DERIVATIVE ASSET PRICING WITH TRANSACTION COSTS¹

Abstract

In the modern theory of finance, the valuation of derivative assets is commonly based on a replication argument. When there are transaction costs, this argument is no longer valid. In this paper, we try to address the general problem of finding the optimal portfolio among those which dominate a given derivative asset at maturity. We derive an interval for its price. the upper bound is the minimum amount one has to invest initially in order to obtain proceeds at least as valuable as the derivative asset. the lower bound is the maximum amount one can borrow initially against the proceeds of the derivative asset. We show that, in some instances, this interval may be strictly bounded above by the price of the replicating strategy. Prima facie, the cost of a dominating strategy should appear to be higher than that of the replicating one. But because trading is costly, it may pay to weigh the benefits of replication against those of potential savings on transaction costs. Copyright 1992 Blackwell Publishers.

Approximate option pricing

“…It is easy to see that ordinary European calls and puts can easily be valued in 0 ( n ) time. However, the valuation of Asian calls and puts is a well-known hard problem in finance and much research has been directed at this problem [3,11,25,27,28]. All known valuation methods for these options either use some form of Monte Carlo estimation or use analytic approximations with no error analysis.…”

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

“…They partially correct a result in Leland (1985), showing that such limiting error equals zero only when the level of transaction costs decreases to zero as the revision interval tends to zero. Bensaid et al (1992) deal with a discrete time model with proportional transaction costs and derive optimal portfolios sequentially, finding dominating strategies of the (S,s)-type and a range within which the derivative price should lie, defining its bid-ask spread.…”

Option pricing with transaction costs using a Markov chain approximation

“…Moreover, restricting the form of the hedging strategy to portfolio rebalancing at ÿxed time intervals may not always be the optimum method of managing the risk from an option trade. Bensaid et al (1992), Edirisinghe et al (1993) and Boyle and Tan (1994) replaced the replication strategy with a "super-replicating strategy" in which the hedging portfolio is only required to dominate, rather than replicate, the option payo at maturity. In a discrete-time setting it can sometimes be cheaper to dominate a contingent claim than to replicate it.…”