Can the Black-Scholes Model Survive under Transaction Costs? An Affirmative Answer
37 Pages Posted: 14 Mar 2008
Date Written: February 20, 2008
Abstract
We examine the stochastic dominance bounds for call options in the presence of proportional transaction costs, developed in a discrete time and for a discrete or continuous state model of the returns of the underlying asset by Constantinides and Perrakis (CP, 2002, 2007). We consider a lognormal diffusion model of these returns and we formulate a discrete time trading version that converges to diffusion as the time partition becomes progressively more dense. Given the existence of a partition-independent and tight upper bound already derived in CP (2002), we focus on the lower bound, for which the results of that study were not available in a useful formulation. We then show that the CP lower bound for European call options converges to a non-trivial and tight limit that is a function of the transaction cost parameter. This limit defines a reservation purchase price under realistic trading conditions for the call options. The limit is a Black-Scholes type expression that becomes equal to the exact Black-Scholes value if the transaction cost parameter is set equal to zero, thus providing the only known generalization of the Black-Scholes model that produces useful results under transaction costs. We also develop a novel numerical algorithm that computes the CP lower bound for any discrete time partition and converges to the theoretical continuous time limit in a relatively small number of iterations. Last, we extend the lower bound results to American index options.
Keywords: option pricing, option bounds,incomplete markets, stochastic dominance, transaction costs, diffusion processes
JEL Classification: G12, G13
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