For a one period economy, we have the price of an asset as:

$ p_0 = E^Q [p_1 * \frac {B0}{B1}] $

where $B0 = e^{-r_0}$ = time 0 price of risk free bond maturing at time =1 and $r_0$ is known at t0. And B1=1

Now lets say the economy is 2 period, but the only risk free instruments are 1 period bonds. Then you can price the asset as follows:

$ P_0 = E^{Q1} [P_1 * \frac {B0}{B1}] $

$ P_1 = E^{Q2} [P_2 * \frac {B1}{B2}] $

Notice $E^{Q1}$ vs $E^{Q2}$ in the two equations. These can be combined:

$ P_0 = E^{Q1} [ \frac {B0}{B1} * E^{Q2} [P_2 * \frac {B1}{B2}]] $

$= E^{Q1} [ e^{-r_0} * E^{Q2} [P_2 *e^{-r_1}]] $

Now I see that the final step is just collapsed into this:

$ P_0 = E^{Q1} [ P_2 *e^{-(r_0 + r1)}]] $

My question is how can you remove $E^{Q2}$ in the end? Do we need to assume the $Q1= Q2$?


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.