Darragh Kelly
Ton up Member
Hi,
Q5(iii)
So by solving the general solution for the discounted share price, e^-rt*St = St,squiggle (given we've already solved SDE dSt = mew*St+sigma*St*dWt, to get an expression for St), using Ito's lemma, and writing in terms of browian motion under the risk-neutral measure Q (using Cameron-Martin-Girsanov-Therom), we get the following expression:
dSt,squiggle = sigma*St,squiggle*dWt,squiggle
So the solution from the Acted exam paper concludes that because this process has 0 drift term, then it is a martingal (which I fully understand, the zero drift is a martingale property).
But the question has asked us to show (using parts (i) and (ii)) that Wt + lambda*t is Browian motion under the risk-neutral proability Q. I'm just struggling how this has been proven through showing that under risk-neutral probability measure Q that, the process is a martingale. Please could you shed some light on what I'm missing?
Q5(v)
Is this in the notes or should we have understood that one-factor stochastic processes based on the same factor have by definition the same price of risk?
Many thanks,
Darragh
Q5(iii)
So by solving the general solution for the discounted share price, e^-rt*St = St,squiggle (given we've already solved SDE dSt = mew*St+sigma*St*dWt, to get an expression for St), using Ito's lemma, and writing in terms of browian motion under the risk-neutral measure Q (using Cameron-Martin-Girsanov-Therom), we get the following expression:
dSt,squiggle = sigma*St,squiggle*dWt,squiggle
So the solution from the Acted exam paper concludes that because this process has 0 drift term, then it is a martingal (which I fully understand, the zero drift is a martingale property).
But the question has asked us to show (using parts (i) and (ii)) that Wt + lambda*t is Browian motion under the risk-neutral proability Q. I'm just struggling how this has been proven through showing that under risk-neutral probability measure Q that, the process is a martingale. Please could you shed some light on what I'm missing?
Q5(v)
Is this in the notes or should we have understood that one-factor stochastic processes based on the same factor have by definition the same price of risk?
Many thanks,
Darragh