of these mechanisms and makes them weakly reliable. This paper aims at designing demand response contracts which allow to act on both the average consumption and its variance. The interaction between a risk--averse producer and a risk--averse consumer is modelled through a Principal--Agent problem, thus accounting for the moral hazard underlying demand response contracts. We provide closed--form solution for the optimal contract in the case of constant marginal costs of energy and volatility for the producer and constant marginal value of energy for the consumer. We show that the optimal contract has a rebate form where the initial condition of the consumption serves as a baseline. Further, the consumer cannot manipulate the baseline at his own advantage. The second--best price for energy and volatility are non--constant and non--increasing in time. The price for energy is lower (resp. higher) than the marginal cost of energy during peak--load (resp. off--peak) periods. We illustrate the potential benefit issued from the implementation of an incentive mechanism on the responsiveness of the consumer by calibrating our model with publicly available data. We predict a significant increase of responsiveness under our optimal contract and a significant increase of the producer satisfaction.

arXiv

Retirement gratuity is the money companies typically pay their employees at the end of their contracts or at the time of leaving the company. It is a defined benefit plan and is often given as an alternative to a pension plan. In Botswana, there is now a new pattern whereby companies give their employees the option to receive their gratuity at various stages before the end of their contracts. In particular, some companies give their employees an option to receive their gratuity on a monthly basis rather than having them wait for a year or more. Many employees find this option attractive, but is it economically sound? This paper sheds light on this question by quantifying the economic benefits of the tax relief provided by government relative to investing the monthly-received funds in a risk-free savings account or helping repay a loan. The principles and methods used herein can be adapted and applied to different taxation systems.

arXiv

In this paper we extend the existing literature on xVA along three directions. First, we extend existing BSDE-based xVA frameworks to include initial margin by following the approach of Cr\'epey (2015a) and Cr\'epey (2015b). Next, we solve the consistency problem that arises when the front-office desk of the bank uses trade-specific discount curves that differ from the discount curve adopted by the xVA desk. Finally, we address the existence of multiple aggregation levels for contingent claims in the portfolio between the bank and the counterparty by providing suitable extensions of our proposed single-claim xVA framework.

arXiv

We propose a simpler derivation of the probability density function of Feller Diffusion using the Fourier Transform and solving the resulting equation via the Method of Characteristics. We also discuss simulation algorithms and confirm key properties related to hitting time probabilities via the simulation.

arXiv

Motivated by the evidence that real-world networks evolve in time and may exhibit non-stationary features, we propose an extension of the Exponential Random Graph Models (ERGMs) accommodating the time variation of network parameters. Within the ERGM framework, a network realization is sampled from a static probability distribution defined parametrically in terms of network statistics. Inspired by the fast growing literature on Dynamic Conditional Score-driven models, in our approach, each parameter evolves according to an updating rule driven by the score of the conditional distribution. We demonstrate the flexibility of the score-driven ERGMs, both as data generating processes and as filters, and we prove the advantages of the dynamic version with respect to the static one. Our method captures dynamical network dependencies, that emerge from the data, and allows for a test discriminating between static or time-varying parameters. Finally, we corroborate our findings with the application to networks from real financial and political systems exhibiting non stationary dynamics.

SSRN

From the perspective of both plaintiffs and defendants, the measurement of the damages quantum is obviously of the utmost importance. Therefore, it is surprising to see this process left entirely to the courtâ€™s discretion â€" especially since the quantum is traditionally considered a factual question. The result is that each litigation becomes a unique case calling for a sui generis outcome.This article shows the limits of that approach. It leads to a structural uncertainty that is detrimental to the legitimate expectations of both parties. In practice, it deeply corrupts the fundamental principle of full recovery. I would argue there exist ways to move towards a model in which the valuation of damages will be a question of law that follows rules and methods whose application will be reviewable. In this article, I begin to explore some of these ways, specifically with respect to damages for breach of contract, using two simultaneous methodologies. The first is a comparison between French civil law, American common law and international commercial law, and the second is an empirical study involving both qualitative interviews with practitioners and the quantitative analysis of a proprietary sample of cases in which damages are difficult to measure. The article concludes with recommendations for judicial practices and a discussion of the possibility of predictive justice through shared compensatory damages schedules, which could eventually lead to artificial intelligence models.

