dorsal/arxiv
View SchemaNon-Parametric Extraction of Implied Asset Price Distributions
| Authors | Jerome V. Healy, Maurice Dixon, Brian J. Read, Fang Fang Cai |
|---|---|
| Categories | |
| ArXiv ID | physics/0607240 |
| URL | https://arxiv.org/abs/physics/0607240 |
| DOI | 10.1016/j.physa.2007.02.013 |
Abstract
Extracting the risk neutral density (RND) function from option prices is well defined in principle, but is very sensitive to errors in practice. For risk management, knowledge of the entire RND provides more information for Value-at-Risk (VaR) calculations than implied volatility alone [1]. Typically, RNDs are deduced from option prices by making a distributional assumption, or relying on implied volatility [2]. We present a fully non-parametric method for extracting RNDs from observed option prices. The aim is to obtain a continuous, smooth, monotonic, and convex pricing function that is twice differentiable. Thus, irregularities such as negative probabilities that afflict many existing RND estimation techniques are reduced. Our method employs neural networks to obtain a smoothed pricing function, and a central finite difference approximation to the second derivative to extract the required gradients. This novel technique was successfully applied to a large set of FTSE 100 daily European exercise (ESX) put options data and as an Ansatz to the corresponding set of American exercise (SEI) put options. The results of paired t-tests showed significant differences between RNDs extracted from ESX and SEI option data, reflecting the distorting impact of early exercise possibility for the latter. In particular, the results for skewness and kurtosis suggested different shapes for the RNDs implied by the two types of put options. However, both ESX and SEI data gave an unbiased estimate of the realised FTSE 100 closing prices on the options' expiration date. We confirmed that estimates of volatility from the RNDs of both types of option were biased estimates of the realised volatility at expiration, but less so than the LIFFE tabulated at-the-money implied volatility.
{
"annotation_id": "7abc60c4-29b9-48af-bcd5-7ae26dfe8671",
"date_created": "2026-03-02T18:01:10.908000Z",
"date_modified": "2026-03-02T18:01:10.908000Z",
"file_hash": "e27c38f5fb65db15a6be5aa4a3328767ebaaf636a87803c5f252841229160b97",
"private": false,
"record": {
"abstract": "Extracting the risk neutral density (RND) function from option prices is well\ndefined in principle, but is very sensitive to errors in practice. For risk\nmanagement, knowledge of the entire RND provides more information for\nValue-at-Risk (VaR) calculations than implied volatility alone [1]. Typically,\nRNDs are deduced from option prices by making a distributional assumption, or\nrelying on implied volatility [2]. We present a fully non-parametric method for\nextracting RNDs from observed option prices. The aim is to obtain a continuous,\nsmooth, monotonic, and convex pricing function that is twice differentiable.\nThus, irregularities such as negative probabilities that afflict many existing\nRND estimation techniques are reduced. Our method employs neural networks to\nobtain a smoothed pricing function, and a central finite difference\napproximation to the second derivative to extract the required gradients.\n This novel technique was successfully applied to a large set of FTSE 100\ndaily European exercise (ESX) put options data and as an Ansatz to the\ncorresponding set of American exercise (SEI) put options. The results of paired\nt-tests showed significant differences between RNDs extracted from ESX and SEI\noption data, reflecting the distorting impact of early exercise possibility for\nthe latter. In particular, the results for skewness and kurtosis suggested\ndifferent shapes for the RNDs implied by the two types of put options. However,\nboth ESX and SEI data gave an unbiased estimate of the realised FTSE 100\nclosing prices on the options\u0027 expiration date. We confirmed that estimates of\nvolatility from the RNDs of both types of option were biased estimates of the\nrealised volatility at expiration, but less so than the LIFFE tabulated\nat-the-money implied volatility.",
"arxiv_id": "physics/0607240",
"authors": [
"Jerome V. Healy",
"Maurice Dixon",
"Brian J. Read",
"Fang Fang Cai"
],
"categories": [
"physics.data-an",
"physics.soc-ph",
"q-fin.PR"
],
"doi": "10.1016/j.physa.2007.02.013",
"title": "Non-Parametric Extraction of Implied Asset Price Distributions",
"url": "https://arxiv.org/abs/physics/0607240"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "8d42a125-884c-4184-b587-1eae6d196f72",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}