Multiperiod conditional valuation of barrier options with incomplete information

Abstract

In this paper, we provide analytical valuation results for barrier options with three different types of information: continuous observations of the underlying asset value, delayed continuous observations and multiple discrete observations. Market, counterparty credit risk management and economic risk capital implications of the valuations with incomplete information are also discussed. We obtain precise analytical solutions using all the information generated by the previous discrete observations of the underlying asset, generated in a consistent fashion by path-dependent simulation. Our results have far-reaching implications for economic capital charges on path-dependent derivatives. We demonstrate that using non-conditional valuation mis-estimates the credit charges on the barrier options with respect to the precise credit charges computed with valuations conditional on the actual available information. The rest of this paper is organized as follows. Section 2 describes the classical case with full, continuous information about the underlying asset. Section 3 deals with the case of delayed continuous information. Section 4 investigates the case of discrete observations at multiple discrete times. Section 5 offers explicit closed-form solutions for the main types of single-barrier options with discrete information and parity results. Section 6 provides valuation results for double-barrier options. Section 7 presents risk management applications for foreign exchange (FX) barrier options, while section 8 concludes our paper.