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stochastic discount factor in a Black Scholes Hull White model
can anyone help me find the stochastic discount factor in a Black Scholes Hull White model?I know how to find a stochastic discount factor in a Black Scholes model, but how I find the stochastic factor in a BSHW model is much more difficult(at least I think it's more difficult), because of the incorporation of the Hull White model and the correlation between the interest rate and the stock price.And is there any literature about this subject?
stochastic discount factor in a Black Scholes Hull White model
Can't you use RN valuation and use exp[-int r(u) du] (i.e. one over the money market account) as stochastic discount factor ? \edit typo
Last edited by AvH on July 2nd, 2008, 10:00 pm, edited 1 time in total.
stochastic discount factor in a Black Scholes Hull White model
I think you're right, but that's not what I intended to do. Perhaps my question wasn't clear enough. I want to have a stochastic discount factor for a porfolio(which depends on the interest rate as well as the stock price) not under the risk neutral measure, but under a "real world" probablity measure. And then RN valuation is no longer possible.
stochastic discount factor in a Black Scholes Hull White model
I already suspected that ;-)Perhaps you can use the fact that both the zero-coupon bond option as well as the stock price follows a log-normal distribution which is equivalent to a two-stock Black-Scholes economy (with correlated assets) ...
stochastic discount factor in a Black Scholes Hull White model
Do you have some nice suggestions for literature on this topic?