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Pricing levered warrants under the CEV diffusion model

Author

Listed:
  • 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))

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.

Suggested Citation

  • Carlos Miguel Glória & José Carlos Dias & Aricson Cruz, 2024. "Pricing levered warrants under the CEV diffusion model," Review of Derivatives Research, Springer, vol. 27(1), pages 55-84, April.
    • Handle: RePEc:kap:revdev:v:27:y:2024:i:1:d:10.1007_s11147-023-09199-1
    DOI: 10.1007/s11147-023-09199-1
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    References listed on IDEAS

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    More about this item

    Keywords

    CEV model; Warrants; Dilution; Debt; Volatility;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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