I'm provided the forward curve and time 0 prices of ATM Caps.

Volatility is 1-factor Gaussian HJM model with specification:

$$ \sigma(t, T) = \nu \exp \{ \beta (T − t) \} $$

Now, I need to calibrate the volatility parameters $\beta$ and $\nu$ to the cap prices weighted by corresponding Black vegas (weighted least squares).

But the problem is I do not know the cap rate (strike rate) and since Black vegas are a function of cap rate (strike rate), I'm lost on how to proceed.

Will be very thankful if someone can point me in the correct direction. The formula for Caplets is:enter image description here

  • $\begingroup$ What are black vegas? $\endgroup$ – Bob Jansen Apr 8 '17 at 10:16
  • 1
    $\begingroup$ In the field of i.r. derivatives,, the Black (1976) formula is applied to the valuation of interest rate caplets [see Cpl(.,.)= formula above] , and Caps (Cap = sum of caplets). The formula depends on implied volatilities v(.,.) , the sensitivity of the cap price to changes in i.v. is called the Black Vega. $\endgroup$ – Alex C Apr 8 '17 at 14:29

Because these are ATM Swaps, strike rates should be equal to the Swap rates which can be computed off the forward curves


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