Timeline for How to deduce the formula of the wealth process of a stochastic volatility model?
Current License: CC BY-SA 4.0
6 events
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| Aug 30, 2018 at 15:42 | vote | accept | Ivan | ||
| Aug 30, 2018 at 12:58 | comment | added | Gordon | Generally, you need another asset, such as the deposit account, to make the investment self-financing. But here we can only heuristically argue like that given that you have only the risky asset. | |
| Aug 30, 2018 at 0:53 | comment | added | Ivan | thanks for your answer. I made the same reasoning. However, if you apply Ito's formula you get $dX_{t} = \dfrac{\alpha_{t}}{S_{t}} dS_{t} + S_{t} d\dfrac{\alpha_{t}}{S_{t}} + d \langle S_{t} , \dfrac{\alpha_{t}}{S_{t}} \rangle$, and then you need to have $ S_{t} d\dfrac{\alpha_{t}}{S_{t}} + d \langle S_{t} , \dfrac{\alpha_{t}}{S_{t}} \rangle = 0$ (to have the dynamics of the wealth process) what seems very convenient and do not have a financial sense. | |
| Aug 29, 2018 at 14:10 | history | edited | Gordon | CC BY-SA 4.0 |
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| Aug 29, 2018 at 13:06 | history | edited | Gordon | CC BY-SA 4.0 |
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| Aug 29, 2018 at 13:00 | history | answered | Gordon | CC BY-SA 4.0 |