A note on options and bubbles under the CEV model: implications for pricing and hedging

Dias, José Carlos; Nunes, João Pedro Vidal; Cruz, Aricson César Jesus da

doi:10.1007/s11147-019-09164-x

Cited by 6 publications

(8 citation statements)

References 43 publications

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“…. 8 In addition to the partial differential equation (PDE) method of Tsai (2014) for computing theta when imposing the theta-matching condition, Larguinho et al (2013) and Dias et al (2019), respectively, provide closed-form solutions of theta under the risk-neutral measure given by…”

Section: Static Replication Methods Under the Cev Modelmentioning

confidence: 99%

“…Table 3 shows the static Column 13 gives the value after applying Richardson extrapolation from 4-time-step DEK to 64-time-step DEK. When imposing the theta-matching condition in the case of the modified DEK method, we employ the theta solutions of Larguinho et al (2013) and Dias et al (2019) coupled with the Benton and Krishnamoorthy (2003) algorithm in the implementation of the noncentral chi-square cumulative distribution function for comparison. Column 14 presents the "exact" (i.e., benchmark) prices offered by the transformed trinomial tree of Boyle and Tian (1999) with 20,000 time-steps.…”

Section: Numerical Experiments and Analysesmentioning

confidence: 99%

“…SeeLarguinho et al (2013) andDias, Nunes, and Cruz (2019). Note that the theta function of a European call for the case of β > 2 given by (A18) inLarguinho et al (2013) is derived with the European call option formula with bubbles and is different from the one given byDias et al (2019).…”

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confidence: 99%

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Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

Guo

Chang

2020

Journal of Futures Markets

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This paper proposes an accelerated static replication approach for continuous European-style barrier options by employing the repeated Richardson extrapolation technique with the Romberg sequence. This approach is developed under the constant elasticity of variance (CEV) model of Cox (1975) and Cox and Ross (1976) using the framework offered by Derman, Ergener, and Kani (1995; DEK) and its modified method of Chung et al. (2010, 2013a, 2013b) andTsai (2014). The numerical results indicate that our method could significantly reduce replication errors for European knock-out call options and may be superior to the imposition of the theta-matching condition on the DEK method.

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Section: Static Replication Methods Under the Cev Modelmentioning

confidence: 99%

Section: Numerical Experiments and Analysesmentioning

confidence: 99%

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Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

Guo

Chang

2020

Journal of Futures Markets

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“…This calibration procedure is standard in the literature and it ensures that CEV models with different values of have the same variance at the beginning of the simulation period, which allows us to make valid comparisons between different CEV models. Additional background on the CEV diffusion process can be consulted, for instance, in Davydov and Linetsky (2001), Dias and Nunes (2011), Larguinho et al (2013), Dias et al (2015) and Dias et al (2020).…”

Section: Setup Of the Modelmentioning

confidence: 99%

Pricing levered warrants under the CEV diffusion model

Glória,

Dias,

Cruz

2024

Rev Deriv Res

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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.

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“…The setting with −1 < β ≤ 0 and constant coefficients µ and σ is studied deeply for instance in Delbaen and Shirakawa [30], where the existence of an equivalent martingale measure is proved and considerations on absence of arbitrage are provided. For further details we also refer to, e.g., Dias et al [31], Heath and Schweizer [32].…”

Section: A Regime Switching Insurance-financial Market Modelmentioning

confidence: 99%

Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

2021

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In this paper, we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the optimal investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.

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A note on options and bubbles under the CEV model: implications for pricing and hedging

Cited by 6 publications

References 43 publications

Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

Pricing levered warrants under the CEV diffusion model

Optimal Investment and Proportional Reinsurance in a Regime-Switching Market Model under Forward Preferences

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