Foreign Exchange Options Research Articles

Multi-regime foreign exchange rate model: Calibration and pricing

To price exotic foreign exchange (FX) options, a model needs to be selected for FX spot rate dynamics. The classic approach of modelling spot rates with Black–Scholes framework makes inappropriate assumptions of constant drift and volatility, resulting in mispricing. In this article, we investigate multi-regime Black–Scholes (MRBS) model for FX rate, with regime-switching behaviour of drift and volatility governed by a Markov chain. We derive an analytic formula for European FX call options via Fourier transform and present a Monte Carlo simulation algorithm for FX barrier option pricing. Further, we propose a calibration strategy with penalty. Finally, the empirical study shows that volatility smile can be recovered by MRBS model; calibrating MRBS with penalty gives stable calibrated parameters and small out-of-sample mean squared errors; combined use of our calibration methods and pricing algorithms provides reasonable prices for FX barrier options. Thus, MRBS model, together with proposed calibration-with-penalty strategy and pricing algorithm, provides a promising approach for FX option pricing.

Analytically pricing foreign exchange options under a three-factor stochastic volatility and interest rate model: A full correlation structure

The current literature usually ignores the dependence between the rate of exchange and two interest rates, i.e., domestic and foreign ones, for the availability of analytical solutions to foreign exchange option prices, while such settings potentially limit the performance of these models. To address this, we introduce two new factors into the Heston–Hull–White model when foreign exchange options are evaluated. This newly formulated three-factor Heston–Hull–White model still admits a closed-form solution to foreign exchange option prices, which is successfully figured out based on the numeraire change technique and the obtained analytical expression of the characteristic function. Based on options on foreign exchange rate between US and Australian Dollar, both the three-factor and one-factor Heston–Hull–White models are calibrated using the Adaptive Simulated Annealing. When evaluating the performance of both models with in- and out-of-sample errors, the greater forecasting ability of the new model equipped with the two new factors over the one-factor Heston–Hull–White model is identified.

Does the left-digit bias affect prices in financial markets?

According to the left-digit bias, people pay more attention to the leftmost digits of a number and tend to disregard the last digits of that number. We investigate whether this bias affects traders' perception and pricing in a large financial market trading foreign exchange options. Our theoretical model predicts that the left-digit bias affects prices, causing a discontinuous jump in expected returns when comparing markets at threshold prices 10,20,…,90 with markets at prices just below these thresholds, such as 9.9,19.99, etc. The model predicts no discontinuity in returns among unbiased traders. Using a regression discontinuity approach over the returns of more than 1 million options, we find significant discontinuities in the expected returns, consistent with mispricing induced by the left-digit bias.

Constructing copulas using corrected Hermite polynomial expansion for estimating cross foreign exchange volatility

A finite order multivariate Hermite polynomial expansion, as an approximation of a joint density function, can handle complex correlation structures. However, it does not construct copulas, because the density function can take negative values. In this study, we propose a formulation of multivariate Hermite polynomial expansion suitable for the application of correction that recovers non-negativity and construct a copula. Several useful expressions for integrals with the copula are derived from this formulation. We also apply this copula to estimate the volatility smile of cross-currency pairs in the foreign exchange option market. In the numerical experiments, we compare the estimation results of the volatility smile of EUR–JPY, GBP–JPY, and AUD–JPY for the proposed and other copulas to confirm the validity of the proposed copula.

Foreign exchange option pricing under the 4/2 stochastic volatility model with CIR interest rates.

. Foreign exchange (FX) options are studied in a new stochastic volatility model (the 4/2 stochastic volatility model), which includes, as special instances, the Heston model and the 3/2 model, for the exchange rate in combination with the Cox-Ingersoll-Ross (CIR) dynamics for the domestic and foreign stochastic interest rates. We allow the correlation between the instantaneous volatility and the dynamics of the exchange rate, whereas the interest rates in both domestic and foreign markets are assumed to be independent of the dynamics of the exchange rate. We provide a semi-analytical formula for the price of the European FX call option via Fourier inversion. Through the change of measure technique, we derived explicit expressions for conditional characteristic functions. Our model is computationally tractable, thereby the pricing procedure is accurate and illustrates more efficiency in comparison to the Monte Carlo simulation method. Finally, we perform calibrations on market data, demonstrating that our model fits the implied volatilities well and outperforms the Heston model with CIR interest rates.

Inverse volatility problem for currency options

In transactions associated with future-oriented financial instruments, such as options, a huge amount of data is available buried inside of which is the market's best guess as to what the future holds. We consider here the possibility of extracting future foreign exchange volatility information from foreign exchange option data with the aid of a new computational inverse algorithm using minimization of a convex functional.
 See also https://ejde.math.txstate.edu/special/02/k1/abstr.html

The Impact of Exchange Rate Fluctuation on Toyota Financial Performance and Its Hedging Strategy

In today's globalised economy, the majority of businesses operate in many nations, utilising foreign exchange for imports and exports to expose them to foreign exchange risk. Every business is more or less affected by foreign exchange risk, which is made up of transaction risk, translation risk, and economic risk. By analyzing Toyota's financial reports and comparing financial data of multiple fiscal years (2018 is the base year), including Toyota's derivatives trading volume, foreign exchange income, exchange rate fluctuations of Japanese yen relative to other major currencies, and the average transaction price of currency trading, this study studied the role of financial derivatives in Toyota's foreign exchange risk management. The research results show that Toyota's derivatives transactions in 2018, including forward foreign exchange future contracts and foreign exchange options, strongly offset the foreign exchange risk caused by the appreciation of the yen against the US dollar and the euro. In addition to the derivatives transactions, Toyota also used other risk management policies to reduce its foreign exchange risk. Although the use of financial derivatives can hedge risks, but it will also bring losses to the enterprise. In today's volatile global business environment, each enterprise must choose the appropriate risk management tools for it.

Uncertain Currency Option Pricing Based on the Fractional Differential Equation in the Caputo Sense

The foreign exchange market comprises the largest global volume, so the pricing of foreign exchange options has always been a hot issue in the foreign exchange market. This paper treats the exchange rate as an uncertain process that is described by an uncertain fractional differential equation, and establishes a new uncertain fractional currency model. The uncertain process is driven by Liu process, and, with the application of the Mittag-Leffler function, the solution of the fractional differential equation in a Caputo sense is presented. Then, according to the uncertain fractional currency model, the pricing formulas of European and American currency options are given. Lastly, the two numerical examples of European and American currency options are given; the price of the currency option increased when p changed from 1.0 to 1.1, and prices with different p were all decreasing functions of exercise price K.

Applications of FX Derivatives in Active Currency Risk Management

Risk managers exhibit heterogeneous behavior as well as shortfall aversion, money illusion, and regret risk when managing portfolio risks. Foreign exchange options provide a flexible risk/return profile that is more likely to achieve such specific investment as well as behavioral objectives. We showcase five practical applications for international currency managers in selecting the appropriate hedging and active strategies for portfolio risk management. These solutions address a wide range of behavioral needs such as regret risk, shortfall aversion, positive skewness, and the increasing need for non-monetary satisfaction in the form of well-being utility.

Financial Innovation of Mass Destruction—The Story of a Countrywide FX Options Debacle

Astonishingly little attention has been paid in academic literature to the 2008–2009 foreign exchange (FX) options debacle in Poland, the scale of which was unheard of. It affected not only an individual organization but a significant part of economy, being an example of a situation in which operational risk at the company level could have impacted systemic risk. The research provides evidence of the dark side of financial innovations through an analysis of a countrywide case on an emerging market, utilizing a primary qualitative content analysis (QCA) of over 750 documents (including press releases, public authorities’ accounts, and corporate statements). It documents that the FX options debacle was caused by financial institutions which shrouded some aspects of innovative securities or took advantage of information asymmetry to exploit uninformed clients. The study concludes that both adequate legal regulations and proper operational risk management are crucial to avoid similar corporate failures.

Foreign Exchange Options on Heston-CIR Model Under Levy Process Framework

Foreign Exchange Options on Heston-CIR Model Under Levy Process Framework

Analysis of the development of the foreign exchange market in the Russian Federation

The article focuses on the financial foreign exchange market, the development and condition of which determines the financial well-being of most commercial enterprises of the Russian Federation. The purpose of the research is to give review of the Russian foreign exchange market’ development and situation. The main factors influencing the level of the exchange rate of foreign currencies expressed in national currency are considered.
 The domestic and international foreign exchange market of Russia for the period 2016-2020 is analyzed. The dynamics of conversion operations, the structure of participants in the domestic foreign exchange market by type of currency. The results of trading on the foreign exchange market, futures and options as a currency instrument, the share of options and futures on the futures market of the Russian Federation, as well as the dynamics of the US dollar against the ruble and exchange trading indicators for the period from 2016 to 2020.
 The conditions, results and prospects of the development of the financial foreign exchange market of the Russian Federation are discussed in this article

Foreign exchange option pricing under regime switching with asymmetrical jumps

In this study, we investigate the valuation of foreign exchange (FX) options by identifying a two-factor Markov-modulated stochastic volatility model with double exponential jumps to capture long- and short-term stochastic volatility and asymmetrical jumps in the underlying spot FX rate. Furthermore, the dynamics of domestic/foreign instantaneous forward interest rates are governed by a Markov-modulated Heath-Jarrow-Morton model. The dynamic measure change technique is employed to determine a pricing kernel for deriving the FX option pricing formula. Finally, numerical illustrations are provided and analyzed.

Pricing foreign exchange options under a hybrid Heston-Cox-Ingersoll-Ross model with regime switching

Abstract In this paper, the pricing of foreign exchange options is considered under a modified Heston–Cox–Ingersoll–Ross hybrid model. This modified model reserves all the characteristics of the Heston–Cox–Ingersoll–Ross model and also additionally assumes regime switching in the key parameters of the volatility as well as the domestic and foreign interest rates. Even though complicated, we have derived a closed-form pricing formula for foreign exchange options after the affinity of this new model is verified. Various properties of the newly derived formula are also shown through numerical experiments. To show the performance of this newly proposed model, an empirical study is also conducted, the result of which suggests that our model is a good alternative to the Heston–Cox–Ingersoll–Ross model for practical purpose.

