Option Pricing with Differential Interest Rates

Yaacov Z Bergman

The Review of Financial Studies, 1995, vol. 8, issue 2, 475-500

Abstract: The classic option pricing model is generalized to a more realistic, imperfect, dynamically incomplete capital market with different interest rates for borrowing and for lending and a return differential between long and short positions in stock. It is found that, in the absence of arbitrage opportunities, the equilibrium price of any contingent claim must lie within an arbitrage-band. The boundaries of an arbitrage-band are computed as solutions to a quasi-linear partial differential equation, and, in generals each end-point of such a band depends on both interest rates for borrowing and for lending. This, in turn, implies that the vector of concurrent equilibrium prices of different contingent claims - even claims that are written on different underlying assets - must lie within a computable arbitrage-oval in the price space. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Date: 1995
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