Questions tagged [affine-processes]
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9
questions
2
votes
0answers
85 views
Feller condition - PDE local analysis
In Paul Wilmott on Quantitative Finance, he claims that we can retrieve the (generalised) Feller condition $\eta \geq -\frac{\beta\gamma}{\alpha} + \frac{\alpha}{2}$ with a local analysis of the ...
4
votes
1answer
89 views
How to determine components of Affine Term Structure for an Ohrnstein-Uhlenbeck process?
I wonder how I can determine the components $A(t,T)$ and $B(t,T)$ for the zero-coupon bond price process $p(t,T)=e^{A(t,T)-r(t)B(t,T)}$? The components are defined in the following link: https://en....
1
vote
0answers
28 views
is it possible to make changes to use the affine property of Normal random variables, rather than the Central Limit Theorem?
I have proven the distribution of a discrete time model, evolving over a uniform mesh with $\delta t = T/L$ is given by
$$S(t_{i+1}) = S(t_i) + \mu \delta t S(t_i) + \sigma\sqrt{\delta t}S(t_i)Y_i,$$
...
4
votes
1answer
403 views
Pricing the discount zero-coupon bond under a jump-diffusion model
I am going to get the price of a zero coupon bond in a jump-diffusion model. The dynamic of interest rate as follow
$$dr_t=\kappa(\theta-r_t)dt+\sigma\sqrt{r_t}\,dW_t+d\left(\sum\limits_{i=1}^{N_t}\,...
1
vote
1answer
99 views
Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)
According to Duffie, Pan and Singleton (2000) for any real number $y$ and any $a$ and $b \in \mathbb{R}^n$, the price of a security that pays $\exp(aX_t)$ at time $T$ in the event that $bX_t \leq y$ ...
1
vote
0answers
86 views
Estimation of Affine Term Structure Model
In this paper the estimation of Affine Term Structure models via ML is discussed. In the Affine $N$-factors model the price of the bond is
$$
P(X_t,t,T;\theta) = \exp(-\gamma_0(T-t;\theta)-\gamma(T-...
1
vote
2answers
64 views
Incorrect characterization of spot rate?
Is the t in the red boxed $R(t,T)$ supposed to be the same as the S in the green boxed $R(S,T)$?
2
votes
1answer
495 views
Do we need Feller condition if volatility process jumps?
It is fairly known that in affine processes, as Heston model
\begin{equation}
\begin{aligned}
dS_t &= \mu S_t dt + \sqrt{v_t} S_t dW^{S}_{t} \\
dv_t &= k(\theta - v_t) dt + \xi \sqrt{v_t} dW^{...
3
votes
0answers
44 views
For an affine process, how do we know the second order term is positive definite?
A regular affine process is defined to have the generator
$Af(x) = \sum_{k,l=1}^d(a_{kl}+\langle a_{I,kl},y\rangle)\frac{\partial^2f(x)}{\partial x_k\partial x_l}+\langle b+\beta x,\nabla f(x)\rangle ...
