A very quick point to clarify about Stock Process
- Thread starter Liming
- Start date
Hi Liming,
The stock price dynamic that we study (e.g., the underlies Black-Scholes-Merton) is GBM.
This is John Hull's: dS/S = mu*dt + sigma * dz
The arithmetic Brownian motion simply has dS on the left; but is not typically used b/c it allows the price to become negagive.
Both of these are continuous, clearly.
The other two questions I had to look up, as i do not know:
1. Is GBM generalized Wiener: my library says Weiner process has four properties, consistent with: http://en.wikipedia.org/wiki/Wiener_process
Clearly, GBM is a Weiner process; it seems to me "generalized" merely adds a drift, and thefore, GBM is a generalized weiner process
2. I am only aware of, and can only seem to find refererence to, "discrete time versions of GBM." GBM isn't discrete, and if the discrete version of has a name, i am not aware
David
The stock price dynamic that we study (e.g., the underlies Black-Scholes-Merton) is GBM.
This is John Hull's: dS/S = mu*dt + sigma * dz
The arithmetic Brownian motion simply has dS on the left; but is not typically used b/c it allows the price to become negagive.
Both of these are continuous, clearly.
The other two questions I had to look up, as i do not know:
1. Is GBM generalized Wiener: my library says Weiner process has four properties, consistent with: http://en.wikipedia.org/wiki/Wiener_process
Clearly, GBM is a Weiner process; it seems to me "generalized" merely adds a drift, and thefore, GBM is a generalized weiner process
2. I am only aware of, and can only seem to find refererence to, "discrete time versions of GBM." GBM isn't discrete, and if the discrete version of has a name, i am not aware
David
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