# Questions tagged [geometric-brownian]

The tag has no usage guidance.

109 questions
Filter by
Sorted by
Tagged with
37 views

### Ito Process: How to calculate expected return?

On page 300 of Hull's Options, Futures and Other Derivatives It is tempting to suggest that a stock price follows a generalized Wiener process; that is, that it has a constant expected drift rate and ...
30 views

### How can we simulate daily return based on multi-factor model?

This is an interesting question for simulation. The question is a bit lengthy but I'm trying my best to make it super clear here. Now I have some multi-factor model, say some US barra risk model from ...
21 views

### High/Low range under GBM - Analytic solution?

Does anybody know of an analytical solution to the expected high / low range for an asset that follows a GBM process over sampling frequency dt? I have ran numerical simulations and find that the ...
54 views

### Reinvesting the dividends of a dividend paying stock

Suppose we have a dividend paying stock that has the following dynamics: $$dS_t=S_t((\mu-q)dt+\sigma dW_t)$$ With a continuous dividend yield $q$. What is the portfolio $Y_t$ that results out of ...
### Price a contingent claim with payoff $(S_{1T}-S_{2T})^+$ at time $T$
Two stocks are modelled as follows: $$dS_{1t}=S_{1t}(\mu_1dt+\sigma_{11}dW_{1t}+\sigma_{12}dW_{2t})$$ $$dS_{2t}=S_{2t}(\mu_2dt+\sigma_{21}dW_{1t}+\sigma_{22}dW_{2t})$$ with $dW_{1t}dW_{2t}=\rho dt$....