Timeline for Intuition Behind Scaling Factor in Variance Swaps
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2017 at 14:41 | vote | accept | Jared | ||
| Jul 10, 2017 at 9:19 | comment | added | fni | @Jared, start from the second equation and rewrite it as $$e^{-rT}\left(f\left( F\right)-E^Q[ f(S_T)]\right)=e^{-rT}\left(log E^Q[S_T]-E^Q[log S_T]\right)=-\left(\int_0^Ff''(K)put(K)dK + \int_F^\infty f''(K)call(K)dK \right)=\int_0^F K^{-2}put(K)dK+\int_F^\infty K^{-2}call(K)dK\propto \sigma^2$$ | |
| Jul 10, 2017 at 0:06 | comment | added | Alex C | Yes, Neuberger showed that to gain exposure to variance you hedge a log contract. Which seemed a clever but useless result because "log contracts" do not exist in any real market. Then someone figured out you can essentially simulate the log-contract (among other payoffs of the form $f(S_T)$ for some $f$) with options using the other formula with the two integrals. | |
| Jul 9, 2017 at 20:23 | comment | added | Jared | Can you clarify the portion "Hence, you see immediately that to recover the price of the log contract you have to compute..."? Is it because hedging the log contract is how I gain exposure to variance (or volatility), and with the log contract the payoff $f(S_T) = \log (S_T)$? | |
| Jul 9, 2017 at 9:22 | history | answered | fni | CC BY-SA 3.0 |