Arbeitspapier

Parametric estimation of risk neutral density functions

This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions determining the risk neutral distributions. We we shall differentiate between the direct and the indirect way. Following the direct way, parameter vectors are estimated which characterize the distributions from selected statistical families to model the risk neutral distributions. The idea of the indirect approach is to calibrate characteristic parameter vectors for stochastic models of the asset price processes, and then to extract the risk neutral density function via Fourier methods. For every of the reviewed methods the calculation of option prices under hypothetically true risk neutral distributions is a building block. We shall give explicit formula for call and put prices w.r.t. reviewed parametric statistical families used for direct estimation. Additionally, we shall introduce the Fast Fourier Transform method of call option pricing developed in [6]. It is intended to compare the reviewed estimation methods empirically.

Language
Englisch

Bibliographic citation
Series: SFB 649 Discussion Paper ; No. 2010-045

Classification
Wirtschaft
Estimation: General
Asset Pricing; Trading Volume; Bond Interest Rates
Contingent Pricing; Futures Pricing; option pricing
Subject
risk neutral valuation principle
risk neutral distribution
logprice risk neutral distribution
risk neutral density function
Black Scholes formula
Fast Fourier Transform method
log-normal distributions
mixtures of log-normal distributions
generalized gamma distributions
model calibration
Merton's jump diffusion model
Heston's volatility model
Optionspreistheorie
Risikoneutralität
Statistische Verteilung
Schätztheorie

Event
Geistige Schöpfung
(who)
Grith, Maria
Krätschmer, Volker
Event
Veröffentlichung
(who)
Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk
(where)
Berlin
(when)
2010

Handle
Last update
20.09.2024, 8:22 AM CEST

Data provider

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Object type

  • Arbeitspapier

Associated

  • Grith, Maria
  • Krätschmer, Volker
  • Humboldt University of Berlin, Collaborative Research Center 649 - Economic Risk

Time of origin

  • 2010

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