Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation

In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation. The operator splitting scheme is used to efficiently solve the 3D time-fractional BS equation. We use a nonuniform grid for pricing 3D options. We compute the three-asset cash-or-nothing European call option and investigate the effects of the fractional-order α in the time-fractional BS model. Numerical experiments demonstrate the efficiency and fastness of the proposed scheme.

A Stochastic Harmonic Oscillator Temperature Model for the Valuation of Weather Derivatives

Stochastic processes are employed in this paper to capture the evolution of daily mean temperatures, with the goal of pricing temperature-based weather options. A stochastic harmonic oscillator model is proposed for the temperature dynamics and results of numerical simulations and parameter estimation are presented. The temperature model is used to price a one-month call option and a sensitivity analysis is undertaken to examine how call option prices are affected when the model parameters are varied.

Stochastic Volatility Estimation of Stock Prices using the Ensemble Kalman Filter

Volatility plays important role in options trading. In their seminal paper published in 1973, Black and Scholes assume that the stock price volatility, which is the underlying security volatility of a call option, is constant. But thereafter, researchers found that the return volatility was not constant but conditional to the information set available at the computation time. In this research, we improve a methodology to estimate volatility and interest rate using Ensemble Kalman Filter (EnKF). The price of call and put option used in the observation and the forecasting step of the EnKF algorithm computed using the solution of Black-Scholes PDE. The state-space used in this method is the augmented state space, which consists of static variables: volatility and interest rate, and dynamic variables: call and put option price. The numerical experiment shows that the EnKF algorithm is able to estimate accurately the estimated volatility and interest rates with an RMSE value of 0.0506.Keywords: stochastic volatility; call option; put option; Ensemble Kalman Filter. AbstrakVolatilitas adalah faktor penting dalam perdagangan suatu opsi. Dalam makalahnya yang dipublikasikan tahun 1973, Black dan Scholes mengasumsikan bahwa volatilitas harga saham, yang merupakan volatilitas sekuritas yang mendasari opsi beli, adalah konstan. Akan tetapi, para peneliti menemukan bahwa volatilitas pengembalian tidaklah konstan melainkan tergantung pada kumpulan informasi yang dapat digunakan pada saat perhitungan. Pada penelitian ini dikembangkan metodologi untuk mengestimasi volatilitas dan suku bunga menggunakan metode Ensembel Kalman Filter (EnKF). Harga opsi beli dan opsi jual yang digunakan pada observasi dan pada tahap prakiraan pada algoritma EnKF dihitung menggunakan solusi persamaan Black-Scholes. Ruang keadaan yang digunakan adalah ruang keadaan yang diperluas yang terdiri dari variabel statis yaitu volatilitas dan suku bunga, dan variabel dinamis yaitu harga opsi beli dan harga opsi jual. Eksperimen numerik menunjukkan bahwa algoritma ENKF dapat secara akurat mengestimasi volatiltas dan suku bunga dengan RMSE 0.0506.Kata kunci: volatilitas stokastik; opsi beli; opsi jual; Ensembel Kalman Filter.

It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option via Joint Physical and Pricing Density Modeling

It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a negative risk premium. The objective of this paper is to investigate the zero-risk premium moneyness level of a European call option, i.e., the strike where expectations on the option’s payoff in both the P- and Q-world are equal. To fully exploit the insights of the option market we deploy the Tilted Bilateral Gamma pricing model to jointly estimate the physical and pricing measure from option prices. We illustrate the proposed pricing strategy on the option surface of stock indices, assessing the stability and position of the zero-risk premium strike of a European call option. With small fluctuations around a slightly in-the-money level, on average, the zero-risk premium strike appears to follow a rather stable pattern over time.

THE EFFECT OF USING FACEBOOK ON ELDERLY PEOPLE DURING COVID-19 PANDEMIC

The use of the Facebook communication network during the pandemic Coronavirus by the elderly was beneficial because it played a role in connecting family and friends, when physical encounters could not take place. Social media has presented numerous benefits on mental health, such as: developing skills in using new technologies that delay cognitive impairment, lower levels of loneliness and positive visions of the future. Many users said that in addition to being close to family, they learned about the pandemic and what it means, but they also expanded their list of friends in the virtual environment. Through the video call option, they were able to communicate with the loved ones and managed to overcome social isolation and the feeling of loneliness. Therefore, the use of Facebook has been beneficial among the elderly, giving them a pleasant environment of social and emotional connection with the loved ones, communication with virtual friends has been developed, and self-confidence has increased. Facebook communication network users obtained a higher score when assessing social satisfaction and increased confidence in technology.

