Fast narrow bounds on the value of Asian options

Abstract

We consider the problem of finding bounds on the value of fixed-strike and floatingstrike Asian options. A good lower bound for both types was derived in Rogers & Shi (1995). We provide an alternative derivation, which leads to a simpler expression for the bound, and also to the bound given by Curran (1992) for fixed-strike options; we derive an analogous bound for floating-strike options. Combining these results with a new upper bound allows the accurate valuation of fixed-strike and floating-strike Asian options for typical parameter values. Keywords: Brownian motion, Asian option, fixed-strike, floating-strike. 1 1 Introduction A fixed-strike Asian (call) option with strike K ? 0 and maturity T on an asset with price process fS t g is a contract with value ( R T 0 S t dt \\Gamma K) + at time T . We assume that T = 1 year and that the asset price follows a geometric Brownian motion S t = S exp(oeB t +ct) where c is a constant, S and oe are positive constants and B t is a Brown...

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