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A Nonparametric Estimate of the Risk-Neutral Density and Its Applications

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posted on 27.10.2017 by Liyuan Jiang
The risk-neutral density for a future payoff of an asset can be estimated from market option prices that expire on the same date. We reformulate the estimation problem into a double-constrained optimization problem to determine its parameters, which can be efficiently solved using numerical implementations in R. Our proposed nonparametric approach for estimating the risk-neutral density using a step function shows promising results. Firstly, it can recover the risk-neutral density very well with market option prices. Secondly, it provides accurate estimates for option prices with any strike, which further presents a practical way to identify profitable investment opportunities in financial markets. We evaluate our method using options written on S&P 500 over twenty years. The cross-validation study shows that our method performs much better than the cubic spline method proposed in the literature. As an application, our approach can reproduce the market prices of long-term variance swaps reasonably well.

History

Advisor

YANG, JIE

Chair

YANG, JIE

Department

Mathematics, Statistics, and Computer Science

Degree Grantor

University of Illinois at Chicago

Degree Level

Doctoral

Committee Member

YANG, MIN WANG, JING OUYANG, CHENG WANG, FANGFANG

Submitted date

May 2017

Issue date

02/03/2017

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