## Glossary

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# Moneyness

Moneyness for a European call option is often defined as the ratio between the current price underlying asset, S, and the strike price, K i.e. S/K. If S>K the option is said to be in the money (ITM), if the S<K the option is said to be out of the money (OTM) and if S=K the option is at the money (ATM).
Sometimes it is more convenient to define moneyness as the ratio between the forward level of the underlying and the strike price. This is also called forward moneyness. The forward level is here defined as $\text{E}^{\mathbb{Q}}[S(T)|\mathcal{F}_t]$. If the short rate is constant and the underlying asset is not paying dividends then $\text{E}^{\mathbb{Q}}[S(T)|\mathcal{F}_t]=S(t)e^{r(T-t)}$. Using forward moneyness can be seen as more appropriate since the forward level is the level where we expect the underlying to be at maturity.