The Stochastic Alpha Beta Rho Stochastic Volatility (SABR-SV) model is widely used in the financial industry for the pricing of fixed income instruments. In this paper we develop a low-bias simulation scheme for the SABR-SV model, which deals efficiently with (undesired) possible negative values in the asset price process, the martingale property of the discrete scheme and the discretization bias of commonly used Euler discretization schemes. The proposed algorithm is based the analytic properties of the governing distribution. Experiments with realistic model parameters show that this scheme is robust for interest rate valuation.
Model Predictive Control (MPC) is a model-based control method based on a receding horizon approach and online optimization. In previous work we have extended MPC to a class of discrete-event systems, namely the max-plus linear systems, i.e., models that are "linear" in the maxplus algebra. Lately, the application of MPC for stochastic max-plus-linear systems has attracted a lot of attention. At each event step, an optimization problem then has to be solved that is, in general, a highly complex and computationally hard problem. Therefore, the focus of this paper is on decreasing the computational complexity of the optimization problem. To this end, we use an approximation approach that is based on the p-th raw moments of a random variable. This method results in a much lower computational complexity and computation time while still guaranteeing a good performance.
Abstract.Research into the direction of specific exotic options -like the Parisians -is often driven by the analysis of structured products. These products contain features that are similar to exotic options. Exchangetrading of the pure exotics is very rare. In the period of rising stock markets, investors were less interested in buying bonds. In order to regain their interest, firms added extra features to the bonds they wanted to issue. One of these features is the right of the bond holder to convert the bond into a given number of stocks under certain conditions. Bonds with this feature are called convertible bonds and are nowadays very common. Most convertible bonds can be re-called by the issuer when the convertible trades above some level for some period. Modelling this feature corresponds to valuation of a Parisian option. In this paper we will point out how we quickly can approximate the Parisian option price by using a standard barrier option with a modified barrier. This is common practice for traders; they increase or decrease the barrier a bit. Here we want to argue what that bit should be. First we will introduce the Parisian contract. Thereafter we list the methods of valuing the Parisian, followed by a section about the implied barrier method. Here we will use concepts from the theory on Brownian excursions and exploit them to derive prices for Parisians that are already in the excursion. We will conclude with a numerical example.
The Parisian ContractLet {S t , F t ; t ≥ 0} be a process defined on the filtered probability space (Ω, F, F t , P). According to the Black-Scholes model we have for the risk neutral price processwhere {B t , F t ; t ≥ 0} denotes a standard Brownian Motion, s 0 the initial value of the stock, r the interest rate and σ the volatility. We can use this risk-neutral stock price process to calculate the price of a derivative V Φ with some (path dependent) pay-off Φ ((S t ) 0≤t≤T ) at time T by,Here Φ is the contract function. A standard barrier option is a derivative that pays off like a put or a call that knocks in or out as soon as the stock price hits M.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.