Chuan-Ju Wang, Ph.D.

Abstract

To minimize the variance of Monte Carlo estimators, we develop a novel exponential embedding technique that extends the classical concept of sufficient statistics in importance sampling. Our method demonstrates bounded relative error and logarithmic efficiency when applied to normal and gamma distributions, especially in rare event scenarios. To illustrate this innovative technique, we address the problem of credit risk measurement in portfolios and present an efficient simulation algorithm to estimate the likelihood of significant portfolio losses, leveraging multi-factor models with a normal mixture copula. Finally, supported by comprehensive simulation studies, our approach offers a more effective and efficient way to simulate moderately rare events.

Abstract

This study investigates importance sampling under the scheme of mini-batch stochastic gradient descent, under which the contributions are twofold. First, theoretically, we develop a neat tilting formula, which can be regarded as a general device for asymptotically optimal importance sampling. Second, practically, guided by the formula, we present an effective algorithm for importance sampling which accounts for the effects of minibatches and leverages the Markovian property of the gradients between iterations. Experiments conducted on artificial data confirm that our algorithm consistently delivers superior performance in terms of variance reduction. Furthermore, experiments carried out on real-world data demonstrate that our method, when paired with relatively straightforward models like multilayer perceptron (MLP) and convolutional neural networks (CNN), outperforms in terms of training loss and testing error.

Abstract

This paper proposes a novel equity-price-tree-based convertible bond (CB) pricing model based on the first-passage default model under stochastic interest rates. By regarding equity values as down-and-out call options on firm values (FVs), at each tree node, we solve the implied FV and equity-price volatility (EPV), and then endogenously settle the default probability (DP) and also the dilution effect subject to CB conversions with the implied FV and capital structure. Our model captures the stylized negative (positive) relationships between the stochastically evolving DP and FV or EP (EPV) that cannot be fully achieved by existing CB pricing models.

Abstract

Options can be priced by the lattice model, the results of which converge to the theoretical option value as the lattice's number of time steps n approaches infinity. The time complexity of a common dynamic programming pricing approach on the lattice is slow (at least O(n^2)), and a large n is required to obtain accurate option values. Although O(n)-time combinatorial pricing algorithms have been developed for the classical binomial lattice, significantly oscillating convergence behavior makes them impractical. The flexibility of trinomial lattices can be leveraged to reduced the oscillation, but there are as yet no linear-time algorithms on trinomial lattices. We develop O(n)-time combinatorial pricing algorithms for polynomial options that cannot be analytically priced. The commonly traded plain vanilla and power options are degenerate cases of polynomial options. Barrier options that cannot be stably priced by the binomial lattice can be stably priced by our O(n)-time algorithm on a trinomial lattice. Numerical experiments demonstrate the efficiency and accuracy of our O(n)-time trinomial lattice algorithms.

Abstract

Item concept modeling is commonly achieved by leveraging textual information. However, many existing models do not leverage the inferential property of concepts to capture word meanings, which therefore ignores the relatedness between correlated concepts, a phenomenon which we term conceptual “correlation sparsity.” In this paper, we distinguish between word modeling and concept modeling and propose an item concept modeling framework centering around the item concept network (ICN). ICN models and further enriches item concepts by leveraging the inferential property of concepts and thus addresses the correlation sparsity issue. Specifically, there are two stages in the proposed framework: ICN construction and embedding learning. In the first stage, we propose a generalized network construction method to build ICN, a structured network which infers expanded concepts for items via matrix operations. The second stage leverages neighborhood proximity to learn item and concept embeddings. With the proposed ICN, the resulting embedding facilitates both homogeneous and heterogeneous tasks, such as item-to-item and concept-to-item retrieval, and delivers related results which are more diverse than traditional keyword-matching-based approaches. As our experiments on two real-world datasets show, the framework encodes useful conceptual information and thus outperforms traditional methods in various item classification and retrieval tasks.

