This thesis is on an advanced method for pricing financial derivatives in a market model,which comprises two stochastic volatilities. Financial derivatives are instruments whosethat is related to any financial asset. Underlying assets in derivatives are mostly financialinstruments; such as security, currency or a commodity. Stochastic volatilities are used infinancial mathematics to assess financial derivative securities; such as contingent claims andoptions for valuation of the derivatives, at the expiration of the contract. This study examinedtheoretical frameworks that evolve around the pricing of financial deriv- atives in a marketmodel and it mainly examines two stochastic volatilities: cubature formula and splittingmethod by analysing how these volatilities affect the pricing of financial derivatives. The studydeveloped an approximation approach with a double stochastic volatilities model in termsof Stratonovich integrals to evaluate the contingent claim, examined the similarities betweenNinomiya–Ninomiya scheme and Ninomiya–Victoir scheme, and rewrite the system of doublestochastic volatility model in terms of the standard Brownian motion.

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