Related papers: Some Control Variates for exotic options
Traders are often faced with large block orders in markets with limited liquidity and varying volatility. Executing the entire order at once usually incurs a large trading cost because of this limited liquidity. In order to minimize this…
This paper is devoted to study the effects arising from imposing a value-at-risk (VaR) constraint in mean-variance portfolio selection problem for an investor who receives a stochastic cash flow which he/she must then invest in a…
The robust option pricing problem is to find upper and lower bounds on fair prices of financial claims using only the most minimal assumptions. It contrasts with the classical, model-based approach and gained prominence in the wake of the…
Consider a process, stochastic or deterministic, obtained by using a numerical integration scheme, or from Monte-Carlo methods involving an approximation to an integral, or a Newton-Raphson iteration to approximate the root of an equation.…
Some expansion methods have been proposed for approximately pricing options which has no exact closed formula. Benhamou et al. (2010) presents the smart expansion method that directly expands the expectation value of payoff function with…
In this article, we show how the scaling symmetry of the SABR model can be utilized to efficiently price European options. For special kinds of payoffs, the complexity of the problem is reduced by one dimension. For more generic payoffs,…
Multifidelity Monte Carlo methods often rely on a preprocessing phase consisting of standard Monte Carlo sampling to estimate correlation coefficients between models of different fidelity to determine the weights and number of samples for…
In commodity and energy markets swing options allow the buyer to hedge against futures price fluctuations and to select its preferred delivery strategy within daily or periodic constraints, possibly fixed by observing quoted futures…
We show that deliberately introducing a nested simulation stage can lead to significant variance reductions when comparing two stopping times by Monte Carlo. We derive the optimal number of nested simulations and prove that the algorithm is…
In this paper, we derive closed-form formulas of first-order approximation for down-and-out barrier and floating strike lookback put option prices under a stochastic volatility model, by using an asymptotic approach. To find the explicit…
We study an optimal control problem under uncertainty, where the target function is the solution of an elliptic partial differential equation with random coefficients, steered by a control function. The robust formulation of the…
We present a Monte Carlo method to compute efficiently susceptibilites or covariances of two physical variables. The method relies on a generalization of the exchange cluster algorithm to any model of interacting particles with any $2$-body…
We investigate the mechanism that leads to systematic deviations in cluster Monte Carlo simulations when correlated pseudo-random numbers are used. We present a simple model, which enables an analysis of the effects due to correlations in…
We develop generic and efficient importance sampling estimators for Monte Carlo evaluation of prices of single- and multi-asset European and path-dependent options in asset price models driven by L\'evy processes, extending earlier works…
Using spectral decomposition techniques and singular perturbation theory, we develop a systematic method to approximate the prices of a variety of options in a fast mean-reverting stochastic volatility setting. Four examples are provided in…
We consider a class of finite time horizon nonlinear stochastic optimal control problem, where the control acts additively on the dynamics and the control cost is quadratic. This framework is flexible and has found applications in many…
The combination of continuum Many-Body Quantum physics and Monte Carlo methods provide a powerful and well established approach to first principles calculations for large systems. Replacing the exact solution of the problem with a…
We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where…
We consider stochastic volatility models under parameter uncertainty and investigate how model derived prices of European options are affected. We let the pricing parameters evolve dynamically in time within a specified region, and…
In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by…