241 research outputs found
Dual Valuation and Hedging of Bermudan Options
Abstract. Some years ago, a different characterization of the value of a Bermudan option was discovered which can be thought of as the viewpoint of the seller of the option, in contrast to the conventional characterization which took the viewpoint of the buyer. Since then, there has been a lot of interest in finding numerical methods which exploit this dual characterization. This paper presents a pure dual algorithm for pricing and hedging Bermudan options
Dual Valuation and Hedging of Bermudan Options
Abstract. Some years ago now, a different characterisation of the value of a Bermudan option was discovered, which can be thought of as the viewpoint of the seller of the option, in contrast to the conventional characterisation which took the viewpoint of the buyer. Since then, there has been a lot of interest in finding numerical methods which exploit this dual characterisation. This paper presents a pure dual algorithm for pricing and hedging Bermudan options
An Irregular Grid Approach for Pricing High-Dimensional American Options
We propose and test a new method for pricing American options in a high-dimensional setting.The method is centred around the approximation of the associated complementarity problem on an irregular grid.We approximate the partial differential operator on this grid by appealing to the SDE representation of the underlying process and computing the root of the transition probability matrix of an approximating Markov chain.Experimental results in five dimensions are presented for four different payoff functions.option pricing;inequality;markov chains
Pricing and hedging American-style options with deep learning
In this paper we introduce a deep learning method for pricing and hedging
American-style options. It first computes a candidate optimal stopping policy.
From there it derives a lower bound for the price. Then it calculates an upper
bound, a point estimate and confidence intervals. Finally, it constructs an
approximate dynamic hedging strategy. We test the approach on different
specifications of a Bermudan max-call option. In all cases it produces highly
accurate prices and dynamic hedging strategies with small replication errors
An Irregular Grid Approach for Pricing High-Dimensional American Options
We propose and test a new method for pricing American options in a high-dimensional setting.The method is centred around the approximation of the associated complementarity problem on an irregular grid.We approximate the partial differential operator on this grid by appealing to the SDE representation of the underlying process and computing the root of the transition probability matrix of an approximating Markov chain.Experimental results in five dimensions are presented for four different payoff functions
A backward dual representation for the quantile hedging of Bermudan options
Within a Markovian complete financial market, we consider the problem of
hedging a Bermudan option with a given probability. Using stochastic target and
duality arguments, we derive a backward numerical scheme for the Fenchel
transform of the pricing function. This algorithm is similar to the usual
American backward induction, except that it requires two additional Fenchel
transformations at each exercise date. We provide numerical illustrations
Sensitivities for Bermudan Options by Regression Methods
In this article we propose several pathwise and finite difference based methods for calculating sensitivities of Bermudan options using regression methods and Monte Carlo simulation. These methods rely on conditional probabilistic representations which allow, in combination with a regression approach, for efficient simultaneous computation of sensitivities at many initial positions. Assuming that the price of a Bermudan option can be evaluated sufficiently accurate, we develop a method for constructing deltas based on least squares. We finally propose a testing procedure for assessing the performance of the developed methods.American and Bermudan options, Optimal stopping times, Monte Carlo simulation, Deltas, Conditional probabilistic representations, Regression methods
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