Abstract

This paper proposes analytically vulnerable vanilla option pricing formulae that simultaneously consider the premature default, the correlation between the underlying asset and the issuer's asset, and other outstanding debts of the issuer. Our pricing formulae can be easily extended to solve the problem of pricing vulnerable barrier options, which has been rarely studied before. We show that previous studies on pricing (non)-vulnerable vanilla options and barrier options are degenerate cases of our formulae. We conduct numerical experiments to analyze the relations among the financial/contract parameters and counterparty risk, and also empirically evaluate vulnerable vanilla warrants on the TAIEX issued by Capital Securities with detailed studies of parameter calibrations to examine the robustness of our approach.

Abstract

Conversational search plays a vital role in conversational information seeking. As queries in information seeking dialogues are ambiguous for traditional ad-hoc information retrieval (IR) systems due to the coreference and omission resolution problems inherent in natural language dialogue, resolving these ambiguities is crucial. In this paper, we tackle conversational passage retrieval (ConvPR), an important component of conversational search, by addressing query ambiguities with query reformulation integrated into a multi-stage ad-hoc IR system. Specifically, we propose two conversational query reformulation (CQR) methods: (1) term importance estimation and (2) neural query rewriting. For the former, we expand conversational queries using important terms extracted from the conversational context with frequency-based signals. For the latter, we reformulate conversational queries into natural, standalone, human-understandable queries with a pretrained sequence-to-sequence model. Detailed analyses of the two CQR methods are provided quantitatively and qualitatively, explaining their advantages, disadvantages, and distinct behaviors. Moreover, to leverage the strengths of both CQR methods, we propose combining their output with reciprocal rank fusion, yielding state-of-the-art retrieval effectiveness, 30\% improvement in terms of NDCG@3 compared to the best submission of TREC CAsT 2019.

Abstract

This paper presents timely open range breakout (TORB) strategies for index futures market trading via using one-minute intraday data. We observe that the trading volumes and fluctuations in returns on each one-minute interval of trading hours in the futures markets reach their peaks at the opening and closing of the underlying stock markets. With these observations, we align the active hours of an index futures market with its underlying stock market and test the proposed TORB strategies on the DJIA, S&P 500, NASDAQ, HSI, and TAIEX index futures from 2003 to 2013. In the experiments, the proposed strategy achieves over 8% annual returns with p-values less than 3% in all of the five markets; the best performance, 20.28% annual returns at a p-value of 3.1x10^{−5}%, is reached in the TAIEX. For each market, we also find the best probing time, which is relatively short in the US market and relatively long in Asian markets. Furthermore, we conduct experiments on a TAIEX futures transaction dataset to analyze the relationship between the TORB signals and trader behavior, and find the TORB signals are in the same direction as institutional traders, especially foreign investment institutions.

Abstract

A catastrophe equity put (CatEPut) is constructed to recapitalize an insurance company that suffers huge compensation payouts due to catastrophic events (CEs). The company can exercise its CatEPut to sell its stock to the counterparty at a predetermined price when its accumulated loss due to CEs exceeds a predetermined threshold and its own stock price falls below the strike price. Much literature considers the evaluations of a CatEPut that can only be exercised at maturity; however, most CatEPuts can be exercised early so the company can receive timely funding. This paper adopts lattice approaches to evaluate CatEPuts with early exercise features. To solve the combinatorial exposition problem due to the trigger of CatEPuts' accumulated loss, our method reduces the possible number of accumulated losses by taking advantage of the closeness of integral additions. We also identify and alleviate a new type of nonlinearity error that yields unstable numerical pricing results by adjusting the lattice structure. We provide a rigorous mathematical proof to show how the proposed lattice can be constructed under a mild condition. Comprehensive numerical experiments are also given to demonstrate the robustness and efficiency of our lattice.

