Paul Wilmott on Quantitative Finance, Chapter 3, First Stochastic Differential Equation

In Chapter 3 I learned how to model asset prices using normal returns, both for discrete time and for continuous time using a Wiener process. The first stochastic differential equation!

Category:

Education

Tags:

• math
• finance
• quantitative finance
• normal
• Wiener
• stochastic
• differential

[alonsela972]

hi

u have an answer for u:

if z is a variable distrebuting normaly with 0 mean and std 1then:

x=z*dt^0.5 E[x] =E[z*dt^0.5]=E[z]*E[dt^0.5]=0

and VAR[z]=VAR[z*dt^0.5]=E[(z*dt^0­.5)^2]-E^2[z*dt^0.5]=E[z^2*dt]­-0=E[z^2]*[dt]=1*dt=dt

therefor x is a wiener process whith E[x]=0 and V[x]=dt

i hope it helps u

alon

[NathanWhitehead]

@alonsela972 Thanks, that actually makes some sense. Although I still *almost surely* don't understand all the technical requirements of Wiener processes. That was almost a joke. ;)

[CHIOLEMO]

Thanks for explain in that way!!!! I can understand now :)

[formchoi2190]

can't believe i found ur vids now!! i could have aced my quant finance class if i had found it a few months earlier. love ur vids!!

[markus713]

Thanks! helped clear that up

[wadtk]

at 3:07, the Ri*Ri+1 cancel. Can we say that this is because the expected value of it is 0? I think you showed that in the brownian motion video. Thanks for answering my questions!

[alonsela972]

meybe i can help u with that a litle bit.

u can talk with me on skype-

look for alonsela972 from israel

:-)