Options and Futures

This document provides a comprehensive overview of options and futures in the financial market. It covers topics such as over the counter derivatives, bond duration, currency hedging, stock price volatility, and option pricing. The document also includes calculations and analysis to help readers understand the concepts better. Whether you are a student or a professional, this document will serve as a valuable resource for learning about options and futures.

Running head: OPTIONS AND FUTURES
Options and Futures
Name of the Student:
Name of the University:
Author’s Note:

1OPTIONS AND FUTURES
Table of Contents
Answer to question 1:.................................................................................................................2
Part a:.....................................................................................................................................2
Part b:.....................................................................................................................................3
Part c:.....................................................................................................................................3
Answer to question 2:.................................................................................................................3
Part a:.....................................................................................................................................4
Part b:.....................................................................................................................................4
Part c:.....................................................................................................................................4
Part d:.....................................................................................................................................4
Part e:.....................................................................................................................................4
Answer to question 3:.................................................................................................................5
Answer to question 4:.................................................................................................................6
Part a:.....................................................................................................................................6
Part b:.....................................................................................................................................6
Answer to question 5:.................................................................................................................7
Part a:.....................................................................................................................................7
Part b:.....................................................................................................................................7
Part c:.....................................................................................................................................7
Answer to question 6:.................................................................................................................7
Answer to question 7:.............................................................................................................8

2OPTIONS AND FUTURES
Part a:.....................................................................................................................................8
Part b & c:..............................................................................................................................8
Part d:.....................................................................................................................................8
Part e:.....................................................................................................................................8
Part f:......................................................................................................................................8
Part g:.....................................................................................................................................8
Part h:.....................................................................................................................................9
Part i:......................................................................................................................................9
References and bibliography:...................................................................................................11
Answer to question 1:
Part a:
Over the counter transactions entered into two or more parties without the
intervention of the exchange. Therefore, derivatives transacted in an over the counter market
is known as over the counter derivatives. There is no standardised form of products and
standard contract volume in the over the counter market. Hence, tailor made size of the
derivatives can be transacted in the over the counter market. Over the counter market is less
regulated and it has a higher degree of counter party default risk. Hence, there are certain
points which are affected by the high volume of the over the counter derivative.
Derivative products derive value from the price of its underlying assets, these are cash
settled in nature. In other words these are one type of bet based on the expectation of the

3OPTIONS AND FUTURES
parties about the price movement of certain underlying assets. Therefore, these are bilateral
contracts in nature without having sufficient collateral underlying assets.
As much as the size of the over the counter derivative market, the degree of counter
party risk is higher and might be the cause of economic destruction. Some authors describes
the over the counter derivatives as the weapon of economic destruction.
As the over the counter derivatives are settled in a future date, participants might
mischief the information and pricing of the underlying assets to gain a benefit from the
contract, which can be disastrous for the economy when the size of the market is too big.
Part b:
Over the counter derivatives market are less regulated in nature and transactions are
entered into by the parties directly without any interference of any exchange. The most
important risk in the over the counter party derivatives market is the counter party default
risk. If a participant seems that the exercise of the contract may lead to a huge amount of loss
to them, then they may not exercise the contract thereby incurring a loss to the counter party.
Another important risk in the over the counter derivatives market is the high bid ask spread of
the stock prices, leading to a very difficult profitable trading in derivatives products in the
over the counter market.
Part c:
Large size of the over the counter derivative market is dangerous for the economy as
well as the society as a whole. As there is no collateral securities for derivatives in the over
the counter derivatives and a high degree of counter party risk may become destructive for
the economy as a whole. Therefore, there is a need for more improved regulation system for
the over the counter market.

4OPTIONS AND FUTURES
Answer to question 2:
Part a:
Face value 1
Term of the bond (Years) 4
YTM (Semi-annually compounded) 3%
Coupon rate (Semi-annually compounded) 4%
Price (In percent) 103.7%
Part b:
Period 1 2 3 4 5 6 7 8
Cash flow 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 0.0200 1.0200
PV 0.0197 0.0194 0.0191 0.0188 0.0186 0.0183 0.0180 0.9055
Weight 0.0190 0.0187 0.0184 0.0182 0.0179 0.0176 0.0174 0.8728
Weighted period 0.0190 0.0374 0.0553 0.0727 0.0895 0.1058 0.1216 6.9824
Maculary Duration (Years) 3.74
Modified duration (Years) 3.63
Part c:
Face value 1
Term of the bond (Years) 4
YTM (Semi-annually compounded) 2.9%
Change in Yield 0.1%
Coupon rate (Semi-annually compounded) 4%
Change in bond price 0.1%
Part d:
Face value 1
Term of the bond (Years) 3.63
YTM (Semi-annually compounded) 2.9%
Coupon rate (Semi-annually compounded) 4%
Price (In percent) 103.8%
Part e:
Bond duration is the indicator of degree of change in market price of the bond with
respect to a change in the yield of the bond. Hence, it is very much helpful for the investors to

5OPTIONS AND FUTURES
forecast about the future market price of the bond with a given yield rate and the duration of
the bond. That is why the bond duration is calculated as a part of the derivative course.
Answer to question 3:
In this case company A will borrow 20 million in the fixed rate of 4% and on the
other hand, B will borrow at the floating rate of Libor+600bps Assuming the Libor rate of
2.03%, the analysis can be shown in the following tables.
Fixed Rate Floating Rate
Company A 4% Libor+5%
Company B 4%+2% Libor+6%
Company A 4% 7.0300%
Company B 6% 8.0300%
Loan amouunt 20000000
Years 10
Year Interest
payment by A
Interest
payment by
B
Total Interest
Expense
1 14,06,000€ 12,00,000€ 26,06,000€
2 13,04,381€ 11,08,958€ 24,13,340€
3 11,95,619€ 10,12,454€ 22,08,073€
4 10,79,210€ 9,10,160€ 19,89,371€
5 9,54,618€ 8,01,728€ 17,56,347€
6 8,21,268€ 6,86,790€ 15,08,058€
7 6,78,542€ 5,64,956€ 12,43,499€
8 5,25,783€ 4,35,812€ 9,61,595€
9 3,62,286€ 2,98,919€ 6,61,205€
10 1,87,294€ 1,53,813€ 3,41,106€
Total 1,56,88,593€
If no SWAP was agreed upon:

