Lihui Zheng () (Department of Economics and Finance, Tonghi University) Jin E. Zhang (Department of Economics and Finance, City University of Hong Kong)
Abstract
This paper studies the option pricing problem with transaction costs in the framework of robust control. In particular, we model uncertainty in stock price as unknown, deterministic functions with an ‘a priori’ bound on its L2 norm, and the hedging and pricing of options are considered in terms of the worst case of the uncertainty. First, an optimization criterion is proposed such that the optimal strategy has the lowest sensitivity to misspecification in the uncertainty bound. Then this sensitivity optimization problem is formulated as a differential game, based on which option prices are defined in the framework of robust control. By reducing dimension of the game, we obtain an expression for the option price, which is discounted value function of the reduced game. We also derive a variational inequality for the value function and prove existence and uniqueness of the Partial Differential Equation (PDE). Finally, a finite-difference scheme is provided to solve the PDE and computer simulations are performed. The results of this paper show that the robust control approach has many advantages over the traditional stochastic methods for the option pricing problem with transaction costs.
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Publisher Info
Paper provided by East Asian Bureau of Economic Research in its series Finance Working Papers with number
233.
Length: 32 pages Date of creation: Mar 2000 Date of revision: Handle: RePEc:eab:financ:233
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Find related papers by JEL classification: G12 - Financial Economics - - General Financial Markets - - - Asset Pricing G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General
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