The Total Return Swap Pricing Model under Fuzzy Random Environments

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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