2013 Fiscal Year Final Research Report
On a derivative pricing theory with jumps and stochastic volatilities
| Project/Area Number |
24830087
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Public finance/Monetary economics
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| Research Institution | Hosei University |
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Principal Investigator |
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| Project Period (FY) |
2012-08-31 – 2014-03-31
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| Keywords | デリバティブ / 確率ボラティリティ / ジャンプ / 確率的時間変更 |
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| Research Abstract |
Firstly, adopting the proportional hazard model, which has been recognized to be statistically meaningful for analyzing and estimating financial event risks such as default risk and prepayment risk, we provided an analytical treatment for the valuation problems. Secondly, we developed an approximate formula based on the Gram-Charlier expansion for pricing average options when the underlying asset price is driven by time-changed Levy processes. The time-changed Levy processes are attractive to use for a driving factor of underlying prices because the processes provide a flexible framework for generating jumps, capturing stochastic volatility as the random time change, and introducing the leverage effect. Thirdly, we proposed a pricing method for discretely monitored path-dependent options under the time-changed Levy processes. The key to the method is to derive a general formula for the multivariate characteristic functions of the intertemporal joint distribution of the processes.
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