• We are pleased to announce that the winner of our Feedback Prize Draw for the Winter 2024-25 session and winning £150 of gift vouchers is Zhao Liang Tay. Congratulations to Zhao Liang. If you fancy winning £150 worth of gift vouchers (from a major UK store) for the Summer 2025 exam sitting for just a few minutes of your time throughout the session, please see our website at https://www.acted.co.uk/further-info.html?pat=feedback#feedback-prize for more information on how you can make sure your name is included in the draw at the end of the session.
  • Please be advised that the SP1, SP5 and SP7 X1 deadline is the 14th July and not the 17th June as first stated. Please accept out apologies for any confusion caused.

Assignment X2 Q2.6 iii)

S

sma09gc

Member
Hi,

i was wondering why we can't just substitute the values for mu, sigma & t=1/2 into the lognormal model to calculate the probability. Why doesn't that work here?
 
The (continuous-time) lognormal model has different parameters to the lognormal distribution that is obtained as a solution to the geometric Brownian Motion SDE, so you need to be careful about which you are given in the question.

In this question, you are given the geometric Brownian Motion SDE, which has solution as shown in (ii), so you use that. This is equivalent to the distribution:

log(St/S0) ~ N((mu-0.5*sigma^2)*t, sigma^2*t)

The form of the (continuous-time) lognormal model is given in Section 1.1 of Chapter 10, and is differently parameterised. Here, the equivalent distribution would be:

log(St/S0) ~ N(mu*t, sigma^2*t)
 
Back
Top