Bond pricing under imprecise information

Agliardi, Elettra; Agliardi, Rossella

doi:10.1007/s12351-010-0087-x

Cited by 11 publications

(10 citation statements)

References 24 publications

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“…However, as far as we know, there are few about credit risk analysis and derivatives pricing model under fuzzy environments. E.Agliardi and R.Agliardi [19][20] first proposed a structural model for defaultable bonds in a fuzzy environment, they assumed the assets value is a fuzzy stochastic process, the assumption is related to the investors' subjective belief about the reliability of the accounting data of the firm, and the duration analysis show that the fuzziness of the stochastic underlying assets have material impact on the term structure of credit spreads. Vassiliou 21 proved that a fuzzy market is viable if and only if an equivalent martingale measure exists, and constructed the forward probability measure, described the evolution of credit migration of a defaultable bond as an inhomogeneous semi-Markov process with fuzzy states, and investigated the asymptotic behaviour of the survival probability in each fuzzy state given in the absence of default.…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

A New Default Intensity Model with Fuzziness and Hesitation

Wu¹,

Zhuang²,

Li³

2016

IJCIS

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With the increased financial market volatility, corporate defaults will suffer from the double impact of the external shocks and internal contagion effects. In the existing stochastic default intensity models, the valuation of sensitivity parameters requires a lot of historical data, however, the limited market data does not guarantee the accuracy of parameter estimation, meanwhile, due to the people have a lot of fuzziness and hesitation judgements on the default process, it is necessary for us to let the corresponding random parameter of the default intensity to be a triangular intuitionistic fuzzy interval value. In this paper, we propose a new default intensity model based on the external shocks and internal contagion effects, and introduce the triangular intuitionistic fuzzy numbers into the credit default swaps (CDS) pricing modeling to describe the fuzziness and hesitation of the default process. In the end, we get a new fuzzy form pricing formula for CDS, and by the simulation analysis, we obtain that, all kinds of fuzziness and hesitation of the market have significant impact on credit spreads, and a model result with a consideration of the fair price of CDS in a fuzzy random environment including a pure random environment result. Compared with the existing stochastic model, these proper interval results can offer the investors more flexible options and can more reflect the impact of market environment on credit spreads.

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Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

A New Default Intensity Model with Fuzziness and Hesitation

Wu¹,

Zhuang²,

Li³

2016

IJCIS

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“…This prevents us from determining the size of shocks accurately. Therefore, inspired by [14][15][16][17][18], fuzzy set theory is adopted to study a looping default credit default swap (CDS) pricing model under uncertain environments. Following this, we set up a new fuzzy form pricing formula for CDS, the simulation analysis of which shows that all kinds of fuzziness in the market have a significant impact on credit spreads.…”

Section: Introductionmentioning

confidence: 99%

A New Default Probability Calculation Formula and Its Application under Uncertain Environments

Mei

2018

Discrete Dynamics in Nature and Society

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In the real world, corporate defaults will be affected by both external market shocks and counterparty risks. With this in mind, we propose a new default intensity model with counterparty risks based on both external shocks and the internal contagion effect. The effects of the external shocks and internal contagion on a company cannot, however, be observed, as uncertainty in the real world contains both randomness and fuzziness. This prevents us from determining the size of the shocks accurately. In this study, fuzzy set theory is utilized to study a looping default credit default swap (CDS) pricing model under uncertain environments. Following this, we develop a new fuzzy form pricing formula for CDS, the simulation analysis of which shows that all kinds of fuzziness in the market have a significant impact on credit spreads, and that the credit spreads, relative to the degree of external shock fuzziness, are much more sensitive. Nevertheless, for a certain degree of fuzziness in the market, credit spreads, relative to changes in counterparty risk, are much more sensitive. Using random analysis and fuzzy numbers, one can think of even more uncertain sources at play than the processes of looping default and investor subjective judgment on the financial markets, and this broadens the scope of possible credit spreads. Compared to the existing related literature, our new fuzzy form CDS pricing model with counterparty risk can consider more factors that influence default and is closer to the reality of the complexity of the dynamics of default. It can also employ the membership function to describe the fuzzy phenomenon, enable the fuzzy phenomenon to be estimated in two kinds of state, and can simultaneously reflect both the fuzziness and randomness in financial markets.

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“…Almost all the literature, however, concentrates on option pricing problems; there has been very little work on credit derivative pricing in fuzzy random environments. When E. Agliardi and R. Agliardi [24,25] first introduced the fuzzy tool into credit risk analysis, they proposed a structural model for defaultable bonds in a fuzzy environment and derived a fuzzy form pricing model for the defaultable bonds. Vassiliou [26] proved that a fuzzy market is viable if and only if an equivalent Martingale measure exists.…”

Section: Introductionmentioning

confidence: 99%

The Total Return Swap Pricing Model under Fuzzy Random Environments

Wang

Liu

et al. 2017

Discrete Dynamics in Nature and Society

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This paper models the jump amplitude and frequency of random parameters of asset value as a triangular fuzzy interval. In other words, we put forward a new double exponential jump diffusion model with fuzziness, express the parameters in terms of total return swap pricing, and derive a fuzzy form pricing formula for the total return swap. Following simulation, we find that the more the fuzziness in financial markets, the more the possibility of fuzzy credit spreads enlarging. On the other hand, when investors exhibit stronger subjective beliefs, fuzzy credit spreads diminish. Using fuzzy information and random analysis, one can consider more uncertain sources to explain how the asset price jump process works and the subjective judgment of investors in financial markets under a variety of fuzzy conditions. An appropriate price range will give investors more flexibility in making a choice.

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Bond pricing under imprecise information

Cited by 11 publications

References 24 publications

A New Default Intensity Model with Fuzziness and Hesitation

A New Default Intensity Model with Fuzziness and Hesitation

A New Default Probability Calculation Formula and Its Application under Uncertain Environments

The Total Return Swap Pricing Model under Fuzzy Random Environments

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