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Re: Options, Futures & Other Derivatives, Hull 9th Ed, p744.

  1. What does "m(t)" represent? I am struggling to understand the definition provided of: "Index for the next reset date at time t; this means that m(t) is the smallest integer such that t <= t_m(t)"

  2. In equation 32.8 (lower half od page 744), what do the parameters "v" represent? I can't seem to find it defined anywhere.

Thank you.

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1 Answer 1

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Regarding 1:

$m(t)$ returns the index in a tenor structure formed by the "reset times" such that $t \leqslant t_{m(t)}$. So, for example, given a tenor structure formed by the reset times $t_1, t_2, \dots$ and a time $t$ such that $t_1 < t_2 < t \leqslant t_3 \dots$, then $m(t) = 3$. Now, it is clear that $m(t)$ refers to the index of the next reset time.

Regarding 2:

$v_k(t)$ seems to be the volatility of the zero coupon bond $P(t, T_k)$, see the equation between (32.7) and (32.8).

Lastly, I would strongly recommend you to follow a different book for these kind of subjects. For example, Interest Rate Modeling from Andersen and Piterbarg. I think that learning quantitative finance from Option, Futures & Other Derivatives is not a great idea.

Thank you!

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