Fuzzy defaultable bonds

doi:10.1016/j.fss.2008.12.017

Fuzzy Sets and Systems

Volume 160, Issue 18, 16 September 2009, Pages 2597-2607

https://doi.org/10.1016/j.fss.2008.12.017 Get rights and content

Abstract

This paper develops a structural model for defaultable bonds in a fuzzy environment. The numerical results calculated from the closed-form solution show that the fuzziness of the stochastic underlying asset and of bankruptcy costs have material impact on the term structure of credit spreads and the duration of defaultable bonds.

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In this respect, some relevant literature contributions are worth mentioning. Agliardi and Agliardi (2009) propose a fuzzy model for defaultable bonds, by fuzzifying the assets value of the considered firms. In so doing, the Authors face the relevant issue of the management of uncertainty when dealing with some types of financial data.
Multiple structural breaks detection for Interval-Valued Time Series (IVTS) is undoubtedly relevant under practical perspectives and challenging under the point of view of the analysis of expert systems. In this respect, financial time series usually show high variability and outliers; moreover, they often exhibit the property of being of high frequency nature; thus, it is naturally advisable to consider them as IVTS type for a given time unit. Despite this relevance, scarce effort has been spent by scholars to apply the methodological advancements in breaks detection for IVTS to the crucial environment of financial time series. This paper contributes to fill this gap. It employs the Atheoretical Regression Trees framework – a very recent tool that is able to automatically locale multiple breaks occurring to unknown dates – to stock prices. Such a procedure is able to estimate in an efficient way the structural breaks of the considered series; at the same time, it keeps into account the main characteristics of the intervals describing the IVTS. For our purposes, we adopt a theoretical proposal of reading daily stock prices as intervals whose bounds are defined through the closing prices. Empirical experiments on the American International Group – whose daily prices have experienced structural breaks in the past – validate the theoretical model and show the usefulness of the proposed procedure.
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Fuzzy methodologies have been widely used in finance to capture a second level of uncertainty—adding to the stochastic environment which is modeled throughout probabilistic tools—and to mimic human behavior. Financial applications of fuzzy methodologies include option pricing theory (Yoshida [18], Kukolj et al. [12]), trading decisions (Gradojevic [8]), structural models for defaultable bonds (Agliardi & Agliardi [1]), reduced-form models for credit derivatives (Wu and Zhuang [17]), technical trading indicators in high frequency finance (Gradojevic [7]), reinforced learning of agent-based systems (Bekiros [5]). Fig. 4 depicts the last submitted order in the extreme situation where all previous orders have not been successful: most quotes are negative (aggressive orders) because, in this scenario, the trader is pressed by the urgency of hitting his target, i.e. the purchase of 300 shares.
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The idea of fuzzifying credit risk models is little exploited, especially in a reduced-form model. Agliardi and Agliardi [15] propose a fuzzy pattern of structural credit risk model, similar literature still can refer to Agliardi and Agliardi [16]. However, this article will puts forward a brand-new default intensity model with randomness and fuzziness, and fuzzifies the market risk-free interest rate and default recovery rate at the same time.
The external shocks and internal contagion are the important sources of default events. However, the external shocks and internal contagion effect on the company is not observed, we cannot get the accurate size of the shocks. The information of investors relative to the default process exhibits a certain fuzziness. Therefore, using randomness and fuzziness to study such problems as derivative pricing or default probability has practical needs. But the idea of fuzzifying credit risk models is little exploited, especially in a reduced-form model. This paper proposes a new default intensity model with fuzziness and presents a fuzzy default probability and default loss rate, and puts them into default debt and credit derivative pricing. Finally, the simulation analysis verifies the rationality of the model. Using fuzzy numbers and random analysis one can consider more uncertain sources in the default process of default and investors’ subjective judgment on the financial markets in a variety of fuzzy reliability so as to broaden the scope of possible credit spreads.
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Ambiguity is pervasive in many environments and is increasingly being introduced into economic and financial models. This paper characterises ambiguity in the form of newly defined Choquet random walks: discrete-time binomial trees with capacities instead of exact probabilities on their branches. We describe the axiomatic basis of Choquet random walks, including dynamic consistency. We also discuss the convergence of Choquet random walks to Choquet–Brownian motion in continuous time. In contrast to previous literature, we derive tractable stochastic processes that allow for a wide range of ambiguity preferences to be represented in continuous time (including ambiguity-seeking preferences). Finally, we apply Choquet–Brownian ambiguity to a model of stationary inter-temporal portfolio choice. We find that both the mean and the variance of the underlying stochastic process are modified. This result opens the way for qualitative and quantitative results that differ from those of standard expected utility models and other models that feature ambiguity.
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Fuzzy defaultable bonds

Abstract

Fuzzy Sets and Systems

Fuzzy Sets and Systems

Information Sciences

European Journal of Operation Research

Journal of Financial Economics

Information and Control

Journal of Banking and Finance

A further empirical investigation of the bankruptcy cost question

Journal of Finance

Corporate Financial Distress and Bankruptcy: Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt

The cost of bankruptcy: Chapter 7 liquidation versus Chapter 11 reorganization

Journal of Finance

Default risk and the duration of zero coupon bonds

Journal of Finance