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13 | | - |
14 | 1 | # Glossary |
15 | 2 |
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16 | 3 | ## Characteristic Function |
17 | 4 |
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18 | | -The [characteristic function](../theory/characteristic.md) of a random variable $x$ is the Fourier transform of ${\mathbb P}_x$, |
| 5 | +The [characteristic function](../theory/characteristic) of a random variable $x$ is the Fourier transform of ${\mathbb P}_x$, |
19 | 6 | where ${\mathbb P}_x$ is the distrubution measure of $x$. |
20 | 7 |
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21 | 8 | \begin{equation} |
@@ -47,24 +34,24 @@ Check this study on the [Hurst exponent with OHLC data](../applications/hurst). |
47 | 34 |
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48 | 35 | ## Moneyness |
49 | 36 |
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50 | | -Moneyness is used in the context of option pricing and it is defined as |
| 37 | +Moneyness, or log strike/forward ratio, is used in the context of option pricing and it is defined as |
51 | 38 |
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52 | 39 | \begin{equation} |
53 | 40 | \ln\frac{K}{F} |
54 | 41 | \end{equation} |
55 | 42 |
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56 | | -where $K$ is the strike and $F$ is the Forward price. A positive value implies strikes above the forward, which means put options are in the money and call options are out of the money. |
| 43 | +where $K$ is the strike and $F$ is the Forward price. A positive value implies strikes above the forward, which means put options are in the money (ITM) and call options are out of the money (OTM). |
57 | 44 |
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58 | 45 |
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59 | | -## Moneyness Time Adjusted |
| 46 | +## Moneyness Vol Adjusted |
60 | 47 |
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61 | | -The time-adjusted moneyness is used in the context of option pricing in order to compare options with different maturities. It is defined as |
| 48 | +The vol-adjusted moneyness is used in the context of option pricing in order to compare options with different maturities. It is defined as |
62 | 49 |
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63 | 50 | \begin{equation} |
64 | | - \frac{1}{\sqrt{T}}\ln\frac{K}{F} |
| 51 | + \frac{1}{\sigma\sqrt{T}}\ln\frac{K}{F} |
65 | 52 | \end{equation} |
66 | 53 |
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67 | | -where $K$ is the strike and $F$ is the Forward price and $T$ is the time to maturity. |
| 54 | +where $K$ is the strike and $F$ is the Forward price and $T$ is the time to maturity and $\sigma$ is the implied Black volatility. |
68 | 55 |
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69 | 56 | The key reason for dividing by the square root of time-to-maturity is related to how volatility and price movement behave over time. |
70 | 57 | The price of the underlying asset is subject to random fluctuations, if these fluctuations follow a Brownian motion than the |
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