Abstract
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.
Highlights
Credit derivatives pricing is a mathematical modeling process derived from the real world, where the environment of the existing and dependent markets has various random and fuzzy characteristics
Let ã be a fuzzy subset of R, if the following conditions are satisfied: (1) ã is a normal and convex fuzzy set, (2) its membership function μã(x) is upper semicontinuous, and (3) the γ-cut set ãγ is bounded for each γ ∈ [0, 1]; ã is called a fuzzy number [31]
The total return swap is a special type of credit derivative; the two sides involved in the contract are generally banks and hedge funds
Summary
Credit derivatives pricing is a mathematical modeling process derived from the real world, where the environment of the existing and dependent markets has various random and fuzzy characteristics. Buckley [1] was the first scholar to introduce fuzzy information into financial analysis He built a new future value, present value, and internal rate of return into the fuzzy form expression, based on the theory of fuzzy mathematics. We use a structural model to infer the probability of default of the reference asset and get the explicit fuzzy form expression of the total return swap pricing model The advantages of this model lie in the following: can we consider the uncertainty of the value jump diffusion process, but we can consider the reliability of an investor’s subjective judgment of the fuzzy information presented to him in the financial market (the subjective judgment of fuzzy information and the assumption of risk neutral pricing are not in conflict). An appropriate price range will give investors more flexibility in making a choice and make the model results more precisely representative of the actual market environment
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