Research articles for the 2019-10-17
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The last decade or so has seen a mushrooming of new sovereign debt databases covering long time spans for several countries. This represents an important breakthrough for economists who have long sought to, but been unable to tackle, first-order questions such as why countries have differential debt tolerance, and how debt levels affect the scope for countercyclical policy in recessions and financial crises. This paper backdrops these recent data efforts, identifying both the key innovations, as well as caveats that users should be aware of. A Directory of existing publicly-available sovereign debt databases, featuring compilations by institutions and individual researchers, is also included.
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This paper investigates the cross predictability of intraday returns across 22 major cryptocurrencies. In contrast to the well-documented positive lead-lag effect in the equity market, we find a significantly negative lead-lag effect ("seesaw effect'') in the cryptocurrency market: The five largest cryptocurrencies (Bitcoin, Ripple, Ethereum, Litecoin, and EOScoin) negatively predict the returns of other coins but small coins do not predict the large coins. Trading strategies that exploit the cross predictability yield highly significant profits. Further analysis suggests that the "flight to hot (large) coins" and "flee from cold (large) coins" jointly drive the seesaw effect.
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We estimate the pricing kernel from options on the S&P 500 index for different horizons and over time. This allows us to compare short- and long-term pricing kernels and analyze their time-series variation. We show that the well documented pricing kernel puzzle â" that is, the non-monotonicity of the pricing kernel â" only exists for short horizons. For longer horizons the puzzle disappears and the level, shape and time-series variation of the pricing kernel are in line with standard rational expectation asset pricing models. Furthermore, we show that the empirical features of the short-term kernel can be explained by a behavioral asset pricing model.
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This paper provides new evidence on the link between financial constraints and corporate cash policy. Using time-series data for US public and private manufacturing firms, we find negative correlation between cash holdings and cost-of-carry for large firms. We find no evidence of such a relation for small firms. We also perform a firm-level analysis supporting our time-series results that unconstrained firms have a propensity to adjust cash when cost-of-carry changes, whereas constrained firms do not exhibit this propensity. We provide a basic model predicting changes in the cost-of-carry drive variations in optimal cash holdings, considerably more for financially unconstrained firms.
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The legacy of non-performing loans and high opportunity cost of government financing ofbank recapitalization impeded the efficiency of financial intermediation and are an importantpolicy issue in Vietnam. This paper presents a theoretical and empirical analysis of the issue.An empirical analysis using corporate data indicates credit misallocation between stateowned enterprises and private firms in Vietnam. On the theoretical side, a micro-foundedbanking model is embedded in a political economy setting to assess the factors determiningthe size of bank recapitalization and its effects on the efficiency of financial intermediation,economic growth and welfare. The analysis suggests that recapitalization depends on anarray of factors, including the tightness of the government budget and the decision maker'sconcern for the favored sector.
arXiv
The Total Economic Time Capacity of a Year 525600 minutes is postulated as a time standard for a new Monetary Minute currency in this evaluation study. Consequently, the Monetary Minute MonMin is defined as a 1/525600 part of the Total Economic Time Capacity of a Year. The Value CMonMin of the Monetary Minute MonMin is equal to a 1/525600 part of the GDP, p.c., expressed in a specific state currency C. There is described how the Monetary Minutes MonMin are determined, and how their values CMonMin are calculated based on the GDP and all the population in specific economies. The Monetary Minutes trace different aggregate productivity, i.e. exploitation of the total time capacity of a year for generating of the GDP in economies of different states.
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This paper examines the effect of creditor rights on the design of bank loan contracts. Focusing on the conflict of interest between creditors, I study how banks respond to a legal change that strengthens the rights of securitization creditors. I find that bank loans granted to firms engaging in securitization process have higher interest rates after the law change. Improving the power of securitization creditors to seize their collateral in bankruptcy would eliminate their incentives to maximize recoveries in chapter 11, thereby increasing the risk of other corporate creditors such as bank lenders. Consistent with this intuition, I further find that loans to firms using securitization are charged with higher fees, have smaller size and include a greater number of covenants, subsequently. These effects are more pronounced for smaller firms, firms with lower z-score and firms with higher ratio of receivables to assets, which is a commonly used asset for securitization. Overall, my findings highlight the unintended consequences of increasing the power of some corporate creditors on companies' financial contracts.
