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.