### 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 language | English (US) |
---|---|

Pages (from-to) | 165-194 |

Number of pages | 30 |

Journal | Applied Mathematical Finance |

Volume | 1 |

Issue number | 2 |

DOIs | |

State | Published - 1994 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Applied Mathematical Finance*, vol. 1, no. 2, pp. 165-194. https://doi.org/10.1080/13504869400000010

}

TY - JOUR

T1 - Dynamic hedging portfolios for derivative securities in the presence of large transaction costs

AU - Avellaneda, Marco

AU - Paras, Antonio

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

KW - hedging

KW - option pricing

KW - transaction costs

UR - http://www.scopus.com/inward/record.url?scp=84972839713&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972839713&partnerID=8YFLogxK

U2 - 10.1080/13504869400000010

DO - 10.1080/13504869400000010

M3 - Article

VL - 1

SP - 165

EP - 194

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 2

ER -