Model-free stochastic collocation for an arbitrage-free implied volatility. I. (English) Zbl 1431.91400
Summary: This paper explains how to calibrate a stochastic collocation polynomial against market option prices directly. The method is first applied to the interpolation of short-maturity equity option prices in a fully arbitrage-free manner and then to the joint calibration of the constant maturity swap convexity adjustments with the interest rate swaptions smile. To conclude, we explore some limitations of the stochastic collocation technique.
MSC:
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
Keywords:
stochastic collocation; implied volatility; quantitative finance; arbitrage-free; risk-neutral densityReferences:
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