Derivatives and Alternative Investments - Finance Assignment Sample

# Finance Assignment Sample on Derivatives and Alternative Investments

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## Finance Assignment Question

### Question 1

A currency swap has a remaining life of 15 months. It involves exchanging interest at 14% on £20 million for interest at 10% on \$30 million once a year. The term structure of interest rates in both the United Kingdom and the United States is currently flat, and if the swap were negotiated today the interest rates exchanged would be 8% in dollars and 11% in sterling. All interest rates are quoted with annual compounding. The current exchange rate (dollars per pound sterling) is 1.6500. What is the value of the swap to the party paying sterling? What is the value of the swap to the party paying dollars?

### Question 2

A financial institution has just sold 1,000 7-month European call options on the Japanese yen. Suppose that the spot exchange rate is 0.80 cent per yen, the exercise price is 0.81 cent per yen, the risk-free interest rate in the United States is 8% per annum, the risk-free interest rate in Japan is 5% per annum, and the volatility of the yen is 15% per annum. Calculate the delta, gamma, vega, theta, and rho of the financial institution's position. Interpret each number.

### Question 3

A corn farmer argues 'I do not use futures contracts for hedging. My real risk is not the price of corn. It is that my whole crop gets wiped by the weather.' Discuss this viewpoint. Should the farmer estimate his expected production of corn and hedge to try to lock in a price for expected production?

## Finance Assignment Solution for Derivatives and Alternative Investments

### Introduction

This assignment is based on three independent questions. First one is based on currency swap, second needs calculation of delta, gamma, vega, theta, and rho of financial institution to show its financial position and the last one is based on futures contracts for hedging. This also highlights on the hedging scenarios and the wise strategy that can be taken. This also explains the Greek letters in details from their derivations to application in a real problem. It also gives an insight on how the value of currency changes with the passage of time.

#### Q.1

This question needs to calculate the swap values of the dollar and euro after a period of 15 months with the given details below.
In this question we have,
Life = 15 months
Exchanging interest rate on £20 million = 14%
Exchanging interest rate on \$30 million = 10%
(Both the United Kingdom and the United States are currently flat)
Negotiated interest rate for swap in dollar = 8%
Negotiated interest rate for swap in sterling = 11%
Current exchange rate (dollars per pound sterling) = 1.6500…

Currency swap is a kind of exchange of liability. It is an exchange of principal and interest at a certain point of time for a certain point of time. This provides financial institutions a competitive advantage by swapping different currencies at different prices for different borrowers. This is normally done when a company looks to expand its operation in different countries. For example; if a British company has agreed to sell its plant in the UK to an American company. Then it is when the American company needs British pounds and thus need to acquire British pound. In case of unavailability of British pound these two companies can agree on currency swap for an interest rate and duration on a common agreement. This is the easy and simple way, in case of unavailability of required currency. As an advantage currency companies looking for business in foreign market can use swap as a hedge to leverage the arbitrage opportunities in foreign market. A currency swap can be either instruments, hedge or arbitrage depending on the situations. It also helps to reduce some risk and cost related to the currency exchange. But at the same the on the other side of the coin currency swap has some limitations as well. If any of the parties who have agreed to currency swaps defaults on the principal amount and agreed interest rate, there are chances that credit risk may happen in the due course of time. Changes in the Government plan and policies in regards to the foreign currencies and at times a country having excessive foreign debts lead to down in the value of domestic currency and thus there is no provision of currency swap in that country. Currency swap in general is done because of two reasons; first one is because there is a commercial need and the second one is due to comparative advantage, which it has due to interest factor added to it. In commercial needs there will be more inclined towards currency swap because of the advantage of beforehand-agreed interest rate. In market there are other bank interest rates available but the advantage of this over other interest rates is that the institutions can be able to fix their on interest rate for their own convenience period. The other motive of comparative advantage is due to the fact currency swap can be used as an instrument in the form of a hedge or arbitrage as per their need. This provides the flexibility in using it as an instrument for comparative advantage over others.

### Q.2

This question suggests about the Greek letters derivations and its application within a call option scenario. This also looks for calculation of delta, gamma, Vega, theta, and rho and their interpretation.

