### Abstract

This paper demonstrates that the risk neutral valuation relationship (RNVR) exists when the aggregate wealth and the underlying variable for derivatives follow a distribution from the family of transformed beta distributions. Specifically, the asset specific pricing kernel (ASPK) is solved for the generalized beta (GB) distribution class, which is extremely flexible to describe various shapes of underlying distributions. With the ASPK in hand, preference free call option formulas are obtained for rescaled and shifted beta distribution of the first kind (RSB1) and for the second kind (RSB2). These distributions include many well known important distributions as special cases. If the preference free formula does not exist under the GB distribution class, then the call price is shown to be numerically calculated without information of preference parameters once the spot price of the underlying is given.

Original language | English |
---|---|

Pages (from-to) | 297-332 |

Number of pages | 36 |

Journal | Review of Derivatives Research |

Volume | 13 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2010 |

### Fingerprint

### Keywords

- Asset specific pricing kernel
- Generalized beta distribution
- Implied volatility
- Risk neutral valuation relationship

### ASJC Scopus subject areas

- Finance
- Economics, Econometrics and Finance (miscellaneous)

### Cite this

**Equilibrium preference free pricing of derivatives under the generalized beta distributions.** / Ikeda, Masayuki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Equilibrium preference free pricing of derivatives under the generalized beta distributions

AU - Ikeda, Masayuki

PY - 2010

Y1 - 2010

N2 - This paper demonstrates that the risk neutral valuation relationship (RNVR) exists when the aggregate wealth and the underlying variable for derivatives follow a distribution from the family of transformed beta distributions. Specifically, the asset specific pricing kernel (ASPK) is solved for the generalized beta (GB) distribution class, which is extremely flexible to describe various shapes of underlying distributions. With the ASPK in hand, preference free call option formulas are obtained for rescaled and shifted beta distribution of the first kind (RSB1) and for the second kind (RSB2). These distributions include many well known important distributions as special cases. If the preference free formula does not exist under the GB distribution class, then the call price is shown to be numerically calculated without information of preference parameters once the spot price of the underlying is given.

AB - This paper demonstrates that the risk neutral valuation relationship (RNVR) exists when the aggregate wealth and the underlying variable for derivatives follow a distribution from the family of transformed beta distributions. Specifically, the asset specific pricing kernel (ASPK) is solved for the generalized beta (GB) distribution class, which is extremely flexible to describe various shapes of underlying distributions. With the ASPK in hand, preference free call option formulas are obtained for rescaled and shifted beta distribution of the first kind (RSB1) and for the second kind (RSB2). These distributions include many well known important distributions as special cases. If the preference free formula does not exist under the GB distribution class, then the call price is shown to be numerically calculated without information of preference parameters once the spot price of the underlying is given.

KW - Asset specific pricing kernel

KW - Generalized beta distribution

KW - Implied volatility

KW - Risk neutral valuation relationship

UR - http://www.scopus.com/inward/record.url?scp=77956885316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956885316&partnerID=8YFLogxK

U2 - 10.1007/s11147-010-9051-4

DO - 10.1007/s11147-010-9051-4

M3 - Article

AN - SCOPUS:77956885316

VL - 13

SP - 297

EP - 332

JO - Review of Derivatives Research

JF - Review of Derivatives Research

SN - 1380-6645

IS - 3

ER -