SSRN

Chinese Abstract: åœ¨ç¤¾åŒºå…¬ç›Šæ´»åŠ¨ä¸ï¼Œæˆ'ä»¬è§‚å¯Ÿåˆ°å¯¹è‡ªèº«ç»æµŽçŠ¶å†µä¸æ»¡æ„çš„äººç¾¤æ›´æœ‰å¯èƒ½è¢«æŠ•èµ„æœºæž„çš„æŽ¨å¹¿ä¿¡æ¯æ‰€å½±å"ï¼Œå‡ºçŽ°è¾ƒé«˜çš„P2Pç½'è´·æŠ•èµ„æ„æ„¿ã€‚è™½ç„¶è¯¥çŽ°è±¡éžå¸¸æ™®éï¼Œç„¶è€Œè¿™å…¶ä¸çš„æœºåˆ¶å´ç¼ºä¹ç "ç©¶ã€‚åœ¨æœ¬ç "ç©¶ä¸ï¼Œæˆ'ä»¬é€šè¿‡ç¨€ç¼ºæ€ç»´ç†è®º (Shah, Shafir, & Mullainathan, 2015) å'Œé"™è¯¯ç®¡ç†ç†è®º (Haselton & Buss, 2009) å¯¹è¿™ä¸€çŽ°è±¡çš„å½¢æˆæœºåˆ¶è¿›è¡Œäº†åˆ†æžã€‚é€šè¿‡ä¸¤ä¸ªå®žéªŒï¼Œæˆ'ä»¬å–å¾—äº†ä¸‰é¡¹ç "ç©¶å'çŽ°ã€‚é¦–å…ˆï¼Œç»æµŽçŠ¶å†µæ»¡æ„ç¨‹åº¦å¯¹P2Pç½'è´·æŠ•èµ„æ„æ„¿æœ‰ç€æ˜¾è'—å½±å"ï¼Œå¯¹è‡ªèº«ç»æµŽçŠ¶å†µä¸æ»¡æ„çš„ä¸ªä½"è¡¨çŽ°å‡ºäº†æ˜¾è'—æ›´é«˜çš„P2Pç½'è´·æŠ•èµ„æ„æ„¿ã€‚å…¶æ¬¡ï¼Œè¿™ä¸€çŽ°è±¡çš„å½¢æˆåŽŸå› æ˜¯å› ä¸ºå¯¹è‡ªèº«ç»æµŽçŠ¶å†µä¸æ»¡æ„çš„ä¸ªä½"ä¼šæ˜¾è'—é«˜ä¼°P2Pç½'è´·ä¸çš„æŠ•èµ„åˆ©ç›Šï¼Œæ˜¾è'—ä½Žä¼°æŠ•èµ„ä¸çš„é£Žé™©ï¼Œä½¿å¾—å…¶åœ¨é¢å¯¹P2Pç½'è´·æŠ•èµ„äº§å"æ—¶æ›´å€¾å'äºŽé€‰æ‹©IIç±»é"™è¯¯ï¼ˆå³å†'ç€é£Žé™©è¿›è¡ŒæŠ•èµ„çš„å–ä¼ªé"™è¯¯ï¼‰ã€‚æœ€åŽï¼Œé¼"åŠ±ç½'è´·æŠ•èµ„çš„æŽ¨å¹¿ä¿¡æ¯åœ¨ç»æµŽçŠ¶å†µæ»¡æ„ç¨‹åº¦å¯¹P2Pç½'è´·æŠ•èµ„æ„æ„¿çš„å½±å"ä¸èµ·äº†æ˜¾è'—çš„æ£å'è°ƒèŠ‚ä½œç"¨ï¼Œæš´éœ²äºŽç½'è´·æŠ•èµ„æŽ¨å¹¿ä¿¡æ¯å¢žå¼ºäº†å¯¹è‡ªèº«ç»æµŽçŠ¶å†µä¸æ»¡æ„çš„ä¸ªä½"åœ¨é¢å¯¹P2Pç½'è´·æŠ•èµ„æ—¶çš„æ„ŸçŸ¥åˆ©ç›Šä¸Šå‡ã€æ„ŸçŸ¥é£Žé™©ä¸‹é™å'ŒæŠ•èµ„æ„æ„¿å‡é«˜çš„å€¾å'ã€‚åŸºäºŽè¿™äº›å'çŽ°ï¼Œæˆ'ä»¬ä¸€æ–¹é¢å»ºè®®æœªæ¥çš„äº'è"ç½'é‡'èžæŠ•èµ„åº"è¯¥è®¾ç«‹ä¸€å®šçš„æŠ•èµ„é—¨æ§›ä»¥é˜²èŒƒç›²ç›®æŠ•èµ„ï¼Œå¦ä¸€æ–¹é¢å»ºè®®åº"è¯¥åŠ å¼ºå¯¹ç½'è´·æŠ•èµ„æŽ¨å¹¿ä¿¡æ¯çš„ç›'ç®¡ã€‚English Abstract: In our community charity activities, we observed that people who are dissatisfied with their financial situation are more likely to be affected by the promotion information from online investment institutions, resulting in higher P2P lending investment intention. Although this phenomenon is very common, the mechanism is lacking in research. In this study, we explored the mechanism of this phenomenon through scarcity mind-set theory (Shah, Shafir, & Mullainathan, 2015) and error management theory (Haselton & Buss, 2009). Through two experiments, we have made three research findings. Firstly, the degree of financial satisfaction has a significant impact on P2P lending investment intention. Individuals who are relatively financial dissatisfied have shown a significantly higher intention in investing in P2P lending. Secondly, the mechanism of the above phenomenon is that individuals in financial dissatisfaction were significantly overestimated the investment benefits in P2P lending, and significantly underestimated the risks in that investment, making them more inclined to choose a type II error (the false negative error, i.e., investing in risk) in P2P lending investment. Finally, the promotion information which encouraging online investment has played as a significant positive moderator between financial dissatisfaction and P2P lending investment intention. After being exposed to investment promotion information, individuals in financial dissatisfaction shown an increasing tendency in overestimate investment benefits and underestimate investment risks, and the intention to invest in P2P lending were much stronger. Based on these findings, we suggest that online financial investment firms should set a certain investment threshold to prevent irrational investment. Moreover, we suggest strengthening the supervision of online investment promotion information.