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This study examines whether personal liability for corporate malpractice deters individuals from serving as independent directors. Exploiting the introduction of personal liability in India, we find that personal liability deters individuals from serving on corporate boards. We find stronger deterrence among firms with a) greater litigation and regulatory risk, b) higher monitoring costs, and c) weak monetary incentive to serve as an independent director. Expert directors are more likely to exit, resulting in 1.16% lower firm value. Overall, our study documents that personal liability deters individuals with high reputational costs and weak monetary incentives from serving as independent directors.
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Mean-variance portfolio optimization is more popular than optimization procedures that employ downside risk measures like the semivariance, despite the latter being more in line with the preferences of a rational investor. I describe strengths and weaknesses of semivariance and how to minimize it for asset allocation decisions. I then apply this approach to a variety of simulated and real data and show that the traditional approach based on the variance generally outperforms it. The results hold even if the CVaR is used, because all downside risk measures are difficult to estimate. The popularity of variance as a measure of risk appears therefore to be rationally justified.
arXiv
Identification and scoring functions are statistical tools to assess the calibration and the relative performance of risk measure estimates, e.g., in backtesting. A risk measures is called identifiable (elicitable) it it admits a strict identification function (strictly consistent scoring function). We consider measures of systemic risk introduced in Feinstein, Rudloff and Weber (2017). Since these are set-valued, we work within the theoretical framework of Fissler, Hlavinov\'a and Rudloff (2019) for forecast evaluation of set-valued functionals. We construct oriented selective identification functions, which induce a mixture representation of (strictly) consistent scoring functions. Their applicability is demonstrated with a comprehensive simulation study.
arXiv
Many countries embroiled in non-religious civil conflicts have experienced a dramatic increase in religious competition in recent years. This study examines whether increasing competition between religions affects violence in non-religious conflicts. The study focuses on Colombia, a deeply Catholic country that has suffered one of the world's longest-running internal conflicts and, in the last few decades, has witnessed an intense increase in religious competition between the Catholic Church and new non-Catholic churches. The estimation of a dynamic treatment effect model shows that establishing the first non-Catholic church in a municipality substantially increases the probability of an attack by a left-wing guerrilla group. Further analysis suggests that the increase in guerrilla attacks is associated with the expectation among guerrilla groups that their membership will decline as a consequence of more intense competition with religious groups for followers.
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Combining market data with a publicly available monthly snapshot of Deutsche Börse's index ranking list, I create a model that predicts index changes in the DAX, MDAX, SDAX, and TecDAX from 2010 to 2019 before they are officially announced. Even though I empirically show that index changes are predictable, they still earn sizeable post-announcement one-day abnormal returns up to 1.42% and -1.54% for promotions and demotions, respectively. While abnormal returns are larger in smaller stocks, I find no evidence that they are related to funding constraints or additional risk for trading on wrong predictions. A trading strategy that trades according to my model yields an annualized sharpe ratio of 0.83 while being invested for just four days a year.
arXiv
Modeling counterparty risk is computationally challenging because it requires the simultaneous evaluation of all the trades with each counterparty under both market and credit risk. We present a multi-Gaussian process regression approach, which is well suited for OTC derivative portfolio valuation involved in CVA computation. Our approach avoids nested simulation or simulation and regression of cash flows by learning a Gaussian metamodel for the mark-to-market cube of a derivative portfolio. We model the joint posterior of the derivatives as a Gaussian process over function space, with the spatial covariance structure imposed on the risk factors. Monte-Carlo simulation is then used to simulate the dynamics of the risk factors. The uncertainty in portfolio valuation arising from the Gaussian process approximation is quantified numerically. Numerical experiments demonstrate the accuracy and convergence properties of our approach for CVA computations, including a counterparty portfolio of interest rate swaps.
