An Improved Convex Model for Efficient Estimation of Option Implied Surfaces
(English)Manuscript (preprint) (Other academic)
Estimation of option implied surfaces that are consistent with observed market prices and stable over time is a fundamental problem in finance. This paper develops a general optimization based framework for estimation of the option implied risk-neutral density (RND) surface, while satisfying no-arbitrage constraints. Our developed framework considers all types of realistic surfaces and is hence not constrained to a certain function class. When solving the problem the RND is discretized, which leads to an optimization model where it is possible to formulate the constraints as linear constraints, making the resulting large-scale optimization problem convex and the solution a global optimum. This is a major advantage of our method compared to most estimation algorithms described in the literature, which are typically cast as non-convex optimization problems with multiple local optima. We show that our method produces smooth local volatility surfaces that can be used for pricing and hedging of exotic derivatives. The stability of our method is demonstrated through a time series study based on historical prices of S&P 500 index options.
Risk-neutral density surface; Non-parametric estimation; Optimization; No-arbitrage constraints; Implied volatility surface; Local volatility surface
Economics and Business
IdentifiersURN: urn:nbn:se:liu:diva-117101OAI: oai:DiVA.org:liu-117101DiVA: diva2:805716