Greek letter derivations are used both in call and put options. But here call the option based question is performed to understand the application of all the Greek words…

In general, delta of an option is characterized as the rate of progress of the option cost in appreciation to the rate of progress of asset prices:

For put and call option, call and put option's price are considered (HULL, & HULL J. 2012). It is the most basic and the most used 'greeks' whether it is the calculation of volatility effects or related measures. Normally delta can be measured from the range of 0.00 to 1.00.
In this question the stock is European call options. The calculation of delta reflects that an increase in the spot price ( ) the value of the value of an option to buy one yen increases by 0.525 times that amount…

#### Use of Vega ( )

It is used to find out the sensitivity as proportional to the changing price of the asset.

The theta of an option, , which decreases with the passing day if the price of an option is also decreasing. This means both of these variables move in the same direction or they are directly proportional to each other. If one increases other also increase and if other decreases the former increases.

In the question, it is seen that there is a decrease in the value of the option by 0.0399 times the amount when the time passage in a small value. With the passing calendar day the value of the option decreases

#### Application of Theta

It reflects the value of the option with the increasing number of days. (GOODSTEIN, D. L., 1985). A long position generally has a positive theta and the options, which have a short position, have negative theta. With the decrease in the time theta also decreases, which means the value of the option, is also decreasing…

#### Conclusion

In general, delta of an option is characterized as the rate of progress of the option cost in appreciation to the rate of progress of asset prices. It shows how a call option behaves once any of the variables, whether the price of the option or the price of the asset increases or decreases. It is also called 'hedge ratio'. For example, in the situation of a call option if there is a delta of 0.50 which essentially means for every 1 unit of stock increase there will be an increase in call option by 0.50.
Gamma has the same variable as delta and thus it is also called chaining delta. It shows the change in delta because of the change in the price of an option (HULL, & HULL J. 2012). With the passage of time, time has an important effect on vega. Vega is time sensitive. If the expiration time of the option is more the value of vega is also more and if the expiration time is less the value of vega is also less. This means both of these are directly proportional. A long position generally has a positive theta and the options, which have a short position, have negative theta. With the decrease in the time theta also decreases, which means the value of the option, is also decreasing. If there is a change in the interest it seems there is use of Rho. It helps to find out the price of an option due to changes in the interest rate. (DUFFIE, D. 2001). Normally when the call option is longer and the put options are short rho is positive and when the call option is short and the put option is long rho is negative.
All these Greek derivatives are sensitive to the option price to the change in the value with regard to other variables. In the question the interest rate has direct relation with the Rho calculation, volatility has direct connection with theta, and vega has direct relation with the principal (asset) (BJÖRK, T., 1998). This all calculations have some limitations attached to them…

### Q.3

This question is about hedging crop in future forward. It can also be called as future forward hedging.

In general forward contracts are done in currency and raw materials like oil and steel. But there is also a trend wherein fruits and crops are hedged for future in forward hedging. For example: If India is exporting banana to US after a forward contract the businessman will get paid in US dollars as per the agreed price at the time of contract. If it is continued there are chances the rupees decrease as compared to dollars and thus there is a gain in the decrease of Indian currency. If the exchange rate is Rs.60 = \$1 at the time of hedge and after hedge if at the agreed time the value of rupees decreases let say Rs.65 = \$1, there is a gain of Rs.5 per dollar…

Producer hedges on a temporary basis. Once the market price of the crop is corrected and they can finally sell the crop directly to the cash market. Hedging takes place where there is opposite but equal opportunities in the cash market and future market.
In this question, the farmer does not hedge the crop to the future contracts of hedging because he is not worried about the price of the crop. He is more interested in saving his crop from the weather damages.

In this respective he is right because he cannot anticipate the volume of damage weather can bring. Here the weather is the key and significant factor to make a decision. The weather holds uncertainty and thus in this situation there are fair chances that the volume of crops to sell cannot be anticipated…

The reason being there will be similar effect to all the farmers and thus the production will be lower for all the farmers. With this decrease in the crop production the price of corn will be relatively high in the market. This is an instant market price increase, but with hedging there could be a price low and thus farmer will make a loss…