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A convertible bond is a bond that can be converted into a certain amount of the company’s stock at specified prices and dates. Convertible bonds are usually issued by young, growing companies that want to raise capital without giving up too much control of their company. For example, a company might issue a $1,000 bond that can be converted into 100 shares of the company’s stock at $10 per share. If the company’s stock price increases to $20 per share, the bondholder can convert their bond into shares and immediately sell them for a $1,000 profit.
Since a convertible bond is part debt, part equity, its valuation is more complex. Reference [1] summarized well the challenging problems when pricing a convertible bond,
Convertible bonds are an important segment of the corporate bond market, however, as hybrid instruments, convertible bonds are difficult to value because they depend on variables related to the underlying stock, the fixed-income part, and the interaction between these components. Besides, embedded options, such as conversion, call, and put provisions are often restricted to certain periods, may vary over time, and are subject to additional path-dependent features of the state variables. Moreover, the most challenging problem in convertible bond valuation is the underlying stock return process modeling as it retains various complex statistical properties.
The usual methods for pricing convertible bonds are:
- Binomial or trinomial trees
- Partial Differential Equations
- Monte-Carlo simulations
The article proposed a novel approach based on neural networks for pricing convertible bonds,
In this paper, we propose DeepPricing, a novel data-driven convertible bonds pricing model, which is inspired by the recent success of generative adversarial networks (GAN), to address the above challenges. The method introduces a new financial time-series generative adversarial networks (FinGAN), which is able to reproduce risk-neutral stock return process that retains the unique statistical properties such as the fat-tailed distributions, the long-range dependence, and the asymmetry structure etc., and then transit to its risk-neutral distribution. Thus it is more flexible and accurate to capture the dynamics of the underlying stock return process and keep the rich set of real-world convertible bond specifications compared with previous model-driven models.
The authors tested their method in the Chinese market and the results are promising.
References
[1] Xiaoyu Tan , Zili Zhang, Xuejun Zhao, and Shuyi Wang, DeepPricing: pricing convertible bonds based on financial time-series generative adversarial networks, Financial Innovation (2022) 8:64
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