Leveling the Playing Field for Risk-Averse Agents in Security-Bid Auctions

We introduce risk-averse bidders in a security-bid auction to analyze how the security design affects bidders’ equilibrium behavior and, as a result, the revenue and efficiency of the auction. We show that steeper securities provide more insurance because they allow bidders to smooth payoffs across realizations. Such insurance levels the playing field for more-risk-averse bidders, inducing them to bid more aggressively. As a consequence, the auction’s allocative efficiency weakly increases when the seller switches from a flatter to a steeper security. Furthermore, we prove that when bidders are homogeneously and sufficiently risk averse, the only security that guarantees Pareto efficiency is the steepest, that is, a call option. We also determine the relationship between the security design and the auction format. In particular, we show that for convex and superconvex families of securities, the first-price auction yields higher expected revenues, provided a technical condition, whereas for subconvex families, the second price yields higher expected revenues, provided that bidders are moderately risk averse. Finally, we show that steeper securities also attract higher entry from an ex ante perspective, when entry is costly, and discuss the effects that the presence of risk aversion has on informal auctions. This paper was accepted by Gustavo Manso, finance.

A Primer on Pumping and Dumping: How Hedge Funds Do It and How Others Might Profit

Pumping and dumping occurs when the price of a stock is artificially inflated and then drops. Here, we illustrate how hedge funds can accomplish pumping and dumping, and argue why this strategy is likely to be successful for them. We illustrate why writing a short-term in-the-money covered call option might constitute an informed speculation when pumping and dumping is suspected. In contradistinction to the usual practice, estimating the returns of a strategy which is based upon the predictable characteristics of pumping and dumping would be best tested prospectively, and social media communities might fruitfully participate in such research.

MENENTUKAN HARGA OPSI DENGAN METODE MONTE CARLO BERSYARAT MENGGUNAKAN BARISAN KUASI ACAK FAURE

An option contract is a contract that gives the owner the right to sell or even to buy an asset at the predetermined price and period time. The conditional Monte Carlo is one of the several methods that is used to determine the option price which in the process uses random numbers with normal standard distribution. At the same time, the random number generator can be substituted by using a quasi-random sequence, as in Faure's quasi-random sequence. The aim of this study is to determine the contract price of the call option with the European type by applying the conditional Monte Carlo method. This method used the Faure quasi-random sequence and compared it with the method of Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The results of this study showed that the call option calculated using the conditional Monte Carlo method using the quasi-random Faure sequence began to stabilize at the 5000th simulation for K = 32575 and K = 34725 and in the 10000th simulation for K = 33000 and K = 33950. Research also show that with the conditional Monte Carlo in using the quasi-random sequence of Faure is more stable. Therefore, it is obtained its real value faster than the Monte Carlo standard, Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. The MAPE value of conditional Monte Carlo in using the quasi-random sequences of Faure and the Monte Carlo standard is smaller than the Monte Carlo standard in using the quasi-random sequence of Faure, and conditional Monte Carlo. Therefore, it can be said to be more accurate when calculating the European type call option price at BBCA.JK stocks.

American Basket Option Pricing Formulas in Uncertain Environment

American basket option is a contract containing multiple underlying assets, and its payoff is correlated with average prices or weighted average prices of these assets on or before the expiration date. The type of option entitles a holder the right to trade at the strike price within a specified date, and this right can be waived. Therefore, there is a certain price to be paid for acquiring this right, which produces the problem of option pricing. A lot of literature shows blackthat basket option price is usually cheaper than option portfolios on individual underlying assets. Based on this advantage, basket option blackbecomes popular among investors. Consequently, this paper predominantly explores four types of American basket option pricing in uncertain financial environment. Specifically they are American arithmetic basket call option, American arithmetic basket put option, American geometric basket call option and American geometric basket put option. Assuming that these stocks prices follow corresponding uncertain differential equations, we derive corresponding option pricing formulas. Some numerical examples are taken to illustrate the feasibility of pricing formulas. Simultaneously, this paper discusses the relationship between option price and some parameters.