Abstract
With various categories of fuzziness in the market, the factors that influence credit derivatives pricing include not only the characteristic of randomness but also nonrandom fuzziness. Thus, it is necessary to bring fuzziness into the process of credit derivatives pricing. Based on fuzzy process theory, this paper first brings fuzziness into credit derivatives pricing, discusses some pricing formulas of credit derivatives, and puts forward a One-Factor Fuzzy Copula function which builds a foundation for portfolio credit products pricing. Some numerical calculating samples are presented as well.
Highlights
Credit derivatives is a general term for a series of financial engineering technologies which strips, transfers, and hedges credit risks from basic assets
The model results and market data are all gradually decreased with time and they are all falling credit curves; this is in accordance with the current market environment of financial crisis
In the fuzzy random environment, the model results fell faster than the market data; this shows that the fuzziness of the market environment has increased the pessimism of investors’ expectations in the future
Summary
Credit derivatives is a general term for a series of financial engineering technologies which strips, transfers, and hedges credit risks from basic assets. With a general view of the literatures available about credit derivatives pricing, their common characteristic can be summarized as that all the pricing processes are built on the base of the theory of random probability. With a lot of fuzziness of the market, the factors influencing financial products pricing have the characteristic of randomness and nonrandom fuzziness. Fuzzy theory is a powerful tool to deal with all kinds of fuzziness Researches on it offer new theoretical foundation for financial product pricing. Different from random financial mathematics, Liu [3] assumed that the stock price follows geometric Liu process rather than a geometric Brownian motion and offered a new European option pricing model based on his stock price model.
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