An Analytic Approach for Pricing American Options with Regime Switching

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the economy which can be interpreted in terms of Markov chains. By means of the homotopy analysis method, an explicit formula for pricing two-state regime-switching American options is presented.

The gravity model of international trade of the EAEU, SCO and BRICS countries

This article discusses the factors influencing the financial and economic cooperation of the countries with the developing marker within the framework of the three blocks – EAEU, BRICS, and SCO, by means of building the gravity model. The countries of the former Soviet Union are considered separately. The research covers the period from the Russian crisis of 2014 up to the present. The subject of this analysis is the financial and economic relations arising in the process of cooperation of the EAEU, SCO, and BRICS member-states with the developing market. The author explores the factors that impact the financial and economic cooperation of the countries with the developing market: depth and scale of foreign trade turnover, per capita GDP, market accessibility index, currency appreciation rate of the import and export country, distance between the countries, belonging of the country with the developing market to such associations as EAEU, BRICS, and SCO. The research is based on the general scientific methods of cognition such as analysis, synthesis, and comparison, presentation of tabular and graphical interpretation of statistics, time series, econometric modelling using the EViews software. The novelty of this article consists in determination of the factors influencing financial and economic cooperation of the countries with the developing market within the framework of the three blocks – EAEU, BRICS, and SCO by means of building the gravity model. The peculiarity of such model lies in the availability of the lagged exchange rates. The inclusion of the lag in the relative exchange rate of the export country rate let to exclusion of the data for 2014 from the sampling. Therefore, it is advisable to take into account the acquired results pertaining to Russia’s cooperation on the bilateral or multilateral basis within the framework of EAEU, BRICS, and SCO.

An exact and explicit formula for pricing lookback options with regime switching

<p style='text-indent:20px;'>This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on states of the economy described by a continuous-time Markov chain process. We derive an exact, explicit and closed-form solution for European-style lookback options in a two-state regime switching model.</p>

Determining the Increase in a Building’s Appreciation Rate Due to a Reconstruction

The reconstruction of buildings generally prolongs their useful life, increases their utility value, and last but not least, leads to an increase in their value. These assumptions only apply if an independent third party reaches the same conclusion together with the owner. However, the undesirable effect of the reconstruction of a building may be a decrease in its value. The aim of this contribution is to determine the change in value of an older sample building assessed in the included case study as a result of its reconstruction. Valuation methods are applied, which, as it turns out, reveal the inaccuracy of the subjective view of the person who reconstructed the building. The resulting change in the value of the sample building is discussed from the point of view of the applied valuation methods and other value-creating aspects (subjective view of the owner on the value of the building, historical value of the building, etc.). The contribution concludes with recommendations for maximizing the increase in value of a property through its reconstruction so as to eliminate the risk of a decrease in its value.

Gravity model of international trade among EAEU, SCO and BRICS countries

This article is dedicated to examination of factors influencing the economic and financial cooperation of countries with developing market, namely EAEU, SCO and BRICS, by means of building a gravity model of trade. Special attention is given to affiliation of the countries to former USSR. The established timeframe starts with the crisis for Russia 2014 and continuous until the present. The subject of this research is the economic and financial relations emerged in the process of cooperation of EAEU, SCO and BRICS member-states with developing market. The author examines the factors affecting economic and financial cooperation of these countries, such as the size of external trade, gross domestic product per capita, trade openness index, currency appreciation rate of importing and exporting countries, distance between the countries, affiliation of the country with developing market to EAEU, SCO and BRICS. Using econometric methods, the author determines the factors impacting the cooperation of countries with developing markets within the three blocks – EAEU, SCO and BRICS based on the gravity model of international trade. This defines the scientific novelty of this work. The peculiarity of this model consists in availability of lag exchange rates. Inclusion of lag in reference to the currency rate of the exporter led to exclusion of 2014 data from sampling. The acquired results should be taken into account Russia’s cooperation on bilateral and multilateral basis within the framework of EAEU, SCO and BRICS.

HEDGING OPTIONS IN A DOUBLY MARKOV-MODULATED FINANCIAL MARKET VIA STOCHASTIC FLOWS

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

Wealth Accumulation in Rotation Forestry – Failure of the Net Present Value Optimization?

We investigate wealth accumulation in forestry, assuming that revenues are re-invested. Three different optimization criteria are compared, two of which are based on cash flows, the third financially grounded. Direct optimization of wealth appreciation rate always yields best results. Procedures gained by maximizing internal rate of return are only slightly inferior. With external discounting interest rate, the maximization of net present value yields arbitrary results, with at worst devastating financial consequences.

Stationary Forestry with Human Interference

Here, we present stationarity criteria for forest stands and establish ecological embodiments using an empirical stand development model. We introduced human interference in terms of diameter-limit cutting. Financial sustainability was investigated as a function of the cutting limit diameter. It was found that nonoperative capitalization along with its appreciation rate dictates the sustainability of management practices. In the absence of nonoperative capitalization, stationary forestry produces high capital return rates at a rather small volume of growing trees. In the case of large but constant nonoperative capitalization, a large operative capitalization resulting in a large harvesting yield provides the best capital returns. A high nonoperative appreciation rate requires a small volume of growing trees.

A Stochastic Flows Approach for Asset Allocation with Hidden Economic Environment

An optimal asset allocation problem for a quite general class of utility functions is discussed in a simple two-state Markovian regime-switching model, where the appreciation rate of a risky share changes over time according to the state of a hidden economy. As usual, standard filtering theory is used to transform a financial model with hidden information into one with complete information, where a martingale approach is applied to discuss the optimal asset allocation problem. Using a martingale representation coupled with stochastic flows of diffeomorphisms for the filtering equation, the integrand in the martingale representation is identified which gives rise to an optimal portfolio strategy under some differentiability conditions.

Modelling the impact of changing the decision to graze from rotation length to ryegrass leaf-stage

We used modelling to test the hypothesis that rotation length based on the emergence of three live leaves per ryegrass tiller (3-leaf principle) would result in greater pasture production, and increased milk production and profit per hectare than rotations based on standardised decision rules (best management practice; BMP). This hypothesis was tested using a computer program designed to model the interactions between climate, paddocks, animals and management policies. The model was set up for a farmlet (Strain Trial, Herd 1, 04/05 season) and simulated over 10 different climate years (93/94-02/03), two different sets of rotation lengths (3- leaf and BMP), and over a range of comparative stocking rates (85 - 100 kg Lwt/t DM). Average return on assets (ROA) was measured with random price sets drawn for milk, the variable cost of purchasing silage, and land appreciation rate. For the systems and climate years tested in this exercise the model predicted a greater (P