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Questions tagged [affine-processes]

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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....
Dreason94's user avatar
  • 311
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1 answer
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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}\,...
user avatar
4 votes
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Why is the Schöbel-Zhu model affine?

In the Schöbel-Zhu model, the stochastic volatility process is $dv_t=\kappa(\theta-v_t)dt+\sigma dW_t$. The characteristic function of the stock process can be found by arguing that the model is ...
Frimousse's user avatar
3 votes
1 answer
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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^{...
Gabriele Pompa's user avatar
3 votes
2 answers
282 views

What is the Q-dynamics of affine bond prices when r is described by the given model?

Assuming an Affine term structure model, where bond prices arebe defined as: $$P(t,T)=\exp({A(t,T)-B(t,T)r_t)}$$ and describing the Q-dynamics of the short rate according to the model: $$dr_t=ar_tdt+\...
Mr Frog's user avatar
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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 ...
Lost1's user avatar
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2 votes
1 answer
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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 $bX_t \leq y$ ...
ChicagoCubs's user avatar
2 votes
0 answers
148 views

Pricing kernel representation

I am reading this paper https://mpra.ub.uni-muenchen.de/4969/1/MPRA_paper_4969.pdf pp.6-7 on discrete-time bond pricing. The model adopted is a a common affine model, the short rate follows \begin{...
pietrosan's user avatar
1 vote
2 answers
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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 $R(S,T)$?
BCLC's user avatar
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1 answer
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Affine term structure for CDS

in papres such as https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2686284 (Exploring Mispricing in the Term Structure of CDS Spreads by Robert A. Jarrow, Haitao Li, Xiaoxia Ye, and May Hu) a ...
d0whes's user avatar
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1 vote
0 answers
31 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 $$S(t_{i+1}) = S(t_i) + \mu \delta t S(t_i) + \sigma\sqrt{\delta t}S(t_i)Y_i,$$ ...
JohnOD25's user avatar
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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-...
AlmostSureUser's user avatar
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1 answer
110 views

Pure jump process in Duffie, Pan and Singleton's paper

In page 1349 or Section 2.1 of "Duffie, D., Pan, J., & Singleton, K. (2000). Transform Analysis and Asset Pricing for Affine Jump-Diffusions. Econometrica, 68(6), 1343-1376" the pure ...
Roberto Palermo's user avatar
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0 answers
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Affine Jump Diffusion

I'm currently looking into affine jump-diffusions. I would like to get to know the literature better and I know the paper by Duffie, Pan, and Singleton (2000) is a very celebrated paper. Although I ...
Marc Allan's user avatar