Timeline for Is forward price trendless under the real-world measure?
Current License: CC BY-SA 3.0
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| Jun 17, 2020 at 8:33 | history | edited | CommunityBot |
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| Mar 13, 2017 at 12:21 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Mar 13, 2017 at 11:18 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 25, 2016 at 14:23 | comment | added | Quantuple | @user9403, sure I see now. Thanks | |
| Nov 25, 2016 at 13:53 | comment | added | user9403 | @Quantuple My point was there are continuous time stochastic processes that are not diffusions (levy processes). Diffusions are continuous in both time and space, but more generic levy processes are only continuous in time (they can "jump" in space). | |
| Nov 25, 2016 at 6:58 | comment | added | Quantuple | I see, thanks for clarifying. Then indeed Girsanov tells you that instantaneous vol will be the same under the 2 measures. The only question remaining is does the vol which historically realised constitute a good estimator of the future vol. But it's à séparateur issue really. | |
| Nov 25, 2016 at 0:46 | comment | added | user138668 | This model from my last comment was estimated using historical data, but the driftless form seem to imply a risk-neutral measure. I guess this model I am looking at from an over-the-season perspective, is not really a local vol model, but a constant vol model? Anyway my question was why one can estimate using historical data even though the model is under risk-neutral measure. | |
| Nov 25, 2016 at 0:42 | comment | added | user138668 | @Quantuple the model I was looking at has the form $$ dF(t,T)=\sigma(t,T)F(t,T)dW(t)$$ where the vol function $\sigma(t,T)=\sigma_s(t)\gamma(T-t)$ is assumed to be deterministic. While the time-to-maturity component has a parameterized form,the spot component is just a generic function that has to be estimated at each point in time, for example, at current time $t$, spot vol is estimated over historical spot prices on the same day of the ``season''. I guess this model resembles a local vol model but may not be exactly the definition of local vol model in the literature. | |
| Nov 24, 2016 at 23:32 | comment | added | Quantuple | By definition the local volatility fonction à la Dupire is defined under the risk-neutral measure. So are you sure? | |
| Nov 24, 2016 at 23:30 | comment | added | user138668 | Thanks for the detailed calculations., especially about the difference between forwards and futures. I suppose the model I was looking at which is a local volatility model is under the measure $Q$. Why can we estimate the local volatility using the historical data? Is it because under this model, the measure change does not affect the local volatility, at least by assumption? | |
| Nov 24, 2016 at 17:16 | comment | added | Quantuple | @user9403. Assume today is $t=0$ and $T=1Y$, further assume that the spot price jumps e.g. a large dividend is paid by the stock at $t^{ex}=0.5$. Do you mean to say that $F(t,T)$ will jump over $[0,T]$ (which is not true)? Or are you thinking of something else? | |
| Nov 24, 2016 at 16:46 | comment | added | user9403 | While I like this answer, I think it should be stressed that this answer is not entirely general: it assumes that asset prices are diffusions while in all likelihood they have discontinuous (in space if not time) paths. | |
| Nov 24, 2016 at 11:49 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 11:40 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 11:31 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 11:25 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 11:15 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 10:43 | comment | added | Richi Wa | very good answer! | |
| Nov 24, 2016 at 9:31 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 9:21 | history | edited | Quantuple | CC BY-SA 3.0 |
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| Nov 24, 2016 at 9:12 | history | answered | Quantuple | CC BY-SA 3.0 |