Abstract

Much of the work on the valuation of levered (and unlevered) warrants assumes that the volatility of the underlying state variable is constant. This paper extends the literature on warrant pricing to a more general assumption for the state variable process, the so-called constant elasticity of variance (CEV) process. The CEV model is well-known for its ability to capture some empirical observations found in the financial economics literature, namely the asymmetry between equity returns and volatility and the implied volatility skew. Using the CEV process, we are able to reduce pricing bias as the volatility becomes a function of the underlying state variable. We price European-style call warrants without restrictions on the debt maturity. When warrants have the same maturity as debt, it is possible to obtain closed-form solutions for warrants prices. When the maturity of warrants is different from the maturity of debt, prices can be computed numerically through very efficient and simple to implement valuation methodologies.

中文翻译：

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CEV扩散模型下的杠杆认股权证定价

摘要

关于杠杆（和无杠杆）认股权证估值的大部分工作都假设基础状态变量的波动性是恒定的。本文将权证定价文献扩展到状态变量过程的更一般假设，即所谓的恒定方差弹性（CEV）过程。CEV 模型因其能够捕捉金融经济学文献中的一些经验观察结果而闻名，即股票回报和波动性之间的不对称性以及隐含波动性偏差。使用 CEV 流程，我们能够减少定价偏差，因为波动性成为基础状态变量的函数。我们对欧式认购权证进行定价，对债务期限没有限制。当认股权证与债务具有相同的期限时，可以获得认股权证价格的封闭式解。当认股权证的到期日与债务的到期日不同时，可以通过非常有效且易于实施的估值方法以数字方式计算价格。