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stochastic processes is a collection of random variables representing the evolution of some system of random values over time.

2 votes
1 answer
803 views

Interpretation of parameters in the CGMY model

I would like to understand role of parameters $C,G,M,Y$ in CGMY model, especially $G$ and $M$. The Lévy measure is $$\nu(x)=C\frac{e^{-Mx}}{x^{1+Y}}1_{x>0}+C\frac{e^{-G|x|}}{|x|^{1+Y}}1_{x<0} $$In one …
Mr.Price's user avatar
  • 433
8 votes
2 answers
3k views

Which process is the most commonly used for modeling stock prices?

I'm thinking of writing a master's thesis about pricing options using Levy processes, but I wonder if these processes are actually used for modeling stock prices or not (and which specifically)? And i …
Mr.Price's user avatar
  • 433
1 vote
0 answers
380 views

Change of Numeraire technique (Cross-currency models)

Hey I have problem with understanding change of numeraire technique. For example we have $dr^d(t)=\kappa_1(\theta_1(t)-r^d(t))dt+\sigma_1 dW_1$ (under measure $Q^1$ associated with domestic bank accou …
Mr.Price's user avatar
  • 433
0 votes
1 answer
166 views

how to price options in reality [closed]

I'm getting to know the Black Scholes model, which apparently is no longer suitable for pricing options on the market. I would like to write a Master's thesis on option pricing but I do not know what …
Mr.Price's user avatar
  • 433