Abstract

This paper presents the persistent behavior hypothesis for financial markets, which is tested statistically on five stock indices from 2001 to 2014. We find significant results in all five stock markets for the full sample period as well as subperiods. A persistent behavior strategy (PBS) on index futures is also presented, the net annual returns of which are significantly higher than 15% in all futures markets including transaction costs. The best performance, about 27%, occurs in the E-mini NASDAQ 100 and TAIEX futures. We also present studies on the impact of investor behavior over market price of TAIEX futures.

Abstract

We attempt in this paper to utilize soft information in financial reports to analyze financial risk among companies. Specifically, on the basis of the text information in financial reports, which is the so-called soft information, we apply analytical techniques to study relations between texts and financial risk. Furthermore, we conduct a study on financial sentiment analysis by using a finance-specific sentiment lexicon to examine the relations between financial sentiment words and financial risk. A large collection of financial reports published annually by publicly-traded companies is employed to conduct our experiments; moreover, two analytical techniques – regression and ranking methods – are applied to conduct these analyses. The experimental results show that, based on a bag-of-words model, using only financial sentiment words results in performance comparable to using the whole texts; this confirms the importance of financial sentiment words with respect to risk prediction. In addition to this performance comparison, via the learned models, we draw attention to some strong and interesting correlations between texts and financial risk. These valuable findings yield greater insight and understanding into the usefulness of soft information in financial reports and can be applied to a broad range of financial and accounting applications.

Abstract

The growing amount of public financial data makes it more and more important to learn how to discover valuable information for financial decision-making. This paper proposes an approach to discovering financial keywords from a large number of financial reports. In particular, we apply the continuous bag-of-words (CBOW) model, a well-known continuous space language model, to the textual information in 10-K financial reports to discover new finance keywords. In order to capture word meanings to better locate financial terms, we also present a novel technique to incorporate syntactic information into the CBOW model. Experimental results on four prediction tasks using the discovered keywords demonstrate that our approach is effective for discovering predictability keywords for postevent volatility, stock volatility, abnormal trading volume, and excess return predictions. Furthermore, we also analyze the discovered keywords which attest the ability of the proposed method to capture both syntactic and contextual information between words; this shows the success of this method when applied to the field of Finance.

Abstract

Although many different aspects of debt structures such as bond covenants and repayment schedules are empirically found to significantly influence values of bonds and equity, many theoretical structural models still oversimplify debt structures and fail to capture phenomena found in financial markets. This paper proposes a carefully designed structural model that faithfully models typical complex debt structures containing multiple bonds with various covenants. For example, the ability for an issuing firm to meet an obligation is modeled to rely on its ability to meet previous repayments, and the default trigger is shaped according to the characteristics of its debt structure such as the amount and schedule of bond repayments. Thus our framework reliably provides theoretical insight and concrete quantitative measurements consistent with extant empirical research such as the shapes of yield spread curves under various firm's financial statuses, and the impact of payment blockage covenants on newly-issued and other outstanding bonds. We also develop the forest, a novel quantitative method to handle contingent changes in the debt structure due to premature bond redemptions. A forest consists of several trees %arranged in layers, that capture different debt structures, for instance those before or after a bond redemption. This method can be used to analyze how poison put covenants in the target firm's bonds influence the bidder's costs of debt financing for a leveraged buyout, or investigate how the presence of wealth transfer among the remaining claim holders due to a bond redemption influences the firm's call policy, or further reconcile conflicts among previous empirical studies on call delay phenomena.

Abstract

This paper provides a novel and general framework for the problem of searching parameter space in Monte Carlo simulations. We propose a deterministic online algorithm and a randomized online algorithm to search for suitable parameter values for derivative pricing which are needed to achieve desired precisions. We also give the competitive ratios of the two algorithms and prove the optimality of the algorithms. Experimental results on the performance of the algorithms are presented and analyzed as well.

Abstract

This paper presents a general and numerically accurate lattice methodology to price risky corporate bonds. It can handle complex default boundaries, discrete payments, various asset sales assumptions, and early redemption provisions for which closed-form solutions are unavailable. Furthermore, it can price a portfolio of bonds that accounts for their complex interaction, whereas traditional approaches can only price each bond individually or a small portfolio of highly simplistic bonds. Because of the generality and accuracy of our method, it is used to investigate how credit spreads are influenced by the bond provisions and the change in a firm’s liability structure due to bond repayments.

