@ericako5970
Thanks a lot for the knowledge. I repeated that several times for better understanding. I have a question about how the lower right dP^s/dQ at 6:30mins comes up?
@johnvanprague9540
I would like to ask whether there is an intuition for the drift of price processes under the Stock numeraire? I find it intuitive that the martingale measure under the Money Market numeraire induces the drift "r" to all price processes (via the appropriate change of measure): with the money market compounding continuously at rate "r", all log-normal price processes need to drift at this rate "r", otherwise the price processes discounted by the money market numeraire would not be martingales (i.e. any price process that wouldn't drift at "r" would give rise to arbitrage between Spot and Forwards, i.e. there would be miss-pricing of Forwards under the money market numeraire if the price process didn't drift at "r"). Same holds for the Discount bond numeraire under deterministic rates (because the Bond numeraire under deterministic rates turns out to be the money market numeraire scaled by a constant). However, I haven't managed to build similar reasoning for the Stock price numeraire. Why does the Stock price numeraire induce the drift: (r+σ^2) ?? Why would (intuitively) being able to borrow at the rate of the stock mean that price processes must have this drift? Thank you so much,
@vatsal9387
Awesome.
@taopaille-paille4992
Using the stock measure, one can obtain the call-put symmetry formula
@johnvanprague9540
If I may ask: what software do you use to type the equations please?
@FF-ms6wq
At 3:00 how do you get “ dZ_t = sigma Z_t dW_t^Q “ ? Intuitively I understand that since it is martingale, there shouldn’t be a dt term (though I didn’t get that from you, since your explanation was too poor for that). But why is the sigma term still the same? It is unclear. Please do better.
@kinghreenleung2933