In this paper, we extend the first-order asymptotics analysis of Fouque etal. to general path-dependent financial derivatives using Dupire's functionalIto calculus. The main conclusion is that the market group parameterscalibrated to vanilla options can be used to price to the same order exotic,path-dependent derivatives as well. Under general conditions, the first-ordercondition is represented by a conditional expectation that could be numericallyevaluated. Moreover, if the path-dependence is not too severe, we are able tofind path-dependent closed-form solutions equivalent to the fist-orderapproximation of path-independent options derived in Fouque et al.Additionally, we exemplify the results with Asian options and options onquadratic variation.
展开▼
