0
$\begingroup$

We have the following model for the short rate $r_t$under $\mathbb{Q}$:

$$dr_t=(2\%-r_t)dt+\sqrt{r_t+\sigma_t}dW^1_t\\d\sigma_t=(5\%-\sigma_t)dt+\sqrt{\sigma_t}dW^2_t$$

What is the PDE of which the solution gives the price of the floorlet with the following payoff in $t=1$:

$$X=0.5\bigg[ 2.5\%-L(0.5,1) \bigg]^+$$

where $L(0.5,1)=(P(0.5,1)^{-1}-1)\frac{1}{0.5}$ is the linearly compounded rate from $0.5$ to $1$.

Improve this question
$\endgroup$
1
  • $\begingroup$ This is a strange model, where does it come from? $\endgroup$
    – jherek
    Oct 19 at 8:02

1 Answer 1

Reset to default
1
$\begingroup$

You can work out the specific PDE by applying the multi-dimensional Itô formula to the (sufficiently smooth) value function $\Pi_t = f(t, r, \sigma)$.

Follow the steps from the regular Heston PDE derivation, e.g. like this section 2 https://www.frouah.com/finance%20notes/The%20Heston%20model%20short%20version.pdf

Improve this answer
$\endgroup$
1
  • 2
    $\begingroup$ Because you have put this in as an answer, it would be much better if you also explained in sufficient detail how the material that you provided a link to answers the question in case the link is broken or the material is changed. $\endgroup$
    – Alper
    Jan 17 at 17:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.