Abstract
We provide ready-to-use formulas for European options prices, risk sensitivities, and P&L calculations under Lévy-stable models with maximal negative asymmetry. Particular cases, efficiency testing, and some qualitative features of the model are also discussed.
Highlights
The pricing of financial derivatives, such as options, is an important yet difficult task in mathematical finance, in particular when one wishes to implement a model capturing realistic market patterns
The Black-Scholes model has become popular among practitioners notably because of its simplicity, and because it admits a closed formula for the option price
Wu (2003) and called Finite Moment Log-Stable (FMLS) option-pricing model, makes the assumption that the instantaneous log returns of the underlying price are driven by a specific class of Lévy process; it is linked to fractional calculus because the model can equivalently be described by replacing the space derivative operator in the diffusion equation by the so-called Riesz-Feller fractional derivative
Summary
The pricing of financial derivatives, such as options, is an important yet difficult task in mathematical finance, in particular when one wishes to implement a model capturing realistic market patterns. Wu (2003) and called Finite Moment Log-Stable (FMLS) option-pricing model, makes the assumption that the instantaneous log returns of the underlying price are driven by a specific class of Lévy process; it is linked to fractional calculus because the model can equivalently be described by replacing the space derivative operator in the diffusion equation by the so-called Riesz-Feller fractional derivative It was introduced by Carr and Wu to reproduce the maturity pattern of the implied volatility maturity smirk (the phenomenon that, for a given maturity, implied volatility are higher for out-of-the-money puts than for out-of-the-money calls); it is widely observed that the smirk (as a function of moneyness) does not flatten out as maturity increases, which is in contradiction with the Gaussian hypothesis: if the risk-neutral density were converging to the normal distribution, the smirk would flatten for longer maturities.
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