Partial quanto lookback options

Financial instruments for hedging and speculating on the foreign exchange rate and equity risks draw the attention of market participants as financial transactions increase across multiple jurisdictions. Notably, a quanto lookback option has been actively traded because it successfully meets market demands. Although the quanto lookback option provides numerous benefits, a high premium due to the lookback feature is the primary culprit that hinders investors from purchasing it. This paper proposes partial quanto lookback options and provides the closed -form pricing formulas when the lookback feature is applied to the exchange rate or equity value, and the extremes are determined by observing them for a shorter period than the life of the option. Because pricing the options is challenging due to their partial path-dependence, we develop the quanto extreme expectation that facilitates deriving the option prices. Extensive numerical examples demonstrate the efficacy of the partial quanto lookback options in lowering the premiums.