Page **1** of **1**

### Errors in Hagan's papers on LGM

Posted: **May 29th, 2014, 10:37 am**

by **newbanker**

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.

### Errors in Hagan's papers on LGM

Posted: **May 29th, 2014, 2:09 pm**

by **kelang**

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.

### Errors in Hagan's papers on LGM

Posted: **May 30th, 2014, 8:04 am**

by **newbanker**

Thank you for reply. I looked again, and you are right. My mistake.