An option to reduce transaction costs

Jonathan Goodman, Daniel N. Ostrov

Research output: Contribution to journalArticle

Abstract

For small transaction costs, we determine the leading order optimal dynamic trading strategy of a portfolio of stock, cash, and options. Except for the transaction costs, our market assumptions are those of Black, Scholes, and Merton. Without transaction costs, the option is redundant in the portfolio. With transaction costs, however, we show that adding the option to the portfolio can significantly reduce overall trading costs compared to optimal strategies that use only stock and cash. The analysis is based on an asymptotic expansion with three scales: macroscopic, mesoscopic, and microscopic. The macroscopic analysis is Merton's optimal investment problem. Within a plane defined by the amount of stock and options held, the macroscopic analysis yields a Merton line of optimal portfolios. We show that there is a particular magic point on the Merton line that minimizes expensive stochastic movement away from the Merton line. The mesoscopic scale governs less expensive deviations of the portfolio away from the magic point but along the Merton line. The microscopic scale governs the more expensive deviations of the portfolio away from the magic point, transverse to the Merton line. The resulting strategy is related to commonly used Delta and Gamma hedging strategies, but our scale analysis implies that some rebalancings are much more effective than others. We do not give rigorous mathematical proofs, only arguments of formal applied mathematics.

Original languageEnglish (US)
Pages (from-to)512-537
Number of pages26
JournalSIAM Journal on Financial Mathematics
Volume2
Issue number1
DOIs
StatePublished - 2011

Fingerprint

Transaction Costs
Line
Costs
Deviation
Trading Strategies
Black-Scholes
Optimal Investment
Optimal Portfolio
Hedging
Optimal Strategy
Applied mathematics
Asymptotic Expansion
Transverse
Transaction costs
Minimise
Imply
Cash

Keywords

  • Asymptotics
  • Merton strategy
  • Optimal rebalancing
  • Transaction costs

ASJC Scopus subject areas

  • Applied Mathematics
  • Numerical Analysis
  • Finance

Cite this

An option to reduce transaction costs. / Goodman, Jonathan; Ostrov, Daniel N.

In: SIAM Journal on Financial Mathematics, Vol. 2, No. 1, 2011, p. 512-537.

Research output: Contribution to journalArticle

Goodman, Jonathan ; Ostrov, Daniel N. / An option to reduce transaction costs. In: SIAM Journal on Financial Mathematics. 2011 ; Vol. 2, No. 1. pp. 512-537.
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