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Public markets are transparent institutions, where disclosure is mandatory and order flow observable. We show that transparency can lead to insufficient information acquisition and inefficient investment. Our model links a firm's preference for public markets to the quality of disclosure metrics. When short-term signals diverge from the long-run value of a project, entrepreneurs prefer opaque private markets where investors can bargain over the costs of acquiring information. Imperfect communication is a mechanism by which mandatory disclosure may destroy value, leading firms to remain private.
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Health insurance in the United States for the working age population has traditionally been provided in the form of employer-sponsored health insurance (ESHI). If employers offered ESHI to their employees, they also typically extended coverage to their spouse and dependents. Provisions in the Affordable Care Act (ACA) significantly alter the incentive for firms to offer insurance to the spouses of employees. We evaluate the long-run impact of the ACA on firmsâ insurance offerings and on household outcomes by developing and estimating an equilibrium job search model in which multiple household members are searching for jobs. The distribution of job offers is determined endogenously, with compensation packages consisting of a wage and menu of insurance offerings (premiums and coverage) that workers select from. Using our estimated model we find that householdsâ valuation of employer-sponsored spousal health insurance is significantly reduced under the ACA, and with an âemployee-onlyâ health insurance contract emerging among low productivity firms. We re-late these outcomes to the specific provisions in the ACA.
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Against the backdrop of an ongoing review of the inflation-targeting framework, this paper examines the real-time inflation forecasts of the Bank of Canada with the aim of identifying potential areas for improvement. Not surprisingly, the results show that errors in forecasting non-core inflation (commodity prices etc.) are found to be the largest contributors to overall inflation forecast errors. Perhaps more importantly, relatively small core inflation forecast errors appear to mask large and offsetting errors related to the output gap and the policy interest rate, partly reflecting a tendency to overestimate the neutral nominal policy rate in real time. Faced with these uncertainties, the Governing Council's gradual approach to changing its policy settings appears to have served it well.
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This paper investigates the co-movement characteristics of global stock markets in the context of the US-China trade war. By applying a set of different trivariate Copulas, our results suggest that markets co-move symmetrically in the pre-trade war period, but exhibit negative downside movements and heavy tails during the trade war. Furthermore, we find evidence for left-tail dependency structures during that period. Most importantly, this study finds that the trade war poses a systematic risk on global markets, which potentially can trigger simultaneous market downside trends. Our results are robust across different European equity market indices.
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This paper studies the optimal design of equity and liquidity regulations in a dynamic macro model with information-based bank runs. Although the latter are privately efficient, since they discipline bank managers efforts into the projects' re-deploying activity, they induce aggregate externalities. Technological inefficiencies arise if bank managers extract rents which are higher than the technological costs of re-deploying projects. Pecuniary externalities arise since, when choosing leverage, bank managers do not internalize the fall in asset price ensuing from the aggregate costs of projects' liquidation in a run event. This creates scope for regulation. Equity and liquidity requirements are complementary, as the first tackles the solvency region, while the second the illiquid-solvent one. Finally, in presence of anticipatory effects prudential policies may have unintended consequences as banks adjust their behaviour when a shift in prudential regime is announced. The more so the higher the credibility of the announcement.
arXiv
This paper presents empirically-estimated average hourly relationships between regional electricity trade in the United States and prices, emissions, and generation from 2015 through 2018. Consistent with economic theory, the analysis finds a negative relationship between electricity prices in California and regional trade, conditional on local demand. Each 1 gigawatt-hour increase in California electricity imports is associated with an average $0.15 per megawatt-hour decrease in the California Independent System Operator's wholesale electricity price. There is a net-negative short term relationship between carbon dioxide emissions in California and electricity imports that is partially offset by positive emissions from exporting neighbors. Specifically, each 1 GWh increase in regional trade is associated with a net 70-ton average decrease in CO2 emissions across the western U.S., conditional on demand levels. The results provide evidence that electricity imports mostly displace natural gas generation on the margin in the California electricity market. A small positive relationship is observed between short-run SO2 and NOx emissions in neighboring regions and California electricity imports. The magnitude of the SO2 and NOx results suggest an average increase of 0.1 MWh from neighboring coal plants is associated with a 1 MWh increase in imports to California.
