Technical papers/Derivatives
Spread options, Farkas's lemma and linear programming
Vladimir Piterbarg derives necessary and sufficient conditions for the existence of a joint distribution consistent with given marginals and the distribution of the spread in terms of no-arbitrage conditions...
Vladimir Piterbarg derives necessary and sufficient conditions for the existence of a joint distribution consistent with given marginals and the distribution of the spread in terms of no-arbitrage conditions...
Derivatives businesses are under enormous pressure to deliver a clear rationale and unprecedented transparency for their products. Specialised quantitative support of structuring is required. Andrei Soklakov...
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More Technical papers/Derivatives articles
Spread options, Farkas's lemma and linear programming
Vladimir Piterbarg derives necessary and sufficient conditions for the existence of a joint distribution consistent with given marginals and the distribution of the spread in terms of no-arbitrage conditions among certain payouts. He also proposes a generic...
From spot volatilities to implied volatilities
Since the pioneering work of Dupire, the local volatility function can be derived from the implied volatility surface. Calculating implied volatilities from local volatilities is classically done by numerically solving the forward equation for call prices....
Cutting edge introduction
Most models are specified in continuous time form, but this can cause discrepancies and convergence headaches when implementing multiple numerical methods for different functions. Laurie Carver introduces this month’s technical section by looking at...
Random grids
In the context of a stochastic local volatility model, Jesper Andreasen and Brian Huge present a numerical solution scheme that achieves full consistency between calibration, finite difference solution and Monte Carlo simulation. The method is based on...
Repricing the cross smile: an analytic joint density
Derivatives contracts on multiple foreign exchange rates must be priced to avoid arbitrage by contracts on the cross-rates. Given the triangle of smiles for two underlyings and their cross, Peter Austing provides an analytic formula for a joint probability...
General short-rate analytics
Alexandre Antonov and Michael Spector present an analytical approximation of zero-coupon bonds and swaption prices for general short-rate models. The approximation is based on regular and singular expansions with respect to low volatility and contains...
From spot volatilities to implied volatilities
Since the pioneering work of Dupire, the local volatility function can be derived from the implied volatility surface. Calculating implied volatilities from local volatilities is classically done by numerically solving the forward equation for call prices....
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