The tag has no wiki summary.

learn more… | top users | synonyms

3
votes
1answer
69 views

Why $W_{t}^3$ is not a martigale?(by Definition)

If $W_t$ be a wiener process then,how can i show that $W_{t}^{3}$ is not a martingale by definition?
2
votes
1answer
87 views

stochastic calculus - brownian motion

I don't know how to prove this : let be $X_t = \int_{0}^{t}\sigma_{u}dW_{u}$ where $\sigma_{t}$ is a predictable process. If $|\sigma_{t}| = c$ a.s. how can I prove that $X_{t}=c*\beta_{t}$ ...
1
vote
3answers
85 views

How to differentiate a brownian motion?

By definition a wiener process cannot be differentiated. But when we use Ito's lemma on F = X^2, where X is wiener process we have total change in ...
1
vote
1answer
104 views

stochastic calculus - Itô formula?

I encounter a problem in the proof below: I don't know how to proove the first line in yellow (cf below): it makes me think about the Itô formula a lot I don't undertand the deduction (ok ...
1
vote
1answer
48 views

equality in distribution

I encounter the following problem : I have the equality in distribution: for all $\lambda >0, ((1/\lambda)*\int_{0}^{\lambda t}\sigma_{u}^{2}du,t\geq0)=(\int_{0}^{t}\sigma_{u}^{2}du,t\geq0)$ ...
1
vote
1answer
42 views

forward option, stochastic calculus

I encounter a problem to understand this: The price of a forward option is : $C(K,t,T)=\mathbb{E}[((S_{T}/S_{t})-K)+]$ OK The option should only depend on $T-t$ because the yield randomness (for a ...
1
vote
0answers
53 views

What are the estimation methods for SV models?

I want to know about some methods like Methods-of-Moments, Quasi-Maximum Likelihood method, Baysian methods using Markov Chain Monte Carlo methods. Is there any reference to have an idea of these ...
0
votes
0answers
46 views

What interest rate dynamics would you suggest to simulate a single swap?

I need to calculate the Potential Future Exposure (PFE) for a single swap (not a portfolio). As far as I know, a stochastic model is needed to simulate the interest rate curves (from here). Could ...
0
votes
0answers
90 views

Stochastic Volatility for Stocks, FTSE

Can someone help me with calculating Stochastic Volatility (of stocks and options) using SAS or R or Matlab please? I am new to SAS and I am trying to use Heston model, White-Hull model or any other ...