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For a european put option, starting from the classical Black-Scholes PDE (assuming constant rate), how do we come up with the Black-Scholes PDE under the Cox-Ingersoll-Ross model (CIR) such as the interest rates follows this process:

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(the stock follows a classical brownian motion, whose Wiener process is not correlated with the one of the interest rates)

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  • $\begingroup$ You first need the bond price, see the "bond pricing" section of en.wikipedia.org/wiki/Cox%E2%80%93Ingersoll%E2%80%93Ross_model. Then you can use Feymann-Kac to price your option. $\endgroup$ – user217285 May 2 '18 at 7:54
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    $\begingroup$ Can you complete your question: Is the option on a stock or a bond? What Wiener process is not correlated with the one of the interest rates? Is there a $B_{1, t}$ and where does it appear? $\endgroup$ – Gordon May 2 '18 at 14:53

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