TY - JOUR

T1 - Exact superreplication strategies for a class of derivative assets

AU - Vanden, Joel M.

N1 - Funding Information:
Research support from the Tuck School of Business is gratefully acknowledged. The author thanks an anonymous referee for helpful comments. Any errors are the author’s.

PY - 2006/3/1

Y1 - 2006/3/1

N2 - A superreplicating hedging strategy is commonly used when delta hedging is infeasible or is too expensive. This article provides an exact analytical solution to the superreplication problem for a class of derivative asset payoffs. The class contains common payoffs that are neither uniformly convex nor concave. A digital option, a bull spread, a bear spread, and some portfolios of bull spreads or bear spreads, are all included as special cases. The problem is approached by first solving for the transition density of a process that has a two-valued volatility. Using this process to model the underlying asset and identifying the two volatility values as s min and s max, the value function for any derivative asset in the class is shown to solve the Black-Scholes- Barenblatt equation. The subreplication problem and several related extensions, such as option pricing with transaction costs, calculating superreplicating bounds, and superreplication with multiple risky assets, are also addressed.

AB - A superreplicating hedging strategy is commonly used when delta hedging is infeasible or is too expensive. This article provides an exact analytical solution to the superreplication problem for a class of derivative asset payoffs. The class contains common payoffs that are neither uniformly convex nor concave. A digital option, a bull spread, a bear spread, and some portfolios of bull spreads or bear spreads, are all included as special cases. The problem is approached by first solving for the transition density of a process that has a two-valued volatility. Using this process to model the underlying asset and identifying the two volatility values as s min and s max, the value function for any derivative asset in the class is shown to solve the Black-Scholes- Barenblatt equation. The subreplication problem and several related extensions, such as option pricing with transaction costs, calculating superreplicating bounds, and superreplication with multiple risky assets, are also addressed.

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U2 - 10.1080/13504860500117560

DO - 10.1080/13504860500117560

M3 - Article

AN - SCOPUS:33645703600

VL - 13

SP - 61

EP - 87

JO - Applied Mathematical Finance

JF - Applied Mathematical Finance

SN - 1350-486X

IS - 1

ER -