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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 $1$.

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  • $\begingroup$ This is a strange model, where does it come from? $\endgroup$
    – jherek
    Commented Oct 19, 2023 at 8:02

1 Answer 1

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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

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    $\begingroup$ 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
    Commented Jan 17, 2023 at 17:06

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