CT8 October 2010 Question 5iii)

Discussion in 'CM2' started by MichaelJR, Mar 22, 2024.

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  1. MichaelJR

    MichaelJR Made first post

    In this question, the risk-neutral pricing model gives us the following equation to solve:

    V_0 = e^(-r(T-t)) * E_Q[S_1^2 | S_0]​

    I understand we need to derive S_t to resolve S_1^2 any further...

    In the next step

    dS_t = r * S_t * dt + sigma * S_t * dZ_t ?​

    What is the reasoning for substituting r in for mu here?

    Thanks in advance!
     
    MichaelJR, Mar 22, 2024
    #1
  2. John Potter

    John Potter ActEd Tutor Staff Member

    When we price, we must do so under the risk-neutral probability measure Q - otherwise we will allow an arbitrage opportunity. Under Q, all risky assets are expected to increase at the same rate as cash (i.e. earn risk-free rate r). So, a quick way to sort this out is just to sub in r for mu. The exact maths behind all of this is a corollary to the CMG theorem but the most important point to understand is that under Q, E[St| Fw] = Sw exp(r(t-w)) we expect the share to go up like cash

    John
     
    John Potter, Mar 26, 2024
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