Abstract

We examine the change of levered firm's capital structures due to different investment decisions of realised tax benefits and various sources of fund to finance coupon and dividend payouts. The complexity is analytically intractable but numerical approaches provide insights. Retaining realised tax benefits and investing them in risk-free assets instead of risky ones result in higher debt capacity and optimal firm value. The impact of positive-net-worth bond covenants on shareholders' investment decisions of realised tax benefits and the related agency problem are analysed. The impact of selling firm's asset (to finance payout) on optimal levered firm value is also analysed.

Abstract

With the rapid growth and the deregulation of financial markets, many complex derivatives have been structured to meet specific financial goals. Unfortunately, most complex derivatives have no analytical formulas for their prices, particularly when there is more than one market variable. As a result, these derivatives must be priced by numerical methods such as lattice. However, the nonlinearity error of lattices due to the nonlinearity of the derivative's value function could lead to oscillating prices. To construct an accurate, multivariate lattice, this study proposes a multiphase method that alleviates the oscillating problem by making the lattice match the “critical locations,” locations where nonlinearity of the derivative's value function occurs. Moreover, our lattice has the ability to model the jumps in the market variables such as regular withdraws from an investment account, which is hard to deal with analytically. Numerical results for vulnerable options, insurance contracts guaranteed minimum withdrawal benefit (GMWB), and defaultable bonds show that our methodology can be applied to the pricing of a wide range of complex financial contracts.

Abstract

Complex financial instruments with multiple state variables often have no analytical formulas and therefore must be priced by numerical methods, like lattice ones. For pricing convertible bonds and many other interest rate-sensitive products, research has focused on bivariate lattices for models with two state variables: stock price and interest rate. This paper shows that, unfortunately, when the interest rate component allows rates to grow in magnitude without bounds, those lattices generate invalid transition probabilities. As the overwhelming majority of stochastic interest rate models share this property, a solution to the problem becomes important. This paper presents the first bivariate lattice that guarantees valid probabilities. The proposed bivariate lattice grows (super)polynomially in size if the interest rate model allows rates to grow (super)polynomially. Furthermore, we show that any valid constant-degree bivariate lattice must grow superpolynomially in size with log-normal interest rate models, which form a very popular class of interest rate models. Therefore, our bivariate lattice can be said to be optimal.

Abstract

This article presents a methodology to derive analytical formulas for a class of complicated financial derivatives with a continuously monitored barrier and a few discretely monitored ones. Numerical results based on concrete numbers for the parameters are presented and analyzed.

Abstract

Derivatives are popular financial instruments whose values depend on other more fundamental financial assets (called the underlying assets). As they play essential roles in financial markets, evaluating them efficiently and accurately is critical. Most derivatives have no simple valuation formulas; as a result, they must be priced by numerical methods such as lattice methods. In a lattice, the prices of the derivatives converge to theoretical values when the number of time steps increases. Unfortunately, the nonlinearity error introduced by the nonlinearity of the option value function may cause the pricing results to converge slowly or even oscillate significantly. The lognormal diffusion process, which has been widely used to model the underlying asset’s price dynamics, does not capture the empirical findings satisfactorily. Therefore, many alternative processes have been proposed, and a very popular one is the jump-diffusion process. This paper proposes an accurate and efficient lattice for the jump-diffusion process. Our lattice is accurate because its structure can suit the derivatives’ specifications so that the pricing results converge smoothly. To our knowledge, no other lattices for the jump-diffusion process have successfully solved the oscillation problem. In addition, the time complexity of our lattice is lower than those of existing lattice methods by at least half an order. Numerous numerical calculations confirm the superior performance of our lattice to existing methods in terms of accuracy, speed, and generality.