Path Dependent Option

Path Dependent Option

An option contract whose price is determined according to some formula involving the price of the underlying asset over time. Most options have prices that are dependent upon the value of the underlying asset at the time the option is exercised. A path dependent option, on the other hand, uses a more complex formula. For example, in some Asian options, the strike price is the average of the prices of the underlying asset over the life of the contract.
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This option is a path dependent option whose final payoff depends on the paths of its underlying asset.
Turbo warrants are barrier options with the rebate whose value is computed by another path dependent option. They can be very sensitive to the change in volatility under stochastic volatility models as pointed out by [12], which is contrary to the case of the Black-Scholes model.
Viswanathan, "Path dependent options, the case of lookback options," The Journal of Finance, vol.
Twelve chapters are: preliminaries of VBA; basic properties of futures and options; introduction to simulation; Brownian motions and ItoAEs rule; black-Scholes model and option pricing; generating random variables; standard simulations in risk management; variance reduction techniques; path dependent options; multiasset options; interest rate models; Markov Chain Monte Carlo methods.
Viswanathan, 1991 , "Path Dependent Options: the Case of Lookback Options," Journal of Finance, XLVI, 5, 1893-1907.
Tschoegl, 1985, "On Inferring Standard Deviations from Path Dependent Options", Economics Letters, 18:377-380