Valuation of piecewise linear barrier options

From Continuous to Discrete: Studies on Continuity Corrections and Monte Carlo Simulation with Applications to Barrier Options and American Options Menghui Cao This dissertation 1) shows continuity corrections for first passage probabilities of Brownian bridge and barrier joint probabilities, which are applied to the pricing of two-dimensional barrier and partial barrier options, and 2) introduces new variance reduction techniques and computational improvements to Monte Carlo methods for pricing American options. The joint distribution of Brownian motion and its first passage time has found applications in many areas, including sequential analysis, pricing of barrier options, and credit risk modeling. There are, however, no simple closed-form solutions for these joint probabilities in a discrete-time setting. Chapter 2 shows that, discrete two-dimensional barrier and partial barrier joint probabilities can be approximated by their continuous-time probabilities with remarkable accuracy after shifting the barrier away from the underlying by a factor of βσ √ ∆t. We achieve this through a uniform continuity correction theorem on the first passage probabilities for Brownian bridge, extending relevant results in Siegmund (1985a). The continuity corrections are applied to the pricing of two-dimensional barrier and partial barrier options, extending the results in Broadie, Glasserman & Kou (1997) on one-dimensional barrier options. One interesting aspect is that for type B partial barrier options, the barrier correction cannot be applied throughout one pricing formula, but only to some barrier values and leaving the other unchanged, the direction of correction may also vary within one

Impediments to customer integration into the innovation process: A case study in the telecommunications industry

Information is considered as a prerequisite for development in today’s world. This belief has led to several measures to make information freely available to the citizens. Use of ICTs for development is a step in that direction, as they are expected to make communication more democratic and easy, leading to developmental outcomes. It is estimated that 60% of all ICT projects in Asia are located in India. Many players - national and state governments, private business organizations and civil society groups are engaged in their implementation. Despite huge investments, studies indicate that the developmental use of such projects is very low. ICTs for development projects have been studied using diverse tools and theories. Failure has been attributed to several factors including various types of barriers, faulty institutions, and technology related issues. This paper places analysis on ICTD projects within the context of CPR (Common Pool Resources) studies. In recent years, the definition of CPR has been expanded to include information as “new commons” and robust institutions are deemed essential for survival of all CPRs. In this paper, ICT based development projects have been interpreted as CPR institutions and CPR design principles have been used to explain the functioning of two ICTD projects. Both these studies were carried out in the state of Uttarakahnd, India and analysis is confined to use of agricultural information by the farming community.KeywordsInformation commonsDesign principlesICT projects

The article discusses the reasons for the emergence of communication barriers in the anticrisis management of the organization. Various types of barriers are described, their classification is given. The author proposes mechanisms for reducing the communication barriers of the organization in the process of the management of anti-crisis communications.

Pricing Bounds on Barrier Options

Barrier option pricing under the 2-hypergeometric stochastic volatility model

Implementation of the modified Monte Carlo simulation for evaluate the barrier option prices

The pricing and static hedging of multi-step double barrier options

Pricing Continuously Monitored Barrier Options Under the Sabr Model: A Closed-Form Approximation

The two barrier values in the double barrier option are the focus in the evaluation simulation and they affect the knock-in and knock-out of the option. This paper, simulates a double barrier option and calculates its option value based on the Black-Scholes Model, using Coca-Cola stock data from January 2022 to the end of July, and verifies the feasibility of the Black-Scholes model. This paper also analyzes the sensitivity of the influence of the two barrier values on the option value, outlining the option value changes under different barrier values. The main finding of this paper is that the Black-Scholes formula is used to verify the value of the Coca-Cola option product. This study enriches the practical examples of the validation of double barrier option products in the Black-Scholes formula.

We discuss here an alternative interpretation of the familiar binomial lattice approach to option pricing, illustrating it with reference to pricing of barrier options, one- and two-sided, with fixed, moving or partial barriers, and also the pricing of American put options. It has often been observed that if one tries to price a barrier option using a binomial lattice, then one can find slow convergence to the true price unless care is taken over the placing of the grid points in the lattice; see, for example, the work of Boyle & Lau [2]. The placing of grid points is critical whether one uses a dynamic programming approach, or a Monte Carlo approach, and this can make it difficult to compute hedge ratios, for example. The problems arise from translating a crossing of the barrier for the continuous diffusion process into an event for the binomial approximation. In this article, we show that it is not necessary to make clever choices of the grid positioning, and by interpreting the nature of the binomial approximation appropriately, we are able to derive very quick and accurate pricings of barrier options. The interpretation we give here is applicable much more widely, and helps to smooth out the ‘odd-even’ ripples in the option price as a function of time-to-go which are a common feature of binomial lattice pricing.

A barrier option is an exotic path-dependent option contract that, depending on terms, automatically expires or can be exercised only if the underlying asset ever reaches a predetermined barrier price. Using a partial differential equation approach, we provide an integral representation of the barrier option price via the Mellin transform. In the case of knock-out barrier options, we obtain a decomposition of the barrier option price into the corresponding European option value minus a barrier premium. The integral representation formula can be expressed in terms of the solution to a system of coupled Volterra integral equations of the first kind. Moreover, we suggest some possible numerical approaches to the problem of barrier option pricing.

Author index of volume 144

In this paper we discuss an option pricing problem in a hidden Markovian regime-switching model with a stochastic interest rate and volatility. Regime switches are attributed to structural changes in an hidden economic environment and are described by a continuous-time, finite-state, unobservable Markov chain. The model is then applied to the valuation of a standard European option. By means of the standard separation principle, filtering and option valuation problems are separated. Robust filters for the hidden states of the economy and their robust filtered estimates of unknown parameters from the expectation maximization algorithm are presented based on standard techniques in filtering theory. Then an explicit expression of a conditional characteristic function relevant to option pricing is presented and the valuation of the option is discussed using the inverse Fourier transformation approach. Using the limiting behavior of the conditional characteristic function, an efficient implementation of the transform inversion integral is considered. Numerical experiments are given to illustrate the flexibility of filtering algorithms and the significance of regime-switching in option pricing.

In this article barrier options are analytically evaluated under the regime-switching model, with the volatility of the underlying price being allowed to jump between different states following a Markov chain. The target barrier option prices are expressed in a Fourier cosine series after a particular approximation formula is obtained. The accuracy and efficiency of the newly derived formula are demonstrated through numerical experiments, demonstrating the formula’s potential for practical applications. TOPICS:Analysis of individual factors/risk premia, factor-based models, options Key Findings • Barrier options are analytically evaluated under the regime-switching model. • This approximation formula is written in the form of a converged Fourier cosine series. • The formula is shown to be very accurate and efficient, and has a great potential to be applied in practice.