Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis

Melick, William R.; Thomas, Charles P.

doi:10.2307/2331318

Cited by 331 publications

(222 citation statements)

References 33 publications

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“…Mixtures of three lognormals were introduced by Melick and Thomas (1997) and then reduced to two lognormals in Bahra (1997). The original spline approach was introduced by Shimko (1993) and refined in Panigirtzoglou (2002, 2004).…”

Section: The Pricing Kernel Puzzlementioning

confidence: 99%

The pricing kernel puzzle: survey and outlook

Cuesdeanu

Jackwerth

2017

Ann Finance

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Section: The Pricing Kernel Puzzlementioning

confidence: 99%

The pricing kernel puzzle: survey and outlook

Cuesdeanu

Jackwerth

2017

Ann Finance

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“…Relaxing the normality assumption of the Black-Scholes model led to parametric (Melick andThomas, 1997, Lim et al, 1998) and semi-parametric (Aït-Sahalia and Lo, 1998) option pricing models. Despite the theoretical appeal of parametric models stemming from their stringent parametric assumptions that allow for simpler functional forms, non-parametric models are more flexible in relaxing the distributional assumptions 1 See Garcia et al (2004) for a recent review.…”

Section: Introductionmentioning

confidence: 99%

Option Pricing With Modular Neural Networks

Gradojević

Gençay

2007

SSRN Journal

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This paper applies a non-parametric modular neural network (MNN) model to price the S&P500 European call options. The modules are defined based on time to maturity and moneyness of the options. The option price function of interest is homogenous of degree one with respect to the underlying index price and the strike price. We find that modularity improves the generalization properties of standard feedforward neural network option pricing models (with and without the homogeneity hint), relative to the Black-Scholes model. This improvement is found to be an increasing function of the number of modules used in an MNN.

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“…The literature on mixtures is enormous and it is impossible to do justice to all this literature here. We just hint at the fact that static mixtures of distributions had been postulated in the past to fit option prices for a given maturity, see for example [24], where a mixture of normal densities for the density of the asset log-returns under the pricing measure is assumed, and subsequently [8,16,20]. In the last decade [2,9,10] have extended the mixture distributions to fully dynamic arbitrage-free stochastic processes for asset prices.…”

Section: Remark 1 (Mixtures For Heavy-tailed and Skewed Distributions)mentioning

confidence: 99%

A Random Holding Period Approach for Liquidity-Inclusive Risk Management

Brigo

Nordio

2015

Innovations in Quantitative Risk Management

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Within the context of risk integration, we introduce risk measurement stochastic holding period (SHP) models. This is done in order to obtain a 'liquidityadjusted risk measure' characterized by the absence of a fixed time horizon. The underlying assumption is that-due to changes in market liquidity conditions-one operates along an 'operational time' to which the P&L process of liquidating a market portfolio is referred. This framework leads to a mixture of distributions for the portfolio returns, potentially allowing for skewness, heavy tails, and extreme scenarios. We analyze the impact of possible distributional choices for the SHP. In a multivariate setting, we hint at the possible introduction of dependent SHP processes, which potentially lead to nonlinear dependence among the P&L processes and therefore to tail dependence across assets in the portfolio, although this may require drastic choices on the SHP distributions. We also find that increasing dependence as measured by Kendall's tau through common SHPs appears to be unfeasible. We finally discuss potential developments following future availability of market data. This chapter is a refined version of the original working paper by Brigo and Nordio (2010) [14].

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Recovering an Asset's Implied PDF from Option Prices: An Application to Crude Oil during the Gulf Crisis

Cited by 331 publications

References 33 publications

The pricing kernel puzzle: survey and outlook

The pricing kernel puzzle: survey and outlook

Option Pricing With Modular Neural Networks

A Random Holding Period Approach for Liquidity-Inclusive Risk Management

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