arXiv subjects

Michel Vellekoop

Publications and source records attributed to Michel Vellekoop.

7 recordsLinked to original sources

arXiv2026

Neural Calibration of a Complete Market Model

We propose a neural calibration method to construct a recombining binomial tree directly from a set of given option prices. Rather than estimating a continuous option pricing function or a local volatility surface as an intermediate object, a neural network is used to deform a benchmark lattice. This leads to a discrete pricing model which is guaranteed to be arbitrage-free, complete, easy to interpret, and can be used directly for pricing and to find replicating trading strategies. Calibration is formulated as a penalized optimization problem that combines a repricing error with an admissibility penalty, and an optional spatial regularization term based on implied local volatilities. Numerical experiments on synthetic and SPX market data show that the proposed approach yields accurate repricing and is very competitive when compared to recently proposed other neural calibration methods. It preserves the computational advantages of lattice-based valuation and hedging. In particular, the calibrated tree can be reused to price contracts that allow early exercise, and could even be calibrated directly with American option prices.

q-fin.CP↗

arXiv2023

Plant Performance in Precision Horticulture: Optimal climate control under stochastic uncertainty

This paper presents a risk mitigating, time-varying feedback control algorithm for crop production when state dynamics are subject to uncertainty. The model based case study concerns a 40 day production round of lettuce in a greenhouse where control input consists of daily and nightly temperature set points. The control problem was formulated in terms of a stochastic Markov decision process with the objective to maximize the expected net revenue at harvest time. The importance of time-varying feedback and of risk mitigation was investigated by making a comparison with a controller that takes uncertainty into account but is static and a controller which is dynamic but ignores the uncertainty in the state dynamics. For the case of heat limited crop growth, and strict requirements on harvest weight precision, the dynamic stochastic controller outperformed the static controller in terms of both maximal expected net revenue (by 19 %) and state precision at harvest time (with 50 % less standard deviation). It also outperformed the deterministic controller for both criteria (15 % in maximal expected net revenue and 8 % less standard deviation). A detailed sensitivity analysis showed that such improvements in performance levels are robust, since they hold over large ranges of uncertainty in state dynamics, required harvest precision levels, starting days, and initial weights. The results provide insights in potential of dynamic feedback and risk mitigation strategies for high precision requirements under uncertainty. Although the results should be interpreted with caution, they illustrate the considerable potential benefit for stochastic greenhouse climate control under uncertainty when high precision is required.

math.OC↗

arXiv2022

Estimating the impact of the COVID-19 pandemic using granular mortality data

We present an extension of the Li and Lee model to quantify mortality in five European countries during the COVID-19 pandemic. The first two factors are used to model the pre-COVID mortality, with the first layer modelling the common trend and the second layer the country-specific deviation from the common trend. We add a third layer to capture the country-specific impact of COVID-19 in 2020 and 2021 in excess of the pre-COVID trend. We use weekly mortality data from the Short Term Mortality Fluctuations Database to calibrate this third factor, and we use a more granular dataset for deaths in the Netherlands to assess the added value of more detailed data. We use our framework to define mortality forecasts based on different possible scenarios for the future course the pandemic.

stat.AP↗

arXiv2018

Minimum reversion in multivariate time series

We propose a new multivariate time series model in which we assume that each component has a tendency to revert to the minimum of all components. Such a specification is useful to describe phenomena where each member in a population which is subjected to random noise mimics the behaviour of the best performing member. We show that the proposed dynamics generate co-integrated processes.We characterize the model's asymptotic properties for the case of two populations and show a stabilizing effect on long term dynamics in simulation studies. An empirical study involving human survival data in different countries provides an example which confirms the occurrence of the phenomenon of reversion to the minimum in real data.

stat.AP↗

arXiv2018

Exact Solutions for Optimal Investment Strategies and Indifference Prices under Non-Differentiable Preferences

We propose an algorithm to calculate the exact solution for utility optimization problems on finite state spaces under a class of non-differentiable preferences. We prove that optimal strategies must lie on a discrete grid in the plane, and this allows us to reduce the dimension of the problem and define a very efficient method to obtain those strategies. We also show how fast approximations for the value function can be obtained with an a priori specified error bound and we use these to replicate results for investment problems with a known closed-form solution. These results show the efficiency of our approach, which can then be used to obtain numerical solutions for problems for which no explicit formulas are known.

q-fin.PR↗

arXiv2010

Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time $t_d$ during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone. In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of $t_d$, and tends to $0$ as time tends to $t_d^-$ with a speed that we can characterize. When the dividend function is linear in a neighbourhood of zero, then we show continuity of the exercise boundary and a high contact principle in the left-hand neighbourhood of $t_d$. When it is globally linear, then right-continuity of the boundary and the high contact principle are proved to hold globally. Finally, we show how all the previous results can be extended to multiple dividend payment dates in that case.

q-fin.CP↗

arXiv2001

Symmetries in jump-diffusion models with applications in option pricing and credit risk

It is a well known fact that local scale invariance plays a fundamental role in the theory of derivative pricing. Specific applications of this principle have been used quite often under the name of `change of numeraire', but in recent work it was shown that when invoked as a fundamental first principle, it provides a powerful alternative method for the derivation of prices and hedges of derivative securities, when prices of the underlying tradables are driven by Wiener processes. In this article we extend this work to the pricing problem in markets driven not only by Wiener processes but also by Poisson processes, i.e. jump-diffusion models. It is shown that in this case too, the focus on symmetry aspects of the problem leads to important simplifications of, and a deeper insight into the problem. Among the applications of the theory we consider the pricing of stock options in the presence of jumps, and Levy-processes. Next we show how the same theory, by restricting the number of jumps, can be used to model credit risk, leading to a `market model' of credit risk. Both the traditional Duffie-Singleton and Jarrow-Turnbull models can be described within this framework, but also more general models, which incorporate default correlation in a consistent way. As an application of this theory we look at the pricing of a credit default swap (CDS) and a first-to-default basket option.

cond-mat↗