Paul
  • Member for 9 years
  • Last seen more than a month ago
  • Paris, France
Help with integrating stochastic calculus expression from yield curve model
Accepted answer
2 votes

It is a Wiener integral as your integrand is a deterministic function of time. It is known that the Wiener integral is stationary gaussian process with independent increments. So $z(t) \sim \mathcal ...

View answer
Why is OU process stationary?
2 votes

I think you misunderstood the definition. Be stationary does not mean not depend of the time as you can check here. (Sorry for putting an wikipedia link here as I suppose you may have read it) ...

View answer
Foward-start option pricing
Accepted answer
1 votes

Note that \begin{align} p(t,x) &:= \mathbb E^{\mathbb Q} \left [ S_1 (S_T/ S_1-\kappa)^+ | S_t=x \right] \\&= x \mathbb E^{\mathbb Q} \left [ (S_T/x-\kappa )^+ | X_t=x \right] \end{align} ...

View answer
Ito's Lemma - Integrand depends on upper limit of integration
1 votes

Note that the $$dX_t = b_t dt + \sigma_s dB_t$$ notation for a (local) semi-martingale $X = (X_t)_{t \in [ t_0, T]}$ is an abreviation for $$ X_t = X_{t_0} + \int _{t_0} ^t b_s~ ds + \int _{t_0} ^t \...

View answer