Option Premium Research Articles

Foreign equity lookback options with partial monitoring

A lookback option on foreign equity reduces the uncertainty of foreign investment by delivering the benefit of hindsight. Despite its high marketability, purchasing the option is stalled due to the failure to meet customized demands. This paper proposes foreign equity lookback options with partial monitoring and floating strike price to control the option premiums. We establish the expected value of the extreme of an underlying process when the specific condition, covering various payoffs of the lookback options, is satisfied. It is exploited to derive the unified closed-form pricing formula. We demonstrate the properties of the option prices through numerical examples.

Analysis of Option Prices Using Black Scholes Model

A mathematical formula used in finance to calculate the theoretical price of an option and ascertain its option premium is known as the Black Scholes option pricing model, which aids option traders in making informed decisions. This article estimates the option premium of various call and put options using the Black Scholes Model. The three distinct option chains chosen for this essay are all Mid-Cap companies that are listed on the Indian National Stock Exchange. The companies are Suzlon Energy, Kalyan jewellers India, and Exide Industries Ltd. The analysis demonstrates that the options are expensive because the Black Scholes model's computation of the option premium is lower than the actual premium in the market. Keywords: Option, Black Scholes Option Pricing Model, Call, Put, Option Premium

A fundamental approach to corporate bond options

It is well known that interest rates and credit spreads are negatively correlated. Any successful model for pricing callable corporate bonds has to take this correlation into account. A new approach for the analysis of corporate bond options is developed by using two correlated geometric Brownian motion (GBM) processes for the spread and interest rate components of corporate bond yields. Analysis of the results and comparison with market prices suggest that the traditional methods of calculating the option premium overestimate the value of the call option. Our analysis can also explain why risk neutral credit spreads are significantly wider than implied by default probability and in fact justify higher spreads.

A Comparison of the Performance of Rainbow Options and Stocks under COVID-19 and Ukraine Conflict

This paper hopes to explore which is the better choice for investors under the different environments of the US stock market, rainbow option or buying a single stock. Due to the improvement of the COVID-19 situation in the United States in 2021 and the introduction of government policies to stimulate the economy, the US stock market showed an upward trend throughout 2021. In 2022, due to the conflict between Russia and Ukraine, the global economy will be impacted, and the US stock market is no exception. In these two long-term bear markets and bull markets, it hopes to find a mutation option to control risks and improve returns. In this case, it focuses on rainbow options, which are options that help investors screen out the better-performing stocks or futures included in them. First, this paper paired 14 stocks in five fields, calculated the option’s payoff according to the rainbow option's rules, and then compared it with the return of the stock alone to explore the superiority of the rainbow option. The return on the rainbow option is higher than the return on any single stock. Then the option is simulated and priced for 1000 future trading days so as to obtain the return of the rainbow option under the assumption of stable fluctuation in the US stock market environment, which is used as the reference for pricing. Finally, the sensitivity analysis of options is conducted to study the main factors affecting the volatility of option premiums. The result is that the moves in rainbow options are always correlated with the stock that is more active.

The impact of VXY and EM-VXY on the implied volatility of ATM option premiums for the USD/MXN exchange rate on the CBOE

A series of econometric tests is proposed to study the impact of the VXY and EM-VXY indices on the implicit volatility of at-the-money options of the USD/MXN exchange rate and the premiums on their call and put options. The objective is to determine if these indicators can predict future changes in implied volatility and be used as entry or exit flags in investment and hedging strategies. Additionally, the volatility index (VIX), the USD/MXN exchange rate, and the Mexican Federal Treasury Certificates and London Interbank Offered Rate rates are included as complementary variables. Results show that although the EM-VXY, VIX, and the exchange rate are statistically significant for implicit volatility modeling, they do not have a predictive power that allows them to be used as entry or exit indicators. None of the variables are significant for modeling the premiums in call and put options. This research contributes to the filtering of instruments that, despite their design, may not contribute to the understanding of markets in emerging countries, such as Mexico. Future studies can extend this methodology to other exchange rates, trying different combinations of rates.

