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Feb 9

Quadrature method for convertible bond pricing

Posted by abiao at 21:50 | Code » Other | Comments(0) | Reads(8039)
A follow up post of my previous entry Using Quadrature method for option valuation, where the accuracy and computational speed are demonstrated briefly with a simple European option based on the paper "universal option valuation using quadrature methods". Today I play the Quadrature method for a vanilla convertible bond, still, the results are promising, for example, below is price performance comparision under Quadrature and PDE (specifically, finite element method) numerical solutions, where the CB has time-to-maturity two years, call barrier 12, call price 110, strike 10, risk-free rate 2%.
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The exact computational time depends on the time steps and asset steps, but generally speaking, since Quadrature has a higher order of convergency rate, it is several times faster than finite element, in my case, Quadrature costs me less than ten seconds but finite elements costs me around one minute.

PS: the y-axis should be relative error.

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