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newbanker
Topic Author
Posts: 43
Joined: June 10th, 2007, 6:30 am

### Errors in Hagan's papers on LGM

In the paper "Evaluating and Hedging swap instruments via LGM", on page 14, displayed equation (5.6), there appears to be a typographicalerror in passing from the second integral to the third. Instead of the square of the differences $(H_i-H_0)^2$, there should appearthe difference of the squares $H_i^2-H_0^2$ (and similarly for the additional term containing $H_n$). Also, the next line should notcontain the term $\zeta_e$ in the gaussian density after the change of variables from $x$ to $y$. In contrast to other typos scattered across this paper, this particular one is not entirely harmless, as it results in wrong equations for the calibration process. In particular, the equation defining the breakeven point $y^*$ is wrong. Two other papers of Hagan on the subject contain exactly the same errors.
Last edited by newbanker on May 28th, 2014, 10:00 pm, edited 1 time in total.

kelang
Posts: 46
Joined: November 14th, 2011, 4:53 pm

### Errors in Hagan's papers on LGM

QuoteOriginally posted by: newbankerIn the paper "Evaluating and Hedging swap instruments via LGM", on page 14, displayed equation (5.6), there appears to be a typographicalerror in passing from the second integral to the third. Instead of the square of the differences $(H_i-H_0)^2$, there should appearthe difference of the squares $H_i^2-H_0^2$ (and similarly for the additional term containing $H_n$). Also, the next line should notcontain the term $\zeta_e$ in the gaussian density after the change of variables from $x$ to $y$. In contrast to other typos scattered across this paper, this particular one is not entirely harmless, as it results in wrong equations for the calibration process. In particular, the equation defining the breakeven point $y^*$ is wrong. Two other papers of Hagan on the subject contain exactly the same errors.i went through the maths long time ago when implementing the model. The formula is correct, you need to carefully rearrange some terms, i.e. rewrite $(H_i^2-H_0^2)/2$ into $((H_i-H_0)^2)/2$ then rearrange the equations.

newbanker
Topic Author
Posts: 43
Joined: June 10th, 2007, 6:30 am

### Errors in Hagan's papers on LGM

Thank you for reply. I looked again, and you are right. My mistake.
Last edited by newbanker on May 29th, 2014, 10:00 pm, edited 1 time in total.