TY - JOUR
T1 - A new representation of the risk-neutral distribution and its applications
AU - Cui, Zhenyu
AU - Xu, Yuewu
N1 - Publisher Copyright:
© 2022 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2022
Y1 - 2022
N2 - This paper establishes a novel model-free representation of the risk-neutral density in terms of market-observed options prices by combining exact series representations of the Dirac Delta function and the Carr-Madan asset spanning formula. Compared to the widely used method for obtaining the risk-neutral densities via the Breeden–Litzenberger device, our method yields estimates of risk-neutral densities that are model-free, automatically smooth, and in closed-form. The closed-form feature of our new representation makes it ideal for many potential applications including a new model-free representation of the local volatility function in the Dupire's local volatility model. The validity of our method is demonstrated through simulation studies as well as an empirical application using S&P 500 index option data. Extension of the method to higher dimensions is also obtained by extending the spanning formula.
AB - This paper establishes a novel model-free representation of the risk-neutral density in terms of market-observed options prices by combining exact series representations of the Dirac Delta function and the Carr-Madan asset spanning formula. Compared to the widely used method for obtaining the risk-neutral densities via the Breeden–Litzenberger device, our method yields estimates of risk-neutral densities that are model-free, automatically smooth, and in closed-form. The closed-form feature of our new representation makes it ideal for many potential applications including a new model-free representation of the local volatility function in the Dupire's local volatility model. The validity of our method is demonstrated through simulation studies as well as an empirical application using S&P 500 index option data. Extension of the method to higher dimensions is also obtained by extending the spanning formula.
KW - Dirac delta function
KW - Hermite expansion
KW - Risk-neutral distribution
KW - Spanning formula
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U2 - 10.1080/14697688.2021.2013520
DO - 10.1080/14697688.2021.2013520
M3 - Article
AN - SCOPUS:85122851252
SN - 1469-7688
VL - 22
SP - 817
EP - 834
JO - Quantitative Finance
JF - Quantitative Finance
IS - 5
ER -