Pricing levered warrants under the CEV diffusion model

Carlos Miguel Glória (), José Carlos Dias and Aricson Cruz
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Carlos Miguel Glória: Instituto Universitário de Lisboa (ISCTE-IUL), Business Research Unit (BRU-IUL)
José Carlos Dias: Instituto Universitário de Lisboa (ISCTE-IUL), Business Research Unit (BRU-IUL)
Aricson Cruz: Instituto Universitário de Lisboa (ISCTE-IUL), Business Research Unit (BRU-IUL)

Review of Derivatives Research, 2024, vol. 27, issue 1, No 3, 55-84

Abstract: 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.

Keywords: CEV model; Warrants; Dilution; Debt; Volatility (search for similar items in EconPapers)
JEL-codes: C63 G13 G32 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11147-023-09199-1

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