# Tag Info

## New answers tagged risk-neutral-measure

0

ATM options are always more liquid. Options with shorter maturities are also more liquid. Best way to learn more is to open a brokerage account that doesn't have any minimum amounts or monthly fees and you can watch some delayed live option quotes across a whole chain of strikes and maturities . The first question you are asking is really how to profit if ...

0

Note that the second expression is not based on a substitution of the first expression; it is a different view: \begin{align*} e^{-rT}E\left((S_T-K)^+\right) &= e^{-rT}E\left(\left(e^{\ln S_T}-e^{\ln K}\right)^+\right)\\ &=e^{-rT}\int_{-\infty}^{\infty}\left(e^{\ln S_T}-e^{\ln K}\right)^+Q(\ln S_T\mid \mathcal{F}_0)\, d\ln S_T\\ ...

1

I think it's ok $$S_T = e^{\ln S_T}$$

1

There is a problem in your last step. Note that \begin{align*} P_{t, T_2}E_{Q_{T_2}}\left(\frac{1}{P_{T_1, T_2}} \mid \mathcal{F}_t \right) &= P_{t, T_2}E_{Q_{T_2}}\left(\frac{P_{T_1, T_1}}{P_{T_1, T_2}} \mid \mathcal{F}_t \right)\\ &=P_{t, T_2} \times \frac{P_{t, T_1}}{P_{t, T_2}}\\ &=P_{t, T_1}. \end{align*}

3

Standard Finance/Utility theory dictates that all future cash-flows are priced via the marginal rate of substitution. For example, say that $X_T$ is the random variable that represents this cash-flow at a future time. Then, the value of this cash-flow today will be valued as $$X_0 = E \left[ \frac{e^{-\rho T}\ U'(W_T)}{U'(W_0)} X_T \right]$$ where $U$ is ...

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