Related papers: Optimal quantization for the pricing of swing opti…
In the present paper, we introduce a numerical scheme for the price of a barrier option when the price of the underlying follows a diffusion process. The numerical scheme is based on an extension of a static hedging formula of barrier…
In the following paper we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of…
This paper presents a multinomial method for option pricing when the underlying asset follows an exponential Variance Gamma process. The continuous time Variance Gamma process is approximated by a discrete time Markov chain with the same…
We consider robust pricing and hedging for options written on multiple assets given market option prices for the individual assets. The resulting problem is called the multi-marginal martingale optimal transport problem. We propose two…
We consider rate swaps which pay a fixed rate against a floating rate in presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error.…
We proposed a two-step Longstaff Schwartz Monte Carlo (LSMC) method with two regression models fitted at each time step to price game options. Although the original LSMC can be used to price game options with an enlarged range of path in…
An American option grants the holder the right to select the time at which to exercise the option, so pricing an American option entails solving an optimal stopping problem. Difficulties in applying standard numerical methods to complex…
Calculation of an optimal tariff is a principal challenge for pricing actuaries. In this contribution we are concerned with the renewal insurance business discussing various mathematical aspects of calculation of an optimal renewal tariff.…
We propose a new method for finding statistical arbitrages that can contain more assets than just the traditional pair. We formulate the problem as seeking a portfolio with the highest volatility, subject to its price remaining in a band…
We develop a numerical method for pricing multidimensional vanilla options in the Black-Scholes framework. In low dimensions, we improve an adaptive integration algorithm proposed by two of the authors by introducing a new splitting…
We consider the problem of pricing discretely monitored Asian options over $T$ monitoring points where the underlying asset is modeled by a geometric Brownian motion. We provide two quantum algorithms with complexity poly-logarithmic in $T$…
This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on…
Options on baskets (linear combinations) of assets are notoriously challenging to price using even the simplest log-normal continuous-time stochastic models for the individual assets. The paper [5] gives a closed form approximation formula…
Computational aspects of the optimal consumption and investment with the partially observed stochastic volatility of the asset prices are considered. The new quantization approach to filtering - density quantization - is introduced which…
In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time…
We introduce a new method to price American options based on Chebyshev interpolation. In each step of a dynamic programming time-stepping we approximate the value function with Chebyshev polynomials. The key advantage of this approach is…
We consider a revenue maximization model, in which a company aims at designing a menu of contracts, given a population of customers. A standard approach consists in constructing an incentive-compatible continuum of contracts, i.e., a menu…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise…
Currency arbitrage capitalizes on price discrepancies in currency exchange rates between markets to produce profits with minimal risk. By employing a combinatorial optimization problem, one can ascertain optimal paths within directed…