DOI: 10.11908/j.issn.0253-374x.2018.12.019

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Conditional Monte Carlo Hybrid Acceleration Method Under Stochastic Interest Rate Model and Its Applications
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ÕªÒª:Ö÷ÒªÑо¿CIR(cox-ingersoll-ross)Ëæ»úÀûÂÊÄ£ÐÍÏÂŷʽÆÚȨ¶¨¼ÛµÄÃÉÌØ¿¨ÂÞ¼ÓËÙÄ£ÄâÎÊÌ⣬Ìá³öÁËÒ»ÖÖеĿØÖƱäÁ¿£¬»ùÓڴ˱äÁ¿½áºÏÌõ¼þÃÉÌØ¿¨ÂÞ·½·¨¿É¶ÔÆÕͨÃÉÌØ¿¨ÂÞ·½·¨ÓÐÏÔÖø¼ÓËÙЧ¹û.ÀíÂÛ¼°ÊýÖµ¼ÆËã±íÃ÷£¬¸Ã·½·¨ÄÜÓÐЧµØÌá¸ß¼ÆËãЧÂÊ.ͬʱ£¬Ìá³öÁË»ùÓÚÌõ¼þÃÉÌØ¿¨ÂÞ·½·¨Çó½âGreeksµÄËã·¨£¬Óë¾­µäµÄÃÉÌØ¿¨ÂÞ·½·¨±È½Ï£¬Äܸü¾«È·¡¢Îȶ¨µØÇó½âGreeksµÄÖµ.ËùÌá³öµÄ·½·¨Í¬ÑùÊÊÓÃÓÚÒ»Àº×ÓÆÚȨ¡¢ÀëɢȡÑùÑÇʽÆÚȨµÈ¸ßάÆÚȨ.



Abstract:This paper mainly studies acceleration methods of the Monte Carlo simulation method for the pricing of European call options under the assumption of the CIR(Coxª²Ingersollª²Ross) stochastic interest rate model. A new control variable based on the combination of the conditional expectation formula and the control variable technique is presented. The theoretical analysis and numerical results show that this method, with a new control variable, can improve the computation efficiency. Then it is applied to the computation of Greeks. The numerical results illustrate that the new method is more accurate and stable than the classical Monte Carlo method. It can also be applied to basket options, Asian option, and other high-dimension cases.





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