Questions tagged [affine-processes]

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0answers
52 views

Simulation of Stochastic Volatility with Correlated Jumps (SVCJ) price paths

I am trying to simulate price paths for Monte Carlo option pricing of the Stochastic Volatility with correlated jumps model as presented in Dufffie et al.(2000), Eraker et. al. (2003) and Eraker (2004)...
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1answer
376 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}\,...
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1answer
88 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 $bX_t \leq y$ ...
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0answers
77 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-...
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2answers
61 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
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1answer
472 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^{...
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0answers
43 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 ...