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Results tagged with stochastic-calculus
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user 92
A branch of mathematics that operates on stochastic processes.
6
votes
Accepted
How do practitioners use the Malliavin calculus (if at all)?
Well the problems where Malliavin Calculus is applicable are mostly regarding greeks of exotic derivatives where some non smoothness in the payoff function creates trouble when trying to get this by f …
- 4,613
31
votes
1
answer
2k
views
Law of an integrated CIR Process as sum of Independent Random Variables
It is known (see for example Joshi-Chan "Fast and Accureate Long Stepping Simulation of the Heston SV Model" available at SSRN) that for a CIR process defined as :
$$dY_t= \kappa(\theta -Y_t)dt+ \omeg …
- 4,613
4
votes
What is the forward rate for a Black-Karasinski interest rate model?
Hi the forward rate equation is not dependent on the model it is calculated upon the prices of zero coupon bonds by the following equation :
$$
P(t,T)=exp{-\int_t^T f_t(u).du}
$$
If you have a con …
- 4,613
4
votes
Accepted
Non-arbitrage theory and existence of a risk premium
For the first one absurd reasoning allows you to construct an arbitrage (as r=0) by investing (or short selling according to the sign of $\mu$) at the time where $\sigma$ is null, or if you prefer as …
- 4,613
11
votes
How to use Itô's formula to deduce that a stochastic process is a martingale?
In general, if you have a process that you can write under the form $F(B_t,t)$ where $F$ is $\mathcal{C}^{2,1}$ then Itô's lemma gives you the drift term and diffusion term of $dF$. Then if the result …
- 4,613
9
votes
What is a stationary process?
A process is defined here and is simply a collection of random variables indexed (in general) by time.
Otherwise I know the concept stated by Shane under the name of "weak stationarity", strong stati …
- 4,613