Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2022, Vol. 39 ›› Issue (3): 487-494.doi: 10.3969/j.issn.1005-3085.2022.03.012

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Pricing of Equity Warrant Bond Based on the Theory of Backward Stochastic Differential Equations

MIAO Jie   

  1. School of Mathematics, Guangdong University of Education, Guangzhou 510303
  • Online:2022-06-15 Published:2022-08-15
  • Supported by:
    The 2021 Ministry of Education Industry-University Collaborative Education Project (202102496004); the Natural Science Foundation of Guangdong Province (2017A030310609); the 2019 University-level Teaching Quality and Teaching Reform Project (2019jxgg10).

Abstract:

The backward stochastic differential equation theory builds a bridge between randomness and certainty, which makes it possible for using deterministic strategies to solve random and uncertain problems, and opens up a new way for the pricing of financial products. Thus, the pricing problem of equity warrant bond is studied by using the theory of backward stochastic differential equations. Firstly, under the no arbitrage assumption, the portfolio is reasonably established. Through the self-financing strategy, we derive a backward stochastic differential equation that the price of equity warrant bond satisfies by using the backward sto-chastic differential equation theory. Then, using the nonlinear Feynman-Kac formula, we get a partial differential equation that the price of equity warrant bond follows, and it is proved that the price of equity warrant bond at time 0 is equal to the conditional expectation of the maturity cash flow. The explicit formula for the price of an equity warrant bond is obtained by the martingale method. Finally, taking the equity warrant bond of Masteel as an example, the empirical analysis verifies that the pricing model obtained in this paper is reasonable.

Key words: equity warrant bond, backward stochastic differential equation, Feynman-Kac formula, self-financing strategy

CLC Number: