Exercise Date Research Articles

British Put Option On Stocks Under Regime-Switching Model

In a plain vanilla option, its holder is given the right, but not the obligation, to buy or sell the underlying stock at a specified price (strike price) at a predetermined date. If the exercise date is at maturity, the option is called a European; if the option is exercised anytime prior to maturity, it is called an American. In a British option, the holder can enjoy the early exercise feature of American option whereupon his payoff is the ‘best prediction’ of the European payoff given all the information up to exercise date under the hypothesis that the true drift of the stock equals a specified contract drift. In this paper, in contrast to the constant interest rate and constant volatility assumptions, we consider the British option by assuming that the economic state of the world is described by a finite state continuous-time Markov chain. Also, we provide a solution to a free boundary problem by using PDE arguments. However, closed form expression for the arbitrage-free price are not available in our setting.

Pricing Multi-Asset Bermudan Commodity Options with Stochastic Volatility Using Neural Networks

It has been recognized that volatility in commodity markets fluctuates significantly depending on the demand–supply relationship and geopolitical risk, and that risk and financial management using multivariate derivatives are becoming more important. This study illustrates an application of multi-layered neural networks for multi-dimensional Bermudan option pricing problems assuming a multi-asset stochastic volatility model in commodity markets. In addition, we aim to identify continuation value functions for these option pricing problems by implementing smooth activation functions in the neural networks and evaluating their accuracy compared with other activation functions or regression techniques. First, we express the underlying asset dynamics using the multi-asset stochastic volatility model with mean reversion properties in the commodity market and formulate the multivariate Bermudan commodity option pricing problem. Subsequently, we apply multi-layer perceptrons in the neural network to represent the continuation value functions of Bermudan commodity options, wherein the entire neural network is trained using the least-squares Monte Carlo simulation method. Finally, we perform numerical experiments and demonstrate that applications of neural networks for Bermudan options in a multi-dimensional commodity market achieve sufficient accuracy with regard to various aspects, including changing the exercise dates, the number of layers/neurons, and the dimension of the problem.

The origin of LYONs: A case study in financial innovation

The origin of LYONs: A case study in financial innovation

Bermudan options pricing formulas in uncertain financial markets

Bermudan options, including Bermudan call option and Bermudan put option, as a kind of financial derivatives provide a series of exercise dates for holder before the expiration time, which can be seen as the combination of European options and American options. This paper investigates the pricing problem of Bermudan options in uncertain financial markets. By means of the extreme value theorems, the generalized pricing formulas of Bermudan options are derived. Apply uncertain stock model to describe the stock price, the explicit pricing formulas of Bermudan options are obtained. Besides, some numerical examples are discussed in this paper.

OPTION VALUE CALCULATION AFFECTED COMPONENTS

As the subprime credit crisis has attracted attention to financial derivative instruments, more frequently arises questions about fairvalue calculations. Over the time, different models had been introduced. All of those models take into account factors affectingprices. Mostly, factors used in calculations on the same type of financial instruments are approximately the same. Therefore questionarises, which factor affects price more and which less, with no matter which model would be used for fair value calculations. One offinancial derivative instrument types is options. Options are agreements, which give to option buyer rights to buy or sell underlyingasset. While the seller or writer of option has obligation to buy or sell underlying asset. This research aims to explore the impact offactors on option fair value calculations and evaluate most important ones from those, which could be chosen by option buyer orseller. To reach the aim of research following tasks are developed: 1) review of fair value calculation models; 2) compare results ofusage of different models and changes in affecting factors; 3) highlight differences between option price affecting factors, modelsused in calculations and results provided. Research includes literature review and analysis of option pricing results. Option pricecalculations are based on historical option prices, using black-Scholes and Binomial option pricing models. KEYWORDS: options, fair value models, strike price, exercise date. DOI: http://dx.doi.org/ 10.15181/rfds.v11i3.617

Association of Fitness Level Early in Pregnancy with Compliance Toward an Exercise Intervention Throughout Gestation in Obese Women

Abstract Objectives Low participant compliance with prenatal exercise trials can result in loss of power to detect intervention effects. The objective of this study was to assess the association of aerobic capacity at enrollment with compliance with an exercise intervention throughout gestation. Methods Fifty-nine sedentary women with obesity who participated in the exercise arm of a randomized controlled trial were assessed at gestation week 12, and compliance was monitored throughout gestation. Fat-free mass index (FFMI, kg/m2) was obtained by DXA and measured height. Submaximal VO2 (Borg score of 15) was measured using an incremental treadmill protocol. VO2 was normalized to FFMI (ml·min−1· FFMI−1). A VO2 cutoff of ≥112.7 (Q3 to highest data point) or ≤69.4 (Q1 to smallest data point) was used to classify women as “High” (n = 17) or “Low” (n = 17) fitness. Compliance (%) was estimated using the date of first exercise and delivery date, assuming a goal of 3 exercise sessions per week. Education level and birth weight were self-reported, whereas gestational weight gain (GWG), and gestational age (GA) were calculated. Results Groups were similar in BMI and LBMI at enrollment. The proportion of women with a college degree differed between groups (High = 100% vs. Low = 29%, P < .0001), and there was interaction between baseline fitness level (VO2) and education level (P = 0.004) in predicting compliance to the exercise intervention. For women with a college degree, there was no difference in compliance between high and low fitness groups (72 ± 5% vs. 60 ± 10%, P = NS). However, compliance was lower in women in the Low group with high school degree than in women in the High group (52 ± 6% vs.72 ± 5%, P = 0.0244). There were no impact of education on compliance for the low fitness group. GWG, GA and birth-weight were similar between groups (P = NS). Conclusions In these preliminary analyses, there was an interaction between fitness and education level on compliance with a prenatal exercise intervention. Compliance was about 20 percentage points lower in women with lower fitness and lower education when compared to women with higher fitness and higher education at enrollment. Funding Sources USDA-ARS Project 6026–51,000-012–06S.

Accrual Management and the Decision to Sell or Hold Shares Acquired from the Exercise of Employee Stock Options

ABSTRACT This study extends the employee stock option literature by examining how the timing of sales of shares acquired at exercise varies with accrual management both before and after the exercise date. We find evidence that accrual management prior to exercise is positively associated with the decision to quickly sell shares after exercise, increasing the profitability of a short-term exercise-and-sell strategy. Alternatively, we find that post-exercise accrual management is associated with executives choosing to delay selling shares, consistent with minimizing personal income taxes. Specifically, our results suggest that executives are more likely to sell immediately after satisfying the minimum (12 month) holding period for long-term capital gain treatment when they have more income-increasing accruals during the holding period. These results expand on prior research that focused on earnings management leading up to option exercise. JEL Classifications: H24; J33; M12; M21; M52. Data Availability: Data are available from the public sources cited in the text.

Machine learning for pricing American options in high-dimensional Markovian and non-Markovian models

In this paper we propose two efficient techniques which allow one to compute the price of American basket options. In particular, we consider a basket of assets that follow a multi-dimensional Black–Scholes dynamics. The proposed techniques, called GPR Tree (GRP-Tree) and GPR Exact Integration (GPR-EI), are both based on Machine Learning, exploited together with binomial trees or with a closed form formula for integration. Moreover, these two methods solve the backward dynamic programing problem considering a Bermudan approximation of the American option. On the exercise dates, the value of the option is first computed as the maximum between the exercise value and the continuation value and then approximated by means of Gaussian Process Regression. The two methods mainly differ in the approach used to compute the continuation value: a single step of the binomial tree or integration according to the probability density of the process. Numerical results show that these two methods are accurate and reliable in handling American options on very large baskets of assets. Moreover we also consider the rough Bergomi model, which provides stochastic volatility with memory. Despite that this model is only bidimensional, the whole history of the process impacts on the price, and how to handle all this information is not obvious at all. To this aim, we present how to adapt the GPR-Tree and GPR-EI methods and we focus on pricing American options in this non-Markovian framework.

Portfolio Investment with Options Based on Uncertainty Theory

In financial markets, there are situations where investors have the future stock prices according to the experts’ evaluations rather than historical data. Thus, the estimations of the stock prices contain much subjective imprecision instead of randomness. This paper discusses a portfolio investment with options in such a kind of situation. Treating the stock index price as an uncertain variable, we build an uncertain mean-chance portfolio model based on uncertainty theory and provide the equivalent form of the model. Furthermore, we make a comparison of the optimal expected return between portfolio investment with options and without options. An important conclusion is reached: The portfolio investment with options produces a no less expected return than that without options. In addition, we make sensitivity analysis and get two vital corresponding results. As an illustration, a numerical example is presented as well. The numerical results reveal that the options should be considered in portfolio investment. And the call option with maximum exercise price is most valuable per premium cost with the same exercise date.

Pricing Bermudan Variance Swaptions Using Multinomial Trees

In a recent study, Zhao et al. (2017) presented a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model; it provided an efficient way of calculating the fair value of the strike for variance swaps. In this article, the authors expand the methodology to price nonlinear derivatives written on realized variance. They introduce a new option contract, a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework they also show how to value forward-start variance swaps, VIX futures, and VIX options. Numerical tests show that the methodology is efficient and accurate.

Sports, physical activity and headache in the classical age: historical descriptions from the first sports textbook, "De arte gymnastica", by Girolamo Mercuriale.

The relationship between physical activity, sports and headache presents a growing interest, testified by numerous papers recently published. The correlation between headache and sporting activities or physical exercise dates back to the classical age. We aim at promoting the development of more studies focused on the relationship between headache and physical activity. We analysed the book "De arte gymnastica", written by Girolamo Mercuriale (Forlì, Italy, 1530-1606), and considered the first "sports medical textbook". We discuss these classical literature findings in the light of the International Classification of Headache Disorders, 3rd edition. The Author's work derives from the systematic revision of Greek, Roman and Arabic literatures about the matter. Despite some references to inveterate headaches or cold-related pains, Mercuriale does not gather specific clinical characterisations of different types of headache. However, interestingly, he reports detailed descriptions of how the same sport, or the same physical activity, could cause or give relief from head pain, depending on the precise way of practising. Mercuriale summarises 18 sports or physical activities that can give relief from headache; conversely, running or heavy activities, such as boxing, appear among the 12 contraindicated sports for people suffering from headache. "De arte gymnastica", by Girolamo Mercuriale, is the first textbook on sports medicine. Headache if often cited along the treatise: different sports and physical activities, or various ways of practising the same action could produce opposite effects for people suffering from headache.

Pricing Bermudan Variance Swaptions Using Multinomial Trees

In a recent study, we present a tree methodology to evaluate the expected generalized realized variance in a general stochastic volatility model. This provides an efficient way of calculating the fair value of the strike for variance swaps. In this article, we expand the methodology to price nonlinear derivatives written on realized variance. Particularly we introduce a new option contract a Bermudan variance swaption, defined as an option on variance swap with early exercise dates. Within the same framework, we also show how to value forward-start variance swaps, VIX futures and VIX options. Numerical tests show that the methodology introduced is efficient and accurate.

Bermudan swaption model risk analysis: a local volatility approach

Prices of callable interest rate derivatives, such as Bermudan swaptions, can be strongly affected by our choice of interest rate model as well as its parameterization and calibration strategy. This paper develops a simple way to handle the inherent model uncertainty. The approach is based on analyzing the exercise deferral premium of Bermudan swaptions with exactly two exercise dates in a “minimal” nonparametric local volatility interest rate model. It is shown that the value of the right to defer exercise once, at a future call date, depends on the inputs obtained from a calibrated nonparametric local volatility model and can, moreover, be decomposed into a portfolio of standard European swaptions. Such a “fair” price can then be compared with one obtained using a calibrated Bermudan Monte Carlo pricer, yielding a practical way of handling the model risk involved in the chosen Bermudan pricer. Numerical examples from the US dollar swaption market are provided.

Regression-Based Complexity Reduction of the Nested Monte Carlo Methods

In this paper we propose a novel dual regression-based approach for pricing American options. This approach reduces the complexity of the nested Monte Carlo method and has especially simple form for time discretised diffusion processes. We analyse the complexity of the proposed approach both in the case of fixed and increasing number of exercise dates. The method is illustrated by several numerical examples.

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 algorithm 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.

Is the Change in Exercise Date of ELS Reasonable?

Is the Change in Exercise Date of ELS Reasonable?

Practical Valuation of Options on Durable Goods

Option theory designed to value puts and calls on traded financial instruments has been profitably extended in many directions, one of which is to “real options.” Real options refer to choices that can become economically valuable in the future and whose existence can be valued in the present using (one hopes) more or less standard option pricing techniques. Most examples involve investment projects and similar choices at the firm level. In this article, Afik looks at some real options that are offered to individuals, that is, car buyers. A customer buys a new car from a dealer, who commits to buy it back as a used car in the future at a pre-specified price. The exercise price may vary according to how old the car is when the customer exercises the option. The option’s moneyness is a function of prices in the used-car market. A second related optional contract allows the customer to swap the old car for a new one of the same type at a fixed price difference. The swap contract (actually an option to exchange one asset for another) is influenced by prices for both used and new cars on the exercise date. The author presents valuation models and a simulation to illustrate valuation of these consumer real options.

Common Factors in Commodity Futures Curves

Commodities, such as oil, gold and metals, trade on the futures markets with a broad array of exercise dates. This paper examines the comovement of factors driving individual commodity futures curves. We adopt the framework of the dynamic Nelson-Siegel model to decompose the commodities futures curves into level, slope and curvature factors. We extend the model by (i) including a seasonal term to account for periodic behavior of commodity futures prices, and (ii) allowing for comovement across commodities by decomposing the factors into global, sector and idiosyncratic components. Our empirical results based on 24 commodities over the period 1995-2012 document that the individual commodity futures curves factors are driven by common components. Around 75% of the individual level factor variation can be explained by global and sector components. Both for the slope and curvature factors, this fraction is around 60%. These results give more insight in the market dynamics and can help in the construction of commodity futures portfolios and hedging decisions.

Stability of Participation in Collective Pension Schemes: An Option Pricing Approach

This paper contributes to the discussion about mandatory participation in collective funded pension schemes. It explores under what circumstances individual participants exercise the option to exit such scheme if participation is voluntary. First, we show how the willingness to participate increases when there are more future exercise dates. Then, we show how the pension fund's set of policy instruments can be designed to minimise the likelihood that cohorts exit the pension scheme. The instruments consist of contribution and indexation policies. Recovery of the funding ratio (ratio of assets over liabilities) to its regulatory target level may be based on uniform contributions or age-dependent contributions which are actuarially fair in expectation. Specifically, while the value of the exit-option deters younger workers from exiting the pension fund, a uniform contribution policy encourages older workers to stay in the pension scheme.

Let there be warrants: the case of Greece

The use of equity warrants has spread at a geometric rate around the world's capital markets. Following the mature equity markets, many Asian stock exchanges have seen the introduction of equity warrants in the past decade. The debt crisis and the need for recapitalisation of banks' capital have brought warrants in the striving Greek market as well. This paper focuses on the so far performance of equity warrants of banks that were introduced in 2013; all of them are Bermuda-type options, call warrants with an exercise date frequency of six months. Hitherto evidence shows that in the majority of the time the warrants remain out-of-the-money with a single case exception. Delta values have been reflecting this situation but investors continue on trading warrants, even exercising them. We support that this is a result of the fact the vast majority of domestic investors are not trained and cannot take rational decisions. Imperfect information combined with the speculation that warrants could be resold at a higher price in the future, are the main reasons of the market's inefficiency.