| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Outline of Final Research Achievements |
In this research, we analyse "an asymptotic expansion approach," known as a useful tool for practitioners in pricing derivatives or risk managements. Especially, we extend the "original" approach which expands the target process around Normal distribution, to the ours expanding the target around more general stochastic processes whose distributions are available. We also try to analyse the mathematical structures in our expansion.
As a result, the underlying problem for solving the stochastic differential equation is transformed into the problem for solving infinite numbers of ordinary differential equations with hierarchical dependence, via projecting correction terms onto the "central" terms in our expansion.
To confirm usefulness and accuracy of our proposing technique, it is applied to practically important examples, such as an expansion of lamuda-SABR model with mean-reversion around original SABR model, and satisfactory results are observed.
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