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3

In swaptions, there is the expiration of the swaption into an underlying swap. When the dealers provide the vol surface, in the first column, they typically put the expiry of the swaption from earliest to farthest. Along the top row, they put maturity of the underlying swap from shortest to farthest. So when the dealers describe the upper left having high ...

-1

It's hard to help without knowing how you tried to solve the problem. However, here's an idea: try to make the model simpler (simpler parameters) and price a simpler claim. Then look at the results. Are they correct now? If yes, then you can look at your code and figure out what might be going wrong when you change the parameters. If your result is ...

5

In a practical manner, here is how you get to the PDE of your option: Use Girsanov theorem to go from the real-world measure to the risk-neutral measure (basically subtract the market price of risk $\mathrm dW^Q_t = \mathrm d W^P_t - \frac{\mu -r}{\sigma} \mathrm dt$). This will change your SDE. Discounted option price $e ^{-rt} v(t, S_t)$ has to be a ...

4

To compute the price of an American option or a callable instrument in general, at each potential exercise date, one is required to compare its continuation value (discounted risk-neutral expectation of what the option would pay off if it was not exercised) to the relevant exercise value/early redemption price. By construction, lattice and finite difference ...

1

Exactly what @Alex C said. It's the time homogeneous diffusion proprety. You can't state such an argument in models where volatility is no longer time homogeneous ( that's being time independant and depending only on the underlyings).

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