Basket Barrier Derivative Pricing Under Correlation Uncertain Environment

It has been four decades since establishment of Chicago Board Options Exchange in 1783 when standardized option contract was first brought in.In Quantitative Finance area,research about option pricing is well developed which results in the great boom of exotic fitting to industrial needs.Compared with overseas derivative markets where pricing mechanics are developed decades,our domestic derivative markets are still incomplete enough.At this stage,there is a strong need for abundant In-the-Market product types.Only HS300-index SZ50-index family linked In-the-Market derivatives traded on board.Derivatives issued on stocks,however,are only traded over the count..Product with good liquidity which may provide valid pricing reference for OTC quotes over correlations between different assets has not come out till now.Considering the rapid development of over-the count derivative market,we set up an uncertainty model to model correlation parameter of multi-asset option.In this thesis,we concentrate on basket barrier option which is a popular structure in OTC market.A dynamic optimization framework based on over-hedge in uncomplete market is adopted.Then we take Monte Carlo via 2-BSDE approach to calculate solution to this HJB equation(a nonlinear PDE)which is derived from optimization problem.Conventionally,for structures with continuous payoff like vanilla options,Iteration based on finite difference methods are frequently adopted to solve this equation.However,for those product with discontinuous payoff like barrier option,finite difference on PDEs with nonlinear diffusions may bring great numerical error due to the singular terminal condition.Besides,The computations would growth exponentially with respect to number of different assets in the basket which is known for Curse of Dimensions.Nonlinear PDE problem which we consider in this thesis is transformed into expectation on solution to 2-BSDE by a generalized Feynman-Kac formula.Then a Monte Carlo algorithm for barrier option is used to generate robust numerical results.We test this algorithm for barrier option under different situations.First,we find results are consistent to Black-Scholes when uncertainty is gone.While under uncertainty environment,quotes based on uncertainty correlation model via 2-BSDE Monte Carlo dominate on Black Scholes quotes.The bid-ask spread is tight.Price with respect to underlying price is smooth enough to generate good Greeks.We then use the algorithm to analyze quote strategy about what practitioner may care..In the last part of this thesis,we summarize our conclusions of this research and future work about this topic.It should also be noted there is still limitations of this work.On the one hand,we could use this framework to pricing more sophisticated structures.On the other hand,there is still improvements on the algorithm.