Retracted: Optimization of Tourism Real Estate Development Project Based on Option Premium Model

Retracted: Optimization of Tourism Real Estate Development Project Based on Option Premium Model

Pricing tenure payment reverse mortgages with optimal exercised prepayment options by accounting for house prices, interest rates, and mortality risk

Prepayment options can be exercised to terminate reverse mortgages (RM hereafter) early and receive house prices, minus loan balances, at the expense of future annuity proceeds. Prior RM evaluation studies use probability or intensity models to calibrate option exercise policies with historical prepayment records and may not apply to countries without sufficient historical records. In addition, these models may fail to capture time-varying policies due to changing market conditions. Accordingly, insurers may run the risk of undervaluing option premiums and overestimating fair annuity rates. To find optimal exercise policies that maximize option premiums and establish the most conservative annuity rates, we propose a three-dimensional tree for modeling stochastic house prices, interest rates, and mortality risks. We analyze the gain and loss to exercise the option in each scenario to determine the optimal policy. Fair annuity rates are evaluated to ensure that expected insurer losses (i.e. loan balances exceeding house values) equal gains (i.e. insurance premiums plus house values exceeding loan balances). We find that such non-optimal exercise policies undervalue option premiums and overestimate fair annuity rates. Increasing upfront premiums, insurance premium rates, and early redemption charges reduce prepayment incentives and increase fair annuity rates. We also analyze influences from factors such as the policyholder's age and volatilities of house prices and interest rates.

Influences of risk‐aversion behavior and purchasing option in a cross‐border dual‐channel supply chain

AbstractConsidering the rapid development of cross‐border e‐commerce, this paper constructs a cross‐border dual‐channel supply chain with a supplier and a retailer in different countries. The supplier directly sells products to overseas market through an online channel and a retail channel. Since the supplier expands the overseas market and bears the potential risk of exchange rate volatility, the supplier is risk‐averse. In the presence of exchange rate volatility, the risk‐averse supplier decides whether to purchase an option to hedge against the risk of exchange rate volatility. Conditional value at risk is applied as a measure of the supplier's risk‐averse behavior. To identify the conditions under which the risk‐averse supplier should purchase an option, we analyze two scenarios: the benchmark model and the option model. By comparing the benchmark model with the option model, we show that if the option premium is lower than a threshold, the risk‐averse supplier prefers to purchase an option, which also makes the retailer better off. Interestingly, when the supplier becomes less risk‐averse, as the exchange rate volatility increases, both players benefit a higher utility in the option model. Finally, we verify the results’ robustness using numerical analysis.

Pricing of Quanto power options and related exotic options

The objective of this work is threefold. Firstly, to derive the no-arbitrage premium of the α-Quanto option with power type payoff. Secondly, to price the Quanto option of power payoff when the underlying foreign currency is driven by Brownian motion and Poisson jumps, via risk-neutral probability measure. Thirdly, derive and analyze the price of the compound call option contingent upon the Quanto power call option. Our approach in deriving the pricing formulas in all three cases would be probabilistic, based on the Feynman–Kac formula.

WTI Crude Oil Options Market Prior to and During the COVID-19 Pandemic

The COVID-19 pandemic has caused turbulence in many areas of the global economy. It also contributed to an increase in volatility on the energy commodities market. This spilled over into the derivatives market, particularly the crude oil futures market. The aim of the article is to compare the costs and effectiveness of using options on WTI oil from before and after the pandemic. The analyzes took into account the value of option premiums and final results obtained by buyers of call options from March 1, 2018 to April 14, 2022. The results showed that buyers of call options during the pandemic, despite paying much higher option premiums, experienced significantly higher payouts and rates of return. They were the highest for options with the longest expiry periods of 21-30 days. Research also showed that during the pandemic, options with strike prices set at a level higher than the price of oil on the contract date had particularly high rates of return, while the highest payout values were achieved by buyers of call options with low strike prices.

Why Does Volatility Uncertainty Predict Equity Option Returns?

Delta-hedged option returns consistently decrease in volatility of volatility changes (volatility uncertainty), for both implied and realized volatilities. We provide a thorough investigation of the underlying mechanisms including model-risk and gambling-preference channels. Uncertainty of both volatilities amplifies the model risk, leading to a higher option premium charged by dealers. Volatility of volatility-increases, rather than that of volatility-decreases, contributes to the effect of implied volatility uncertainty, supporting the gambling-preference channel. We further strengthen this channel by examining the effects of option end-users net demand and lottery-like features, and by decomposing implied volatility changes into systematic and idiosyncratic components.

