Options with embedded early exercise features are of fundamental importance in finance. A simple example is the hedge of a multi-callable bond. This instrument is hedged using a Bermudan swaption.Bermudan swaptions also play a key role when pricing callable constant maturity swaps or flexible...

Two of the most important areas in computational finance: Greeks and, respectively, calibration, are based on efficient and accurate computation of a large number of sensitivities. This paper gives an overview of adjoint and automatic differentiation (AD), also known as algorithmic...

We present a simple method for “inverting” a volatility smile: that is, generating a CDF and inverse CDF given a discrete set of implied volatilities. The method is based on constructing a piece-wise linear CDF that is guaranteed to exactly reprice any non-arbitrageable input volatilities....

A new algorithm for calibrating agent-based models is proposed, which employs a popular gradient boosting framework. Machine learning techniques are not used to develop a surrogate model, but rather assist in narrowing down the parameter space during the search for optimal parameters. Our...

Ricardo Chacoacute;n generalized Johan Gielis's superformula by introducing elliptic functions in place of trigonometric functions. In this paper an attempt has been made to fit the Chacoacute;n-Gielis curves (modified by various functions) to simulated data. Estimation has been done by the...

In this paper we consider the object oriented implementation of numerical algorithms where arithmetic operators (add, mult, exp) operate on objects with more complex structure (compared to floating point numbers). Examples are objects representing vectors instead of scalars, random variables,...

Robust optimization (RO) is a young and active research field that has been mainly developed in the last 15 years. RO techniques are very useful for practice and not difficult to understand for practitioners. It is therefore remarkable that real-life applications of RO are still lagging behind;...

One of the most important factors to control for the achievements of investment portfolio returns is risk. If we only think that a 100% positive return is needed to recover a portfolio loss of 50%, we can understand why. With the advent of the exponential growth of technology usage in markets,...

In the economics of joint production one often distinguishes between the two cases: the one in which a firm produces multiple products each produced under separate production process, and the other "true joint production" where a number of outputs are produced from a single production process,...

Adjustable robust optimization (ARO) is a technique to solve dynamic (multistage) optimization problems. In ARO, the decision in each stage is a function of the information accumulated from the previous periods on the values of the uncertain parameters. This information, however, is often...