Modelling dependence in finance using copulas - Thierry Roncalli's ...
Modelling dependence in finance using copulas - Thierry Roncalli's ...
Modelling dependence in finance using copulas - Thierry Roncalli's ...
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An example of the computation of the implied parameter ˆρ<br />
• BS model: LN distribution calibrated with ATM options; Pric<strong>in</strong>g<br />
kernel = LN distributions + Normal copula<br />
ˆρ 1 = −0.341<br />
• Bahra model: mixture of LN distributions calibrated with eight<br />
European prices; Pric<strong>in</strong>g kernel = MLN distributions + Normal<br />
copula<br />
ˆρ 2 = 0.767<br />
Remark 3 ˆρ 1 and ˆρ 2 are parameters of the Normal Copula. ˆρ 1 is a<br />
Pearson correlation, not ˆρ 2 .<br />
⇒ BS model: negative <strong>dependence</strong> / Bahra model: positive<br />
<strong>dependence</strong>.<br />
<strong>Modell<strong>in</strong>g</strong> <strong>dependence</strong> <strong>in</strong> f<strong>in</strong>ance us<strong>in</strong>g <strong>copulas</strong><br />
New pric<strong>in</strong>g methods with <strong>copulas</strong> 4-8
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