Research On the Pricing of Oil Spread Option Based on Geometric Brownian Motion

On Monday, 21 April 2020, for the first time ever in its existence, the price of US crude oil declined. This study constructs a spread option using geometric Brownian motion and simulates the prices of WTI oil and heating oil, both from the Chicago Mercantile Exchange (CME) Group, and processes and simulates them on a Microsoft Excel basis. This paper predicts the pricing of spread option by the heating oil price and compared to the Asian and European options. The results obtained showed that the volatility of the heating oil price affects the premium of the spread option. The significance of this paper is for investors to compare different options and find profit opportunities to make investment decisions.

Extrapolation of Crude Oil Futures Implied Return by Black Scholes Model and Monte Carlo Simulation

Since the global COVID-19 outbreak in 2020, central banks around the world have adopted loose monetary policies to hedge against the downward pressure on the economy through quantitative easing. With the gradual increase in the number of currencies, from the beginning of 2022, global commodity prices began to rise continuously. Among them, the price of fossil fuels such as oil has hit record highs due to the intensification of geopolitical conflict between Russia and Ukraine. During this period, as the divergence in oil prices intensified, speculation opportunities in the derivatives market also emerged one after another. [1] Therefore, in this article, the principles of two pricing models, the Black Scholes Model and the Monte Carlo Model, are used to predict the price trend of Crude oil in the future. The implied volatility calculated according to the Black Scholes model will be used as the volatility of the oil futures price trend in the Monte Carlo model, and the current option premium will be used to reverse the implied return in the Monte Carlo simulation. It serves as a forecast of future yields for oil futures. By using the data from March to September 2022, the correlation coefficient between the predicted return and the actual return is 0.67, which is a relatively convincing prediction accuracy. However, the volatility of the predicted return will be higher than the actual return due to factors such as the volatility smile.

IS THE BLACK–SCHOLES MODEL GOOD ENOUGH FOR RETAIL INVESTORS IN CHINA?

This study answers a simple question for Chinese investors, especially Chinese retail investors: Is the Black–Scholes model good enough for them to make investment decisions? Using the absolute out-of-sample error as a measure of model efficiency, I find that the volume-weighted mean absolute out-of-sample error is 12.03% of the option premium and investors have to tolerate more than 1% absolute error in almost all subsample groups. The significant out-of-sample error indicates that using the Black–Scholes model solely in the decision-making process may have a negative impact on the investments’ performance.

THE PRINCIPLE OF EXERCISING OPTIONS ON THE ELECTRICITY MARKET

Continual price fluctuations are possible to hedge by using various financial instruments, including options. An option buyer buys the right to the settlement price of an underlying asset such as electricity. Due to the volatility of the asset price, the buyer is not obliged to exercise the option. In such a case, the buyer’s only loss is the purchased right or the option premium, which is equal to the option price. Mathematical models for option pricing have been developed in the last hundred years. These models were very popular during the 1970s, owing to the application of the Black-Scholes formula for the calculation of theoretical option prices. In this article, options are distinguished according to various criteria, specific exercising methods are described and the historical development of option pricing models is reviewed. An example of option exercising with closing out of the margins on the largest Middle European electricity exchange, EEX, is presented.

Penentuan Harga Opsi Put dan Call Terhadap Saham Nokia dengan Menggunakan Model Black-Scholes

Options are a derivative instrument. High volatility makes options an attractive investment. Volatility can describe risk or gain. Volatility describes the probability of a stock's price over a period of time. Nokia is the code used in the stock of Nokia Corporation. The research method used in this research is descriptive method. The price of the call option premium is determined by using the Monte Carlo simulation method. The data used is Nokia stock data, with the determination of the 3 month put option expiration period from October 2020 to October 2021. In this study, the recommended or non-recommended stocks were found in the buy and sell options with several option prices (last price) on both options. The researcher uses the black scholes model and it is found that Nokia shares are considered attractive to choose and become a recommendation for both buy and sell options for investors. Further findings can be seen in this study.

