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12
votes
1answer
304 views
Parameter estimation of Ornstein–Uhlenbeck and CIR processes
I would like to estimate Ornstein–Uhlenbeck process' parameters via Kalman filter.
My process is the following one:
$\text{d}x_{t}=\alpha(\theta-x_{t})\text{d}t+\sigma\text{d}W_{t}$
I'm interested ...
0
votes
1answer
79 views
Change option B&S pricing
Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion
$$dX_t= \mu X_t dt+ \sigma X_tdW_t$$
$$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$
Supposing the market is ...
6
votes
0answers
129 views
Consistency of economic scenarios in nested stochastics simulation
I am interested in references on research regarding the consistency of economic scenarios in nested stochastics for risk measurement.
Background:
Pricing by Monte-Carlo:
For pricing complex ...
6
votes
0answers
129 views
How to get an analytic result for option price based on this model?
I defined such a model for stock price
(1)....
$$dS = \mu\ S\ dt + \sigma\ S\ dW + \rho\ S(dH - \mu) $$
, where $H$ is a so-called "resettable poisson process" defined as
(2)....
$$dH(t) = ...
3
votes
0answers
102 views
Is it random walk?
I would like to ask a question about random walk. Campbell, Lo & Mackinlay defined the random walk, in the following way (RW3):
$$
cov[f(r_{t}),g(r_{t+k})]=0,\qquad k\neq0
$$
for all $f(\cdot)$ ...
2
votes
0answers
168 views
Does the geometric Ornstein-Uhlenbeck process have stationary variance?
I know that the long run variance of the standard OU process is
$\lim_{s\rightarrow \infty}\mbox{Var}(P_{t+s}|P_t) = \frac{\sigma^2}{2\theta}$
I'm using the geometric version of the process. I ...
2
votes
0answers
105 views
Measure change in a bond option problem
This is not a homework or assignment exercise.
I'm trying to evaluate $\displaystyle \ \ I := E_\beta \big[\frac{1}{\beta(T_0)} K \mathbf{1}_{\{B(T_0,T_1) > K\}}\big]$, where $\beta$ is the ...
2
votes
0answers
82 views
Difference between kappa and delta in mixed-effects model
(This question is a crosspost from Cross Validated)
I have a following stochastic model describing evolution of a process (Y) in space and time. Ds and Dt are domain in space (2D with x and y axes) ...
1
vote
0answers
148 views
Call options portfolio: what would the underlyings' moments to be maximized?
Let you have only three underlyings, like SPY, TLT and GLD, and you want to buy $n_{1}$ Call options on SPY, $n_{2}$ Call options on TLT and $n_{3}$ Call options on GLD... with a limited budget, that ...
0
votes
0answers
59 views
Exact value of mean reversion rate knowing terminal value of the process
Let you have the following mean reverting process:
$\text{d}x_{t}=a(\theta-x_{t})\text{d}t$,
where the diffusion term is absent, that is this process is not stochastic.
Let you know the value of ...