Forward start options under Heston affine jump-diffusions and stochastic interest rate

This paper presents a generalization of forward start options under jump diffusion framework of Duffie et al. [Duffie, D, J Pan and K Singleton (2000). Transform analysis and asset pricing for affine jump-diffusions, Econometrica 68, 1343–1376.]. We assume, in addition, the short-term rate is governed by the CIR dynamics introduced in Cox et al. [Cox, JC, JE Ingersoll and SA Ross (1985). A theory of term structure of interest rates, Econometrica 53, 385–408.]. The instantaneous volatilities are correlated with the dynamics of the stock price process, whereas the short-term rate is assumed to be independent of the dynamics of the price process and its volatility. The main result furnishes a semi-analytical formula for the price of the Forward Start European call option. It is derived using probabilistic approach combined with the Fourier inversion technique, as developed in Ahlip and Rutkowski [Ahlip, R and M Rutkowski (2014). Forward start foreign exchange options under Heston’s volatility and CIR interest rates, Inspired By Finance Springer, pp. 1–27], Carr and Madan [Carr, P and D Madan (1999). Option valuation using the fast Fourier transform, Journal of Computational Finance 2, 61–73, Carr, P and D Madan (2009). Saddle point methods for option pricing, Journal of Computational Finance 13, 49–61] as well as Levendorskiĩ [Levendorskiĩ, S (2012). Efficient pricing and reliable calibration in the Heston model, International Journal of Applied Finance 15, 1250050].

Foreign exchange rate volatility smiles and smirks

AbstractWe study the implied volatilities of three foreign exchange (FX) option markets: EUD/USD, GBP/USD, and AUD/USD. We find that they are distinct from each other. The implied volatilities of the EUD/USD market tend to be more U‐shaped than those of other markets. Local volatility models such as the constant elasticity of variance (CEV) model and stochastic volatility models, such as the Heston model, may fail to capture this type of convexity. We choose a stochastic‐local volatility model to obtain an implied volatility formula for the corresponding FX options. The formula is given by the CEV formula with additional terms reflecting the (pure) stochastic volatility nature of FX rates. Based on this result, we show that the stochastic‐local volatility model is a suitable universal choice for the pricing of these FX options.

Expansion method for pricing foreign exchange options under stochastic volatility and interest rates

Some expansion methods have been proposed for pricing options approximately in analytical form. One of these is the smart expansion method based on the Malliavin calculus, which is used to price options in the Heston stochastic volatility model with deterministic interest rates. In this paper, we apply the method to the Heston–Hull–White model, which admits stochastic interest rates to enhance the model, and we obtain the expansion formula for pricing options in the model up to second order. Then numerical studies are performed to compare our approximation formula with the Monte Carlo simulation. Our formula shows numerically comparable results with another method using the approximation of the characteristic function, and can also be applied for parameter configurations where the latter method is not useful. The control variate is also used to improve the accuracy for high volatility-of-volatility cases.

SECOND-ORDER STOCHASTIC VOLATILITY ASYMPTOTICS AND THE PRICING OF FOREIGN EXCHANGE DERIVATIVES

We consider models for the pricing of foreign exchange derivatives, where the underlying asset volatility as well as the one for the foreign exchange rate are stochastic. Under this framework, singular perturbation methods have been used to derive first-order approximations for European option prices. In this paper, based on a previous result for the calibration and pricing of single underlying options, we derive the second-order approximation pricing formula in the two-dimensional case and we apply it to the pricing of foreign exchange options.

OPERATING BANKS OPERATIONS WITH FOREIGN OPTIONS AND FUTURES OF FOREIGN BANKS: FOREIGN EXPERIENCES AND THEIR FEATURES

Currency options and futures are a reliable means of protecting foreign exchange reserves against currency risk as a widely used financial instrument in international banking. However, there are no currency options and futures in the banking practice of the Republic of Uzbekistan. This raises the need for scientific research on the introduction of currency options and futures into banking practice. This article describes the theoretical foundations of commercial banks' operations on currency options and futures based on the opinions and conclusions of famous scientists. Problems of currency options and futures operations in banking practice of the Republic of Uzbekistan are studied and scientifically justified suggestions and recommendations are given. It should also be noted that the status of foreign exchange options and futures in foreign countries, namely the United States, Europe, Asia, and Latin America, has also been studied. The author has developed his own scientific recommendations using foreign experience in commercial banks' operations related to currency options and futures.

Acceleration of the Strike Calculation for Foreign Exchange Options Using FPGA

Traditionally GPU and multi-core CPUs are used for task parallelism. In recent years the use of FPGA for Monte Carlo simulation had been researched. The strength of FPGA lies in the pipeline parallelism which can be beneficial not only for Monte Carlo simulations. In this paper we demonstrate that the pipeline parallelism of Newton method can be efficiently implemented on FPGA cards. We apply Newton method to determine the strike of the foreign exchange options when the convention is to include the premium in delta quotation. Moreover, we improve the initial guess of the iterative method through the Taylor expansion of the delta equation.