3
votes
Accepted
Find the parameter $d$ of the Affine Option Pricing Model in Duffie, Pan and Singleton (2000)
$d$ is a vector that collapses the $n$-dimensional vector into a real number. In the BS case $d=1$. There is nothing to be estimated. Also not that in practice affine pricing is done through FFT (and ...
- 4,307
3
votes
Accepted
How to determine components of Affine Term Structure for an Ohrnstein-Uhlenbeck process?
Let $\mathrm{d}r_t=\mu(t,r_t)\mathrm{d}t+\sigma(t,r_t)\mathrm{d}W_t$ be a model for the short rate under the risk-neutral measure $\mathbb{Q}$. Starting from the bond PDE
\begin{align*}
P_t + \mu(t,r) ...
- 15.3k
1
vote
Pricing the discount zero-coupon bond under a jump-diffusion model
If I understood well, your model falls into the generic case of affine models.
This reference might help you : http://arxiv.org/pdf/1512.03677v1.pdf
- 2,412
1
vote
Accepted
Pure jump process in Duffie, Pan and Singleton's paper
Essentially yes - $Z_t$ is a compound Poisson process, except that the underlying counting process $N_t$ has intensity $\lambda(X_t)$. I.e
$$
N_t - N_s \sim Pois\bigg( \int_s^t \lambda(X_u) \mathrm{d}...
- 69
1
vote
What is the Q-dynamics of affine bond prices when r is described by the given model?
Just adding my two cents. Without taking the logarithm of the price, the Ito's Lemma should result in:
$d p(t,T) = \left( \partial_t A(t,T) - \partial_t B(t,T) r + \frac{1}{2}\sigma^2B(t,T)^2 \right)p(...
- 11
1
vote
Accepted
What is the Q-dynamics of affine bond prices when r is described by the given model?
You can simply use Ito's lemma under the risk neutral measure $Q$.For the log-bond price $p(t,T)$ this gives
$$dp(t,T)=(A_t(t,T)-B_t(t,T)r_t)dt-B(t,T)dr_t$$
$$=[A_t(t,T)-(B_t(t,T)+B(t,T)a)r_t]dt-B(t,T)...
- 1,707
1
vote
Accepted
Affine term structure for CDS
In a (very small) nutshell, the estimation idea is the following:
Quoted CDS contracts are driven by a risk neutral default probability $PD_Q(\tau\leq T)$.
The default probability is again modeled ...
- 6,470
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