Implied risk-neutral probability density functions from option prices

Bahra, Bhupinder

doi:10.1016/b978-075066942-9.50011-x

Cited by 19 publications

(23 citation statements)

References 32 publications

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“…7 This follows immediately from the relation between the density functions for return ðg * t;T Þ and security ðf * t;T Þ : g * t;T ðuÞ ¼ S t e u f * t;T ðS t e u Þ. 8 See also Bahra (1996Bahra ( , 1999. 9 For a discussion of the implications of the mixture approach, for example, with respect to the calculation of moments and the structure of the volatility smiles, see Brigo and Mercurio (2002).…”

Section: Rnds As Finite Mixtures Of Log-normal Distributionsmentioning

confidence: 94%

“…7 Ritchey (1990) was among the first to employ a mixture of (normal) distributions in option pricing. Subsequent research, including Bahra (1997), 8 Melick and Thomas (1997), Söderlind and Svensson (1997), Gemmill and Saflekos (2000), Kim and Kim (2003), Rebonato and Cardoso (2004), assumes that the density of the terminal distribution is a linear combination of log-normal densities. 9 A 'natural' economic interpretation is the assumption of multiple alternative regimes.…”

Section: Rnds As Finite Mixtures Of Log-normal Distributionsmentioning

confidence: 98%

“…26 In the special case of the Black/Scholes model, the transformation from the physical to the risk-neutral return distribution only affects the expected value while the standard deviation remains unchanged. In more general cases, Bahra (1997), for example, states that both real and risk-neutral distributions do not usually differ substantially, especially for shortterm options. Therefore, when comparing model-implied moments to future realized values, we expect to detect a functional relation, although its theoretical foundation is not investigated or preliminarily proven.…”

Section: Hypothesesmentioning

confidence: 99%

“…9 A 'natural' economic interpretation is the assumption of multiple alternative regimes. The main advantage of the mixture approach is the high flexibility, allowing the approximation of a large 5 For slightly different typologies see, for example, Bahra (1997). Many models from categories b. and c. are reviewed by Jackwerth (1999).…”

Section: Rnds As Finite Mixtures Of Log-normal Distributionsmentioning

confidence: 99%

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The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market

Wilkens

Röder

2006

Global Finance Journal

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Section: Rnds As Finite Mixtures Of Log-normal Distributionsmentioning

confidence: 94%

Section: Rnds As Finite Mixtures Of Log-normal Distributionsmentioning

confidence: 98%

Section: Hypothesesmentioning

confidence: 99%

Section: Rnds As Finite Mixtures Of Log-normal Distributionsmentioning

confidence: 99%

See 2 more Smart Citations

The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market

Wilkens

Röder

2006

Global Finance Journal

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“…The use of log-normal mixtures to model the risk neutral distribution of S T was initiated by [22] and became further popular even in financial industries by the studies [2], [20] and [26]. The idea is to model the risk neutral density function as a weighted sum of probability density functions of possibly different log-normal distribution.…”

Section: Estimation Using Log-normal Mixturesmentioning

confidence: 99%

Parametric Estimation of Risk Neutral Density Functions

Grith

Krätschmer

2011

Handbook of Computational Finance

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Summary. 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.

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Forward‐Looking Monetary Policy Rules and Option‐Implied Interest Rate Expectations

Sihvonen

Vähämaa

2013

Journal of Futures Markets

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This paper examines the association between option-implied interest rate distributions and macroeconomic expectations in the context of a forward-looking monetary policy rule. We presume that market participants view the policy rule as a guide to the path of future policy rates and price interest rate options in accordance with the policy rule fundamentals. Using data from the UK, we confirm that Libor expectations implied by option prices are consistent with the policy rule variables. The results demonstrate that changes in the distributional form of Libor expectations are strongly associated with changes in the expected inflation and output gaps and financial uncertainty.The original model of Taylor (1993), which was later dubbed "the Taylor rule", is a linear model in which a central bank's target short-term nominal interest rate is defined by the equilibrium real interest rate, current inflation, and the deviations of current inflation and output from their target levels.

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Implied risk-neutral probability density functions from option prices

Cited by 19 publications

References 32 publications

The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market

The informational content of option-implied distributions: Evidence from the Eurex index and interest rate futures options market

Parametric Estimation of Risk Neutral Density Functions

Forward‐Looking Monetary Policy Rules and Option‐Implied Interest Rate Expectations

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