Path Dependent Option

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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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In recent literatures [14-17], Hull-White stochastic interest rate which is analytically tractable has been incorporated into one-factor stochastic volatility model for pricing path-dependent options. Therefore, the model which incorporates multifactor stochastic volatility and stochastic interest rate maybe more reasonable for pricing barrier options.
A barrier option is a path-dependent option which is exterminated (knocked out) or initiated (knocked in) if the underlying spot price hits the specified barrier level during the life of the option.
(2017) [25] studied the pricing of vulnerable path-dependent options using double Mellin transforms and obtained an explicit form pricing formula or semianalytic formula in each path-dependent option.
Things are more complicated in the case of path-dependent options. The analytical solution of the pricing problem is not available and numerical approximations must be used.
It is one kind of path-dependent options where the payoff is based on the maximum or the minimum of the underlying asset price during the drift of the option.
Asian options are a kind of common strong path-dependent options, whose value depends on the average price of the underlying asset during the life of the option.
Linetsky, "Pricing and hedging path-dependent options under the CEV process," Management Science, vol.
Kou, 1999, "Connecting Discrete and Continuous Path-Dependent Options," Finance and Stochastics, 3, 55-82.
Their model is general enough to deal with any complex final payoff generated by European path-dependent options. They also account for the bankrupt event by considering the liabilities of the company as a risky (defaultable) bond.
Yen, "Pricing discrete path-dependent options under a double exponential jump-diffusion model," Journal of Banking and Finance, vol.
Efficient procedures for valuing European and American path-dependent options. Journal of Derivatives 1, 21-23.
Chapter 15 looks at advanced derivative designs and strategies including portfolio insurance, customized products, and exotic options such as binary and path-dependent options. Finally, the book ends with a chapter entitled "Financial Risk Management," which discusses the structure of the derivatives industry (d ealers) and miscellaneous issues, including accounting for derivatives.