Automated Option Pricing: Numerical Methods
23 Pages Posted: 5 Dec 2011
Date Written: December 5, 2011
Abstract
In this paper, we investigate model-independent bounds for option prices given market instruments.This super-replication problem can be written as a semi-infinite linear programming problem. As these super-replication prices can be large and the densities Q which achieve the upper bounds quite singular, we restrict Q to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral Weighted Monte-Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.
Keywords: sub/super-replication, model-independent bounds, semi-infinite linear programming, duality, primal-dual interior-point, cutting-plane, risk-neutral weighted Monte-Carlo
JEL Classification: C00, C60
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
Transform Analysis and Asset Pricing for Affine Jump-Diffusions
By Darrell Duffie, Jun Pan, ...
-
Transform Analysis and Asset Pricing for Affine Jump-Diffusions
By Darrell Duffie, Jun Pan, ...
-
The Impact of Jumps in Volatility and Returns
By Michael S. Johannes, Bjorn Eraker, ...
-
Implied Volatility Functions: Empirical Tests
By Bernard Dumas, Jeff Fleming, ...
-
Recovering Risk Aversion from Option Prices and Realized Returns
-
Recovering Probabilities and Risk Aversion from Option Prices and Realized Returns
-
Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options
By Gurdip Bakshi, Nikunj Kapadia, ...
-
Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options
By Nikunj Kapadia, Gurdip Bakshi, ...
-
Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices
By Yacine Ait-sahalia and Andrew W. Lo