# Questions tagged [brownian-motion]

In mathematics, Brownian motion is described by the Wiener process; a continuous-time stochastic process named in honor of Norbert Wiener.

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### Price of Call Option with or without jumps

Suppose two assets in Black Scholes world have the same volatility, but one has downward jumps at random times. How does this affect the option prices? I would have thought that downward jumps would ...
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### Find a formula for the price of a derivative paying $\max(S_T(S_T-K),0)$

Develop a formula for the price of a derivative paying $$\max(S_T(S_T-K))$$ in the Black Scholes model. Apparently the trick to this question is to compute the expectation under the stock measure. So,...
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### How to do Monte Carlo simulation given the stochastic ODE of a Brownian motion [closed]

I've learn the theoretical basis and lots of Brownian motion in quantitate finance. But i'm wondering how to actually simulate something based on brownian motion and make into something code-able or ...
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### How to price a down-and-out leveraged barrier call option using Brownian motion?

I am trying to price a type of leveraged down-and-out (LDAO) barrier call option, using geometric Brownian motion. My python script is below. I am not sure how to correctly model the increasing ...