Since the birth of the Chicago Board of Options Exchange (CBOE), the option market has grown dramatically in its trading volume and the types of options traded. At the end of the 1970s and the beginning of the 1980s, financial institutions began to develop exotic options as alternatives to plain-vanilla options in order to meet their particular needs and increase their business. However, most of the research on pricing exotic options focuses on a monitoring period comprising the whole life of the exotic options. In contrast, this thesis derives explicit pricing formulas for barrier options, floating-strike lookback options and fixed-strike lookback options whose monitoring periods start at an arbitrary date and end at another arbitrary date before maturity.; Another problem that this thesis addresses is pricing equity-indexed annuities embedded with exotic options. Although sales of equity-indexed annuities (EIAs) have rapidly increased since the first offering in 1995, the growth rates in sales have recently shown signs of slowing down because the current volatile equity market increases the costs of the options embedded in EIAs and hence decreases the participation rates. New EIAs need to be designed that are similar to existing EIAs but have a higher participation rate and more desirable properties. As exotic options are good alternatives to plain-vanilla options, EIAs embedded with exotic options may be good alternatives to the existing EIAs. This thesis proposes four types of EIAs embedded with these exotic options: barrier EIAs, annual reset EIAs with barriers, a partial-time lookback EIA and a partial lookback EIA with variable guarantee. In addition, this thesis, applying the pricing formulas for these exotic options, derives explicit pricing formulas for the proposed EIAs.
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