TY - JOUR
T1 - Importance Sampling for Option Greeks with Discontinuous Payoffs
AU - Tong, Shaolong
AU - Liu, Guangwu
PY - 2016
Y1 - 2016
N2 - The Greeks are derivatives of option price with respect to market parameters and play an important role in financial risk management. Among various simulation methods for estimating the Greeks, the pathwise method typically has a low variance. However, when the option payoff is discontinuous, the pathwise method is not applicable and the Greek involves a conditional expectation taken over a hypersurface that is a probability-zero set. In this paper, we propose an importance sampling (IS) method to estimate this conditional expectation. More specifically, IS is applied in a way that all simulated observations fall into a set constructed by thickening the hypersurface. Allowing the thickness of the set to go to zero then leads to a new representation of the Greek as an ordinary expectation, thus leading to an unbiased estimator. The resulting estimator makes use of the pathwise derivatives and can be viewed as an extension of the pathwise method to cases with discontinuous payoffs. Numerical results show that the proposed IS method works well.
AB - The Greeks are derivatives of option price with respect to market parameters and play an important role in financial risk management. Among various simulation methods for estimating the Greeks, the pathwise method typically has a low variance. However, when the option payoff is discontinuous, the pathwise method is not applicable and the Greek involves a conditional expectation taken over a hypersurface that is a probability-zero set. In this paper, we propose an importance sampling (IS) method to estimate this conditional expectation. More specifically, IS is applied in a way that all simulated observations fall into a set constructed by thickening the hypersurface. Allowing the thickness of the set to go to zero then leads to a new representation of the Greek as an ordinary expectation, thus leading to an unbiased estimator. The resulting estimator makes use of the pathwise derivatives and can be viewed as an extension of the pathwise method to cases with discontinuous payoffs. Numerical results show that the proposed IS method works well.
KW - simulation
KW - importance sampling
KW - risk management
KW - Greek letters
UR - http://www.scopus.com/inward/record.url?scp=84969909637&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84969909637&origin=recordpage
U2 - 10.1287/ijoc.2015.0674
DO - 10.1287/ijoc.2015.0674
M3 - 21_Publication in refereed journal
VL - 28
SP - 223
EP - 235
JO - ORSA journal on computing
JF - ORSA journal on computing
SN - 0899-1499
IS - 2
ER -