Details
| Original language | English |
|---|---|
| Pages (from-to) | 409-444 |
| Number of pages | 36 |
| Journal | Applied Mathematical Finance |
| Volume | 23 |
| Issue number | 6 |
| Publication status | Published - 1 Nov 2016 |
Abstract
The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density based on the implied moments of the implicit European contract under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalized Edgeworth expansion, where the moments of the American density are obtained by a reverse engineering application of the least-squares method. The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness and kurtosis swaps.
Keywords
- American multi-asset options, higher order moments, Multi-asset risk-neutral density
ASJC Scopus subject areas
- Economics, Econometrics and Finance(all)
- Finance
- Mathematics(all)
- Applied Mathematics
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In: Applied Mathematical Finance, Vol. 23, No. 6, 01.11.2016, p. 409-444.
Research output: Contribution to journal › Article › Research › peer review
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TY - JOUR
T1 - A moment-based analytic approximation of the risk-neutral density of American options
AU - Arismendi, J. C.
AU - Prokopczuk, Marcel
PY - 2016/11/1
Y1 - 2016/11/1
N2 - The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density based on the implied moments of the implicit European contract under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalized Edgeworth expansion, where the moments of the American density are obtained by a reverse engineering application of the least-squares method. The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness and kurtosis swaps.
AB - The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density based on the implied moments of the implicit European contract under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalized Edgeworth expansion, where the moments of the American density are obtained by a reverse engineering application of the least-squares method. The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness and kurtosis swaps.
KW - American multi-asset options
KW - higher order moments
KW - Multi-asset risk-neutral density
UR - http://www.scopus.com/inward/record.url?scp=85014730413&partnerID=8YFLogxK
U2 - 10.1080/1350486X.2017.1297726
DO - 10.1080/1350486X.2017.1297726
M3 - Article
AN - SCOPUS:85014730413
VL - 23
SP - 409
EP - 444
JO - Applied Mathematical Finance
JF - Applied Mathematical Finance
SN - 1350-486X
IS - 6
ER -