Bounds on prices of contingent claims in an intertemporal economy with proportional transaction costs and general preferences

Abstract. Analytic bounds on the reservation write price of European-style contingent claims are derived in the presence of proportional transaction costs in a model which allows for intermediate trading. The option prices are obtained via a utility maximization approach by comparing the maximized utilities with and without the contingent claim. The mathematical tools come mainly from the theories of singular stochastic control and viscosity solutions of nonlinear partial differential equations.

[1]  H. Leland..  Option Pricing and Replication with Transactions Costs , 1985 .

[2]  A. Skorohod,et al.  On the possibility of hedging options in the presence of transaction costs , 1997 .

[3]  Guy Barles,et al.  Option pricing with transaction costs and a nonlinear Black-Scholes equation , 1998, Finance Stochastics.

[4]  R. C. Merton,et al.  Continuous-Time Finance , 1990 .

[5]  P. Lions.  Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniqueness , 1983 .

[6]  P. Wilmott,et al.  Hedging Option Portfolios in the Presence of Transaction Costs , 2000 .

[7]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[8]  G. Constantinides.  Multiperiod Consumption and Investment Behavior with Convex Transactions Costs , 1979 .

[9]  P. Ritchken.  On Option Pricing Bounds , 1985 .

[10]  Stephen Figlewski.  Options Arbitrage in Imperfect Markets , 1989 .

[11]  P. Lions.  Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Part I , 1983 .

[12]  E. Grannan,et al.  MINIMIZING TRANSACTION COSTS OF OPTION HEDGING STRATEGIES , 1996 .

[13]  H. Soner,et al.  There is no nontrivial hedging portfolio for option pricing with transaction costs , 1995 .

[14]  H. Soner,et al.  Optimal Investment and Consumption with Transaction Costs , 1994 .

[15]  P. Boyle,et al.  Option Replication in Discrete Time with Transaction Costs , 1992 .

[16]  G. Constantinides,et al.  Bounds on Derivative Prices in an Intertemporal Setting with Proportional Transaction Costs and Multiple Securities , 1999 .

[17]  A. Tourin,et al.  Numerical schemes for investment models with singular transactions , 1994 .

[18]  K. Toft..  On the Mean-Variance Tradeoff in Option Replication with Transactions Costs , 1996, Journal of Financial and Quantitative Analysis.

[19]  D. Liu.  European Option Pricing with Transaction Costs , 2000 .

[20]  R. Uppal,et al.  Optimal Replication of Options with Transactions Costs and Trading Restrictions , 1993, Journal of Financial and Quantitative Analysis.

[21]  Thaleia Zariphopoulou.  Investment-consumption models with transaction fees and Markov-chain parameters , 1992 .

[22]  A. R. Norman,et al.  Portfolio Selection with Transaction Costs , 1990, Math. Oper. Res..

[23]  H. Soner.  Optimal control with state-space constraint I , 1986 .

[24]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[25]  H. Pagès,et al.  DERIVATIVE ASSET PRICING WITH TRANSACTION COSTS , 1992 .

[26]  P. Lions,et al.  Hamilton-Jacobi equations with state constraints , 1990 .

[27]  A. Marco,et al.  Dynamic hedging portfolios for derivative securities in the presence of large transaction costs , 1994 .

[28]  H. Levy.  Upper and Lower Bounds of Put and Call Option Value: Stochastic Dominance Approach , 1985 .

[29]  Stylianos Perrakis,et al.  Option Pricing Bounds in Discrete Time , 1984 .

[30]  P. Lions,et al.  Viscosity solutions of fully nonlinear second-order elliptic partial differential equations , 1990 .

[31]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.