# Questions tagged [stochastic-drift]

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### risk-premium if we leave risk-neutral world

Risk neutral pricing in the Black-Scholes-Model makes life easy since it solves the challenge of the choice of two parameters simultanuously: the drift-parameter $\mu$ in the underlying geometric ...
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### What are $\mu$ and $a$ in $\mu = a + \frac{\sigma^2}{2}$

Considering GBM: $$S(t_i) = S_0 \exp(a \cdot t_i + \sigma \cdot W(t_i)) = S_0 \exp\left((\mu - \frac{\sigma^2}{2}) \cdot t_i + \sigma \cdot W(t_i)\right)$$ I am interested ...
168 views

### Pricing European Options with Monte Carlo

Given the following code (S0 = Initial Share Price, r= (risk-free) interest rate, K=Strike, Sigma= Standard Deviation, T=years, nExp=Number of Experiments) ...
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### Bessel Correction and Geometric Brownian Motion

Does it make sense to use bessel's correction for standard deviation and variance when fitting the drift and volatility parameters of geometric brownian motion to historical return data for a security....
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1 vote
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### Mean instantaneous drift from option prices

I'm going through the paper "Pricing European Options in Realistic Markets" by Schaden (2002) as its formulation for instantaneous mean drift seemed really interesting. On page 14, the ...
1k views

### Risk Neutral Valuation, Drifts and Calibration

Lets consider a pricing model like Vasicek. Apparently, if you calibrate a derivatives pricing model to market prices this gives you risk neutral parameters. Its not clear to me as to WHY this will ...
• 2,552
I have repeatedly come across the statement that "a process with a drift cannot be a martingale". Is this true also for stochastic drifts? Suppose I have a process with a stochastic drift: ...