6OPTIONS AND FUTURES
Year Interest
payment by A
Interest
payment by
B Bank charges
Total Interest
Expense
1 8,00,000€ 16,06,000€ 40,000€ 24,46,000€
2 7,33,367€ 14,95,296€ 40,000€ 22,68,664€
3 6,64,069€ 13,75,703€ 40,000€ 20,79,773€
4 5,91,999€ 12,46,507€ 40,000€ 18,78,506€
5 5,17,046€ 11,06,936€ 40,000€ 16,63,983€
6 4,39,096€ 9,56,158€ 40,000€ 14,35,253€
7 3,58,027€ 7,93,272€ 40,000€ 11,91,299€
8 2,73,715€ 6,17,307€ 40,000€ 9,31,021€
9 1,86,031€ 4,27,211€ 40,000€ 6,53,242€
10 94,839€ 2,21,851€ 40,000€ 3,56,690€
Total 1,49,04,431€
Net Benefit 7,84,163€
If a SWAP agreement is entered into:
Answer to question 4:
Part a:
Three principle methods of currency hedging are spot contracts, currency option
contracts and currency future contracts. Though, the spot contracts are for a very short period
of time, currency futures and currency options can be used for a longer period of time.
Part b:
The Germen Company can enter into a currency future contract to buy 5 million AUD
at a specified exchange rate at three months hence. The rate such contracted into should be
lower than the expected rate, thereby covering the foreign currency fluctuation risk to a large
extent.
As the company is having the liability to be paid off after three months, the company
has a risk of loss if the Euro to AUD exchange rate increases. Hence, the company should
enter into a EUR to AUD currency futures to hedge against the risk. The company should

7OPTIONS AND FUTURES
enter into 5000 such currency future contract of a lot size of 1000. The company should buy
such contracts.
Answer to question 5:
Part a:
Risk free interest rate 1%
Dividend yield 2%
Present stock index 1000
Future stock index 1050
Dividend payable 5
Interest cost 2.5
Fair value 997.5
Part b:
Yes there is an arbitrage opportunity available.
Part c:
Amount can be borrowed for the risk free rate of investment and it can be invested
into stocks. Then a future contract can be entered into to sell the stocks. After three months
the stocks or the underlying assets can be delivered at the strike price thereby making a
significant amount of profit.
Answer to question 6:
Ralph Lauren Company’s stocks are traded in the New York stock exchange. For the
calculation of the volatility of stock price of the company, indexes of New York stock
exchange can be used.

8OPTIONS AND FUTURES
Answer to question 7:
Part a:
Annualized volatility 33.07%
Part b & c:
Stock price 118.40
Implied volatiltiy 33.07%
Strike Price 120
Risk free rate 1.91%
Time of maturity in months 4
Dividend yield 0%
d1 0.058504
d2 -0.132421
Value of Call option 8.62$
Valueo of Put option 9.46$
Part d:
Cost of buying the call or put is USD is 8.62 and 9.46
Part e:
The price must move up or down by 33.07% to make a profit from the strategy
Part f:
Using call put parity formula:
Cost of call 8.62$
Cost of put 9.47$
Part g:
Delta is the change in the price of the call option with a change of $1 in the
underlying assets. This is the rate of change in the call option price with respect to change in
the price of the underlying assts. Call options have positive delta, which implies with the rise
in price of underlying assets, the value of the option also rises.

9OPTIONS AND FUTURES
In the same way the delta for a put option is the rate of change in the value of the put
option with respect to change in the price of the underlying assets. The delta for put option
ranges from -1 to 0. With respect to rise in price of the underlying assets the value of the put
option decreases. Therefore, the net delta of the call and put option together is always zero.
Part h:
Part i:

10OPTIONS AND FUTURES

11OPTIONS AND FUTURES
References and bibliography:
Borio, C.E., McCauley, R.N. and McGuire, P., 2017. FX swaps and forwards: missing global
debt?. BIS Quarterly Review September.
Destais, C., 2016. Central bank currency swaps and the international monetary
system. Emerging Markets Finance and Trade, 52(10), pp.2253-2266.
Du, W. and Schreger, J., 2016. Local currency sovereign risk. The Journal of Finance, 71(3),
pp.1027-1070.
Dyhrberg, A.H., 2016. Hedging capabilities of bitcoin. Is it the virtual gold?. Finance
Research Letters, 16, pp.139-144.
Ewing, B.T. and Malik, F., 2016. Volatility spillovers between oil prices and the stock market
under structural breaks. Global Finance Journal, 29, pp.12-23.
Fan, K., Shen, Y., Siu, T.K. and Wang, R., 2015. Valuing commodity options and futures
options with changing economic conditions. Economic Modelling, 51, pp.524-533.
Garcia, P., Irwin, S.H. and Smith, A., 2015. Futures market failure?. American Journal of
Agricultural Economics, 97(1), pp.40-64.
Hilander, I., 2014. Short-term funding in foreign currency by major Swedish banks and their
use of the short-term currency swap market. Sveriges Riksbank economic review, 1, pp.1-23.
Jarrow, R., 2019. Modelling fixed income securities and interest rate options. Chