OK. smth doesn't add up Suppose we have dynamics of a stock price paying continuous dividend yield g so that the dynamics of accumulated dividend up to time t called Dt is as follows .we want to price a derivative on S. Now, S itself is not tradable...if we have S0 today by time t we have not just St but accumulated dividends as well. we construct a tradable by holding a portfolio of 1 stock at time zero costing S0 and, after each time step dt as we get gSdt, we reinvest dividends in the stock buying gdt new stocks. So, by time t we have exp(gt) stocks with the value of our portfolio at time = .This is tradable, right??? so discounted it must be a martingale, so we can see that the drift of St under Q should be r-g, so we can proceed with pricing...Now, in the above construction of tradable, why can't I reinvest the dividends in bonds???Isn't normalised gain process a martingale as well??

anyone?

QuoteOriginally posted by: FedorEOK. smth doesn't add up Suppose we have dynamics of a stock price paying continuous dividend yield g so that the dynamics of accumulated dividend up to time t called Dt is as follows .we want to price a derivative on S. Now, S itself is not tradable...if we have S0 today by time t we have not just St but accumulated dividends as well. we construct a tradable by holding a portfolio of 1 stock at time zero costing S0 and, after each time step dt as we get gSdt, we reinvest dividends in the stock buying gdt new stocks. So, by time t we have exp(gt) stocks with the value of our portfolio at time = .This is tradable, right??? so discounted it must be a martingale, so we can see that the drift of St under Q should be r-g, so we can proceed with pricing...Now, in the above construction of tradable, why can't I reinvest the dividends in bonds???Isn't normalised gain process a martingale as well??Yes is tradable - hence a martingale - but it's not nearly as convenient to deal with as the rolled up reinvested divs process. This is because the div payments are proportional to stock price. If the stock instead paid a discrete dividend not proportional to stock price, then you'd consider the divs reinvested in riskless bonds.Note that there was another thread in the General Forum not long ago on this. Several people were trying to explain this to someone who didn't understand the issue and thought that Miller-Modigliani was somehow at odds with option pricing theory in the presence of dividends.

QuoteOriginally posted by: FedorEOK. smth doesn't add up Suppose we have dynamics of a stock price paying continuous dividend yield g so that the dynamics of accumulated dividend up to time t called Dt is as follows .we want to price a derivative on S. Now, S itself is not tradable...S is not tradeable? You think that the stock price - S(t) - doesn't represent the value of a tradeable asset?

it's not. because, as I wrote earlier, if we have S0 today by time t we have not just St but accumulated dividends as well. if it was tradable it's discounted process would be a martingale. it's not in this case. Athleticothanks for confirming! I thought I misunderstood smth..

So is this site a hoax?

please read my post carefully.also look at Financial Calculus by Rennie&Baxter, page 107, and Arbitrage theory in continuous time by Bjork, page 234.