Evaluation of efficiency of hedging strategies with option portfolios for buyers of the currency US dollar/Colombian peso

This paper evaluates the efficiency to mitigate the exchange rate risk of nine hedging strategies with financial options. Strategies to hedging the purchase of US dollar Colombian peso (USDCOP) by importers in Colombia were raised. In this way, the traditional strategy with call options and eight strategies with investment portfolios were evaluated. These portfolios of options for hedge are offered by financial entities in Colombia. These nine hedged scenarios were compared with the unhedged scenario that corresponds to the foreign exchange risk exposure of importers. The USDCOP currencies were modeled with a mean reversion with jumps models, option premiums were valued with the black-scholes method and the best hedging strategy was determined through a Monte Carlo simulation. According to the results obtained, the nine hedging strategies manage to mitigate risk, but the most efficient was the option portfolio called collar.

Efficiency of Financing Transactions of the Real Sector of the Economy with the Use of a Currency Barrier Option in the Conditions of Economic Imbalance 2013—2018

Goals. A comprehensive author’s study of the eff ectiveness of financing transactions in the real sector of the economy using a currency option with a barrier suspensive condition in conditions of economic imbalance. Assessment of the Russian practice of insuring market risks throughover-the-counter derivative financial instruments. Methods. The study used a mathematical model of Rayner and Rubinstein were used to calculate the fair value of options. Results. The sale of a call option of the «foreign exchange delivery option with a barrier condition» type allows the company to receive an option premium, but at the same time the company assumes an unlimited risk of losses. If the transaction is concluded by the parties for speculative purposes, then the symmetry and balance of the positions is achieved due to the amount of the premium paid by the buyer. The recommendations given in the article on the use of currency barrier options and the assessment of their value will improve the efficiency of market risk management systems in real sector companies. Conclusions. In the period from 2013 to 2018, companies actively used derivative financial instruments in their practice, both for the purpose of hedging or obtaining an option premium, and for the purpose of reducing the cost of ruble financing. Incorrect assessment of their risks, insufficient experience in the use and evaluation of derivatives led to the fact that by the end of 2014—2018, in fact, most of the largest Russian companies suff ered a loss from the use of derivative financial instruments. The competent use of derivatives for the purposes of hedging market risks will allow companies toavoid losses in conditions of increased risk.

MОDEL OF DETERMINING STOCK MARKET VOTALITY

The article considers different approaches to determining stock market volatility. It is one of the most important indicators of the financial market and characterizes the degree of fluctuations in asset prices, reflects how high the deviations of price changes relative to the general trend. The obtained values of volatility make it possible to analyze the duration of the process in the stock market, make adjustments and concrete steps to improve the situation to optimize the financial strategies of both market participants and economic agents in general. Volatility is an indicator of the meaningfulness of the actions of stock market participants. Thus, volatility is a key concept for assessing market risk and making investment decisions. Derivatives on volatility indicators are very popular among foreign investors. Such instruments allow you to hedge the risks associated with increasing stock market fluctuations, and due to the negative correlation with stock indices increase the benefits of investment diversification if they are in the investment portfolio, especially in a declining market. The calculation of market volatility is based on the following pattern – the size of the option premium directly depends on the current market volatility. The stronger the fluctuations in the market, the greater the risk of the seller of the option, and hence the amount of payment for this risk – the option premium. A further step in the development of volatility indicators is the creation of new derivatives, which means that investors will also be able to hedge risks associated with growing fluctuations in financial markets and earn additional profits by improving the efficiency of portfolio management.

A Valuation Formula for Chained Options with n‐Barriers

This study examines chained options that are connected in the sense that another barrier option becomes active continuously after the underlying asset price crosses a primary barrier. These barrier options have several advantages. First, they preserve the merit of regular barrier options, but demand far lower option premiums, which appeal to option traders. Second, they reduce the higher risk of loss of double barrier options, making option strategies more profitable in certain cases. Third, they have closed‐form pricing formulas, unlike double‐barrier options, and, thus, avoid the complexity of option pricing. Therefore, they help to enlarge the range of trader’s choice according to a variety of demand of buyers. The values of chained options are compared to those of similar single‐ and double‐barrier options. This study extends the chained option with two barriers to a generalized chained option with n‐barriers. In addition, this paper proves the closed formulas of generalized chained options with n‐barriers using mathematical induction.