Lookback Option Pricing Problem of Uncertain Mean-reverting Currrency Model

A lookback option is a maturity option that pays off based on the maximum or minimum stock price over the life of the option. This paper investigates the problem of pricing a lookback currency option based on the uncertain mean-reverting currency model and designs the algorithms to calculate the formulations. Furthermore, disscussions about parameters and result are drawn in the paper.

A Theory of Dissimilarity Between Stochastic Discount Factors

This paper proposes a measure of dissimilarity between stochastic discount factors (SDFs) in different economies. The SDFs are made comparable using the respective bond prices as the numeraire. The measure is dimensionless, synthesizes features of the risk-neutral moments of excess currency returns, and can be extracted from currency option prices. Linking theory to data, we provide evidence gathered from (i) the cross section of 45 currency option prices, (ii) the time series of currency returns, (iii) estimated SDFs using model-free restrictions, and (iv) structural models in international finance. This paper was accepted by David Simchi-Levi, finance.

ASSESSMENT OF OPTION PRICE VOLATILITY

Financial derivatives are becoming increasingly popular on a daily basis. As markets become more unpredictable, companies and individual investors are increasingly using these tools to manage risk, leverage, and increase investment returns. The most important aspect of any contract is the contract price, as the financial result of the contract depends on the price. Also for an options. In each case, the option price depends on many factors that are difficult to define and predict in advance. The price sensitivity of the option allows you to determine where and on what the option price depends. Knowing this, the investor can manage the risk of the options. The purpose of the article is to assess the sensitivity of different options to market factors based on scientific literature and real market data. The study uses the Black-Scholes option pricing model, calculating and analyzing the value of Greek letters for the determination and valuation of transaction price sensitivity. The study showed that the most sensitive to changes in the underlying asset price, volatility and risk-free interest rate is the price of the currency option, and the price of the gold option is most sensitive over time (although in theory, gold retains its value in the long run). Knowing which components a particular option is sensitive to and capable of predicting changes in those components, you can predict changes in the option price and avoid additional risk.

EQUILIBRIUM VALUATION OF CURRENCY OPTIONS UNDER A DISCONTINUOUS MODEL WITH CO-JUMPS

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Markov modulated jump-diffusions for currency options when regime switching risk is priced

In the current literature, regime-switching risk is NOT priced in the Markov-modulated jump-diffusion models for currency options. We therefore develop a hidden Markov-modulated jump-diffusion model under the regime-switching economy where the regime-switching risk is priced. In the model, the dynamics of the spot foreign exchange rate captures both the rare events and the time-inhomogeneity in the fluctuating currency market. In particular, the rare events are described by a compound Poisson process with log-normal jump amplitude, and the time-varying rates are formulated by a continuous-time finite-state Markov chain. Unlike previous research, the proposed model can price regime-switching risk, in addition to diffusion risk and jump risk, based on the Esscher transform conditional on a single initial regime of economy. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the currency option prices does not seem significant in contradictory to the findings made by Siu and Yang [Siu, TK and H Yang (2009). Option Pricing When The Regime-Switching Risk is priced. Acta Mathematicae Applicatae Sinica, English Series, Vol. 25, No. 3, pp. 369–388].

Investors Perception towards Investments in Derivatives

The most significant aspect of derivatives is risk management not about the elimination of risk. For Conducting ordinary mode of business operations financial derivatives affords a powerful tool for limiting risks to the investors. There are various derivative instruments like index futures. Stock futures, index option, stock options, interest rate futures, currency option, currently traded in these exchanges. The derivative investors ought to perceive the market trend, market reforms, government policies, market regulations; factors influencing derivatives investment [Motivating Factors], return, investment opportunities obviously and adequately take prudent investment decisions. The present study investigates the investors perception towards investments in the derivatives market at Hyderabad region. The data were collected through questionnaire survey from 322 respondents in Hyderabad region