Dynamic hedging portfolios for derivative securities in the presence of large transaction costs

Marco Avellaneda, Antonio Paras

Research output: Contribution to journalArticle

Abstract

We introduce a new class of strategies for hedging derivative securities in the presence of transaction costs assuming lognormal continuous-time prices for the underlying asset. We do not assume necessarily that the payoff is convex as in Leland's work or that transaction costs are small compared to the price changes between portfolio adjustments, as in Hoggard et al.'s work. The type of hedging strategy to be used depends upon the value of the Leland number A = y/2/ir (k/cry/Tt), where k is the round-trip transaction cost, a is the volatility of the underlying asset, and St is the time-lag between transactions. If A <1 it is possible to implement modified Black-Scholes delta-hedging strategies, but not otherwise. We propose new hedging strategies that can be used with A = 1 to control effectively the hedging risk and transaction costs. These strategies are associated with the solution of a nonlinear obstacle problem for a diffusion equation with volatility aA = cr\/l + A. In these strategies, there are periods in which rehedging takes place after each interval 6t and other periods in which a static strategy is required. The solution to the obstacle problem is simple to calculate, and closed-form solutions exist for many problems of practical interest.

Original languageEnglish (US)
Pages (from-to)165-194
Number of pages30
JournalApplied Mathematical Finance
Volume1
Issue number2
DOIs
StatePublished - 1994

Fingerprint

Transaction Costs
Hedging
Derivatives
Derivative
Costs
Obstacle Problem
Volatility
Black-Scholes
Time Lag
Strategy
Transaction costs
Derivative securities
Dynamic hedging
Closed-form Solution
Diffusion equation
Transactions
Nonlinear Problem
Continuous Time
Adjustment
Hedging strategies

Keywords

  • hedging
  • option pricing
  • transaction costs

ASJC Scopus subject areas

  • Finance
  • Applied Mathematics

Cite this

Dynamic hedging portfolios for derivative securities in the presence of large transaction costs. / Avellaneda, Marco; Paras, Antonio.

In: Applied Mathematical Finance, Vol. 1, No. 2, 1994, p. 165-194.

Research output: Contribution to journalArticle

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