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Improving on [Jäc06] and [Vog07], we show how Black's volatility can be implied from option prices with as little as two iterations to maximum attainable precision on standard (64‐bit floating point) hardware for all possible inputs. The method is based on four rational function branches for the initial guess adapted to the log‐moneyness, two of which are combined with nonlinear transformations of...
The ECB is increasingly reliant on influencing market sentiment to buy time; hoping growth, inflation and structural reforms restore the Euro‐Zone's fortunes.
Prices of CSA instruments are observed in a world which is not natural for LIBOR based payoffs in the sense that LIBOR forward is not martingale under CSA‐forward measure. From a theoretical perspective, pricing models for collateralized LIBOR based payoffs should account for CSA‐convexity, implied when changing from CSA‐forward measure to LIBOR‐forward measure. In practice CSA‐convexity effect is...
If you are not starting from the position of being a gamekeeper turned poacher it behooves recruiters well to ensure that they are almost as technically literate as the candidates they seek to hire.
The semi‐analytical valuation of CEV American options is either computationally expensive when it delivers sufficiently accurate prices, lacks accuracy when computations are faster, or involves functions whose computations can be unstable. Trinomial schemes have the disadvantage that there are no built‐in ways to compute hedging sensitivities and re‐runs are required for the computation of deltas...
We consider the problem of reducing the variance of Monte Carlo estimators of high‐dimensional estimation problems by combining the variance reduction techniques Latin hypercube sampling with dependence (LHSD), control variates and importance sampling. Under some standard conditions, the resulting estimators are consistent and asymptotically unbiased, and a central limit theorem holds. The effectiveness...
A book's delta risks are usually calculated by bumping the rate of each stripping instrument, re‐stripping the discount curve, and re‐valuing the book using the new discount curve. The difference between the new and old value of the book is the book's bucket delta risk with respect to that stripping instrument. After finding the bucket delta risks with respect to all the stripping instruments, the...
A recently published book makes proposals for an economic and monetary reformation that go beyond ideas of narrow‐ or limited‐purpose banking. In so doing, the claim is made that boundary problems and shadow banking‐induced crises will be a thing of the past. With the faint death knell of the OTC derivatives markets ringing in our ears, Wilmott corresponds with the ‘author’ of The End of Banking in...
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