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Exploiting confidential data from the euro area, we show that sound banks pass negative rates on to their corporate depositors without experiencing a contraction in funding and that the tendency to charge negative rates becomes stronger as policy rates move deeper into negative territory. The negative interest rate policy (NIRP) provides stimulus to the economy through firms' asset rebalancing. Firms with high current assets linked to banks offering negative rates appear to increase their investment in tangible and intangible assets and to decrease their cash holdings to avoid the costs associated with negative rates. Overall, our results challenge the commonly held view that conventional monetary policy becomes ineffective when policy rates reach the zero lower bound.
arXiv
This article applies a long short-term memory recurrent neural network to mortality rate forecasting. The model can be trained jointly on the mortality rate history of different countries, ages, and sexes. The RNN-based method seems to outperform the popular Lee-Carter model.
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We formulate a generalization of the traditional medium-of-exchange function of money in contexts where there is imperfect competition in the intermediation of credit, settlement, or payment services used to conduct transactions. We find that the option to settle transactions directly with money strengthens the stance of sellers of goods and services vis-a-vis intermediaries. We show this mechanism is operative even for sellers who never exercise the option to sell for cash, and that these latent money demand considerations imply monetary policy remains effective through medium-of-exchange channels even if the share of monetary transactions is arbitrarily small.
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When do wholesalers issue green bonds to finance their socially responsible activities instead of charging a premium for the products they produce? We show that in less competitive retail markets when retailers can "skim" more of the premium that end consumers pay for socially responsible products, green bonds provide additional funds to help cover the cost of a wholesaler's socially responsible activities. Similar incentives arise if the wholesaler's input is a small component of the end consumers' product, or if it is difficult for end consumers to identify the wholesaler's socially responsible activities.
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Given the inherent complexity of financial markets, a wide area of research in the field of mathematical finance is devoted to develop accurate models for the pricing of contingent claims. Focusing on the stochastic volatility approach (i.e. we assume to describe asset volatility as an additional stochastic process), it appears desirable to introduce reliable dynamics in order to take into account the presence of several assets involved in the definition of multi-asset payoffs. In this article we deal with the multi asset Wishart Affine Stochastic Correlation model, that makes use of Wishart process to describe the stochastic variance covariance matrix of assets return. The resulting parametrization turns out to be a genuine multi-asset extension of the Heston model: each asset is exactly described by a single instance of the Heston dynamics while the joint behaviour is enriched by cross-assets and cross-variances stochastic correlation, all wrapped in an affine modeling. In this framework, we propose a fast and accurate calibration procedure, and two Monte Carlo simulation schemes.
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Proxy access, a long debated governance measure, was directed at reducing shareholder costs in nominating directors. However, since it was first initiated, proxy access raised vigorous opposition, and more important, significant and wide skepticism that shareholders will ever use it to nominate directors.This Article studies the first systemic implementation of proxy access and finds that while proxy access was rarely used to nominate directors, it was used indirectly â" as a bargaining tool â" to improve board diversity. Accordingly, the study finds that firms with a low number or low proportion of female directors, and firms with all-male boards, were significantly more likely to be targeted by the NYC Comptrollerâs proxy access proposals.While promoting diversity wasnât one of the goals that proxy access was designed to achieve, the resulting effects might not be remote from those intended. Given that institutional investors are not likely to nominate directors, diversity might provide an alternative, pragmatic channel, to increase board independence, monitoring and accountability.
