For simplicity it has been assumed that the options have been exercised. However, as the transaction date is prior to the maturity date of the options the company would in reality sell the options back to the market and thereby benefit from both the intrinsic and time value of the option. By exercising they only benefit from the intrinsic value. Hence, the fact that American options can be exercised at any time up to their maturity date gives them no real benefit over European options, which can only be exercised on the maturity date, so long as the options are tradable in active markets.
The exception perhaps is traded equity options where exercising prior to maturity may give the rights to upcoming dividends. Much of the above is also essential basic knowledge. You are unlikely to be given the spot rate on the transaction date. However, the future spot rate can be assumed to equal the forward rate which is likely to be given in the exam. The ability to do this may earn up to six marks in the exam.
Equally, another one or two marks could be earned for reasonable advice. This article will now focus on other terminology associated with foreign exchange options and options and risk management generally. All too often students neglect these as they focus their efforts on learning the basic computations required.
However, knowledge of them would help students understand the computations better and is essential knowledge if entering into a discussion regarding options. For instance, if you own shares in a company you have a long position as you presumably believe the shares will rise in value in the future. You are said to be long in that company. You are said to be short in that company. To create an effective hedge, the company must create the opposite position. This has been achieved as, within the hedge, put options were purchased. Therefore, the position taken in the hedge is opposite to the underlying position and, in this way, the risk associated with the underlying position is largely eliminated.
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However, the premium payable can make this strategy expensive. It is easy to become confused with option terminology. For instance, you may have learnt that the buyer of an option is in a long position and the seller of an option is in a short position. However, an option buyer is said to be long because they believe that the value of the option itself will rise. The hedge ratio equals N d 1 , which is known as delta.
Students should be familiar with N d 1 from their studies of the Black-Scholes option pricing model. What students may not be aware of is that a variant of the Black-Scholes model the Grabbe variant — which is no longer examinable can be used to value currency options and, hence, N d 1 or the hedge ratio can also be calculated for currency options. This information can be used to provide a better estimate of the number of options the company should use to hedge their position, such that any loss in the spot market is more exactly matched by the gain on the options:.
This article has revisited some of the basic calculations required for foreign exchange futures and options questions using real market data, and has additionally considered some other key issues and terminology in order to further build knowledge and confidence in this area.
Exchange traded foreign exchange derivatives. Foreign exchange futures — the basics Scenario Imagine it is 10 July. Setting up the hedge Date? As the expected transaction date is 26 August, the September futures which mature at the end of September will be chosen. How many contracts? This conversion will be done using the chosen futures price.
Leading global foreign exchange futures and options contracts traded 2018, by volume
Hence, the total gain could be calculated in the following way: 0. Summary All of the above is essential basic knowledge. Foreign exchange futures — other issues Initial margin When a futures hedge is set up the market is concerned that the party opening a position by buying or selling futures will not be able to cover any losses that may arise. Marking to market In the scenario given above, the gain was worked out in total on the transaction date. At the end of the next trading day Monday 14 July , a similar calculation would be performed:. Maintenance margin, variation margin and margin calls Having set up the hedge and paid the initial margin into their margin account with their broker, the company may be required to pay in extra amounts to maintain a suitably large deposit to protect the market from losses the company may incur.
Foreign exchange options — the basics Scenario Imagine that today is the 30 July. The choice is made in the same way as relevant futures contracts are chosen. Which exercise price? This is calculated below:. Summary Much of the above is also essential basic knowledge. Foreign exchange options — other terminology This article will now focus on other terminology associated with foreign exchange options and options and risk management generally.
We then study the dynamic hedging problem in the framework of the quadratic utility. Proposition 2. Assume that exchange rate futures and exchange rate option markets are unbiased. The first-order conditions of the objective function are Due to the operational rules of covariance, 19 and 20 can be rewritten as Let , , , , , and , then we have By solving equations, we can obtain the optimal positions of the exchange rate futures and options presented in Proposition 1. Corollary 3. Suppose that has a symmetric distribution function of , then.
In one-stage hedging, the optimal positions of exchange rate futures and options are. The study above is to establish the optimal hedging model of exchange rate futures and options in one-stage, while, in actual hedging practice, the enterprise has to adjust the positions dynamically according to the market conditions so as to maximize its utility based on the final wealth.
We then extend the one-stage hedging problem to a multiperiod dynamic case and derive the dynamic positions of exchange rate futures and options. Proposition 4. Suppose that the markets of exchange rate futures and option are unbiased. Let , , and. Then, the optimal hedging model can be described as follows: We use the dynamic programming method to solve the problem.
To begin with, at stage , the firm decides the optimal position to maximize its utility. Let where. Then, the first-order conditions of 29 satisfy Let , , , , , and. Comparing 30 and 32 with 19 and 20 , we can obtain the optimal positions at stage are At stage , let then the first-order conditions of 33 can be expressed by Since and is independent on and , we have According to 37 and 40 , we obtain the optimal positions at stage as In this way, we can deduce the optimal positions of futures and options on the basis of mathematical induction at stage are.
Corollary 5. Suppose that has a symmetric distribution function , then. Assume the firm export products to the foreign market at the terminal time. That is, , ,. In the case of multistage, the optimal positions of exchange rate futures and options are where , , , and.
China has become a major producer and consumer of silver, also a big importer and exporter.
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According to the accessible data, we assume there is a firm in China exports silver to the US dollar region countries. The firm intends to buy the exchange rate futures and options for hedging. Data resources are from Wind database. From Figure 1 , we can observe that the returns of the silver price and the exchange rate show cluster effect that is, large fluctuations are often accompanied by large fluctuations, and small fluctuations are often accompanied by small fluctuations.
Table 1 gives the statistical description of ARCH effects test results with regard to the silver price and the exchange rate. The returns also have peak thick tails.
Based on LM statistic, the ARCH effects corresponding to the first 20 lags of the two exchange rate returns are further confirmed In order to save space, the specific numerical value is omitted here. The main objective of this paper is to examine the hedging roles of the currency futures and options. We further to test the nonnormal of the returns. That is, the hypothesis of normal distribution under J-B test is rejected.
Three fitting criteria measured by LLF optimized log-likelihood objective function value , AIC Akaike information criteria , and BIC Bayesian information criteria are used to test how the outlined models fit the in-sample data. Then, we use GARCH-t model to fit the return series for the returns of silver price and the exchange rate.
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K is the conditional variance constant. GARCH means the coefficients related to lagged conditional variances. ARCH is the coefficients related to lagged innovations residuals , and C denotes the conditional mean constant. The method to estimate for the parameters could be artificial algorithm.
We let the information set. The joint density function can then be written as. Given data the log-likelihood is as follows:. This can be evaluated using the model volatility equation for any assumed distribution for the error term. Here, can be maximized numerically to obtain. The estimation results can be seen in Table 5.