We consider the Cauchy problem associated with a general parabolic partial differential
equation in d dimensions. We find a family of closed-form asymptotic approximations for the …

The implied volatility is a crucial element of any financial toolbox, since it is used for quoting
and the hedging of options as well as for model calibration. In contrast to the Black-Scholes …

In this paper, we introduce the concept of standardized call function and we obtain a new
approximating formula for the Black and Scholes call function through the hyperbolic …

We prove asymptotic convergence results for some analytical expansions of solutions to
degenerate PDEs with applications to financial mathematics. In particular, we combine short …

This research paper introduces a new form of Implied Volatility calculation with Symbolic
Regression suited for high-frequency trading. The solutions are easily migratable to …

Asymptotic methods can be used to analyze and simplify pricing and portfolio optimization
problems. Broadly speaking, there are two methods of setting up asymptotic expansions for …

In this paper it is proved that the Black–Scholes implied volatility satisfies a second order
non-linear partial differential equation. The obtained PDE is then used to construct an …

We find approximate solutions of partial integro-differential equations, which arise in
financial models when defaultable assets are described by general scalar Lévy-type …

We introduce a method to construct a bivariate rational approximation particularly suited to
accurately and compactly represent the inverse of a bivariate function. At the core of the …

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Interest Rate Problems: Implied Volatility of Options on Bonds and Forward Rates, and Optimal …