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Expectations affect economic decisions, and therefore inaccurate expectations are costly. Expectations can be wrong in ways that are systematic (bias) or unsystematic (noise). We provide a general method for quantifying the noise component. The method is based on the insight that theoretical models of expectation formation predict a factor structure for individual expectations. This insight leads to a widely applicable factor-based measurement procedure. Using data from professional forecasters, we find that noise is large and pervasive. Our findings have implications for forecast combination, macro models with incomplete information, and empirical research using micro data on expectations.
arXiv
This paper studies deep learning methodologies for portfolio optimization in the US equities market. We present a novel residual switching network that can automatically sense changes in market regimes and switch between momentum and reversal predictors accordingly. The residual switching network architecture combines two separate residual networks (ResNets), namely a switching module that learns stock market conditions, and the main module that learns momentum and reversal predictors. We demonstrate that over-fitting noisy financial data can be controlled with stacked residual blocks and further incorporating the attention mechanism can enhance powerful predictive properties. Over the period 2008 to H12017, the residual switching network (Switching-ResNet) strategy verified superior out-of-sample performance with an average annual Sharpe ratio of 2.22, compared with an average annual Sharpe ratio of 0.81 for the ANN-based strategy and 0.69 for the linear model.
SSRN
Recent reforms give regulators broad powers to "bail-in" bank creditors during financial crises.
arXiv
Quantitative finance has had a long tradition of a bottom-up approach to complex systems inference via multi-agent systems (MAS). These statistical tools are based on modelling agents trading via a centralised order book, in order to emulate complex and diverse market phenomena. These past financial models have all relied on so-called zero-intelligence agents, so that the crucial issues of agent information and learning, central to price formation and hence to all market activity, could not be properly assessed. In order to address this, we designed a next-generation MAS stock market simulator, in which each agent learns to trade autonomously via model-free reinforcement learning. We calibrate the model to real market data from the London Stock Exchange over the years $2007$ to $2018$, and show that it can faithfully reproduce key market microstructure metrics, such as various price autocorrelation scalars over multiple time intervals. Agent learning thus enables model emulation of the microstructure with greater realism.
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One of the main causes of the past crisis was the inability of financial institutions to acquire funding at appropriate costs. The importance of applying a good liquidity risk measurement system becomes apparent. The present paper provides an approach to the measurement of liquidity maturity transformation risk within a stress testing framework, for middle-sized banks. The costs of liquidity arising due to a downturn in refinancing conditions are calculated by using modern risk measures. The forward-looking way is based on a liquidity gap report, where the consideration of the counterbalancing capacity enables to gain an insight into the real liquidity needs. The measurement of both, the portfolio-value in the respective time bucket and liquidity costs, is possible. Applying the expected shortfall can easily be included into the calculation. The results show that by using historical simulation, if no sufficient data are available, expected shortfall delivers an approximate value. Still, it can serve as an indicator of insurance against extreme events. The present approach combines a scenario-based view to a possible distress with a quantitative risk measurement. Therewith, it contributes to the bankâs wide stress testing as required by the regulatory authorities.
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This is the supplemental material to the paper titled "Inalienable Customer Capital, Corporate Liquidity, and Stock Returns." It includes additional empirical, theoretical, and quantitative results. It also includes illustration for the numerical algorithm for our model solution.
SSRN
The Black-Litterman Model (BLM), created by Fischer Black and Robert Litterman, is a sophisticated portfolio construction method that overcomes the problem of unintuitive, highly-concentrated portfolios, input-sensitivity, and estimation error maximization. The BLM uses a Bayesian approach to combine the subjective views of an investor regarding the expected returns of one or more assets with the market equilibrium vector of expected returns (the prior distribution) to form a new, mixed estimate of expected returns. The resulting new vector of returns (the posterior distribution), leads to intuitive portfolios with sensible portfolio weights. (Idzorek, 2004). BLM was first introduced in Black and Litterman (1990) and further explained in Black and Litterman (1991) and Black and Litterman (1992) It is an asset allocation model which has its roots in mean-variance (MV) optimization model and capital asset pricing model (CAPM). Model builds on MV optimization and CAPM by using a Bayesian framework that allows investors to incorporate their views on markets effectively into asset allocation process. Main contribution of BLM is that it enables investors to construct sensible portfolios without using unnecessary constraints which also reflect their views on markets. It is well known to both academics and practitioners that standard MV optimization is very sensitive to expected returns and often generates extreme portfolios (concentration in very few assets, large long and short positions). BLM overcomes these issues by choosing a neutral reference point, CAPM equilibrium. It also allows investors to express their views with varying confidence levels and integrate these views into CAPM prior by using a Bayesian framework. As a result, since its introduction BLM has been increasingly used among practitioners and allowed asset allocation decisions to be in more of a quantitative nature rather than qualitative because of the apparent shortcomings of MV optimization model.
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This paper develops a unified quantitative account of credit cycles and their macroeconomic consequences based on information frictions in debt markets. Using a dynamic model with endogenous default, we highlight a novel âherdingâ mechanism whereby uninformed debt investors learn about firmsâ creditworthiness from publicly-available survey information on quarter-ahead corporate profits. We show that: 1) short-term changes in expectations of corporate profits strongly forecast credit spreads and real economic aggregates over up to two years horizons; 2) credit spreads and defaults are counter-cyclical; 3) the mechanism can account quantitatively for the historically large spike in spreads during the financial crisis.
SSRN
We study the transmission of monetary policy in credit economies where money serves as a medium of exchange. We find that-in contrast to current conventional wisdom in policy-oriented research in monetary economics-the role of money in transactions can be a powerful conduit to asset prices and ultimately, aggregate consumption, investment, output, and welfare. Theoretically, we show that the cashless limit of the monetary equilibrium (as the cash-and-credit economy converges to a pure-credit economy) need not correspond to the equilibrium of the nonmonetary pure-credit economy. Quantitatively, we find that the magnitudes of the responses of prices and allocations to monetary policy in the monetary economy are sizeable-even in the cashless limit. Hence, as tools to assess the effects of monetary policy, monetary models without money are generically poor approximations- even to idealized highly developed credit economies that are able to accommodate a large volume of transactions with arbitrarily small aggregate real money balances.
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This paper presents a detailed analysis of how liquid money market instruments â?? sterling bills of exchange â?? were produced during the first globalisation. We rely on a unique data set that reports systematic information on all 23,493 bills re-discounted by the Bank of England in the year 1906. Using descriptive statistics and network analysis, we reconstruct the complete network of linkages between agents involved in the origination and distribution of London bills. Our analysis reveals the truly global dimension of the London bill market before the First World War and underscores the crucial role played by London intermediaries (acceptors and discounters) in overcoming information asymmetries between borrowers and lenders on this market. The complex industrial organisation of the London money market ensured that risky private debts could be transformed into extremely liquid and safe monetary instruments traded throughout the global financial system.
SSRN
Well-intended policies often have negative unintended consequences if they fail to foresee the different ways in which individuals may respond to the new set of incentives. When widespread and persistent, these may lead to a net reduction of social welfare. Focusing on the case of anti-drug policies, in this paper we show that the recent unprecedented surge in the growing of illicit coca crops in Colombia was the result of a naive and untimely policy announcement during peace negotiations between the government and the FARC guerrillas. On May 2014, the partiesâ peace delegations issued a press release announcing that coca-growing farmers would receive material incentives for voluntary crop substitution once a final agreement had been reached. To evaluate the anticipation effect of this announcement we exploit the cross sectional variation on both the cost advantage of growing coca (using an ecological measure of coca suitability) and the expected benefits of doing so (using a predicted measure of where the material benefits would have been targeted). Coca plantations levels remained high even after the implementation of the announced incentivesâ scheme. We explain this persistence by documenting that the surge in coca growing is differentially higher in areas with presence illegal armed groups, that benefited financially from availability of a key input in the drug trade.
arXiv
We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential L\'evy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of the time-to-maturity; these series are obtained via a factorized integral representation in the Mellin space evaluated by means of residues in $\mathbb{C}$ or $\mathbb{C}^2$. Comparisons with numerical methods and efficiency tests are also discussed.
arXiv
We reconsider the microeconomic foundations of financial economics under Knightian Uncertainty. We remove the (implicit) assumption of a common prior and base our analysis on a common order instead. Economic viability of asset prices and the absence of arbitrage are equivalent. We show how the different versions of the Efficient Market Hypothesis are related to the assumptions one is willing to impose on the common order. We also obtain a version of the Fundamental Theorem of Asset Pricing using the notion of sublinear pricing measures. Our approach unifies recent versions of the Fundamental Theorem under a common framework.
SSRN
Chinese Abstract: è¡ç"æ§é'èåå"çåºæ¬è¨å¹çè«ï¼æ¯æ ¹æ¤æ¼ä¸åå¨å¥å©æ©æèå®å ¨å¸å ´åè¨ï¼å®çå°çå'½é¡æ¯åå¨å"¯ä¸ç風éªä¸ç«æ¸¬åº¦ãé¡è¿°ä»¥ä¸å®ççç´è¦ºãç²¾ç°¡æ¨¡åæ¯å®æãäºè³ç"¢ä¸"äºçæ çäºé 樹模åï¼å æ¤ï¼åæçè¡ç"æ§é'èåå"æç§'æ¸ï¼é½å°äºé 樹模å宿'å¨å¸é·å ä¿®æ¯é£çºæé"模åä¹åãç¶èï¼å¤§é¨åç䏿æç§'æ¸å»å°äºé 樹模å宿'å¨é£çºæ¨¡åä¹å¾ï¼èä¸"æ®é忽ç¥é¢¨éªä¸ç«è¨å¹çå¿ è¦æ¢ä»¶ï¼ç¡å¥å©æ©æåè¨ï¼ä»¥å忽ç¥é¢¨éªä¸ç«æ©çå"¯ä¸åå¨çå¿ è¦æ¢ä»¶ï¼å®å ¨å¸å ´ãæ¬æå©ç"¨å®æãä¸çæ èä¸ç¨ç«åºç¤è³ç"¢åè¨ï¼å'ç¾ä¸ç¶åº¦å ±é ¬ççå形表é"ãé¡è¿°ä¸åå¨å¥å©æ©æå¸å ´ãå®å ¨å¸å ´èå¹³è³æ¸¬åº¦æ©ççç´è¦ºææ¶µãæå¾ï¼æ¬æå表æ¯"è¼åæ¸åæç§'æ¸å°æ¼æ¬æè¨è«è°é¡ç表é"æ¹å¼ï¼ä¸¦ä¸"æåºè©è«ãæ¬æä½è ç¸ä¿¡ï¼ä¹è©¦åçºæè²¨è鏿"æ¬æç§'æ¸è²¢ç»æ¸ æ¥ãå´è¬¹çå¸çææ¶µï¼ä¹åç¼å°ç¡å¥å©å¸å ´ãå®å ¨å¸å ´èå¹³è³æ¸¬åº¦çè§£è®ãEnglish Abstract: The fundamental pricing theory of derivatives is based on the assumptions of arbitrage-free and complete markets, which is equivalent to the unique existence of a risk-neutral measure. A single-period binomial-tree model with two assets and two states provides an intuitive and concise way to interpret this theory. As a result, English textbooks on derivatives present binomial-tree models before the Black-Scholes continuous-time model. However, most Chinese textbooks on derivatives present them in reverse order. In particular, they tend to neglect that the assumption of arbitrage-free markets is a necessary condition for the legitimacy of risk-neutral pricing, and that a condition of complete markets is for the uniqueness of a risk-neutral measure. The objective of this paper is to provide an intuitive interpretation of arbitrage-free and complete markets, as well as martingale measures, in three-dimensional figures. It is done by presenting discrete single-period models with three states, accompanied by three underlying assets. Finally, this paper compares and critiques the contents of more than ten textbooks. This paper intends to contribute to a clearer theoretical illustration of arbitrage-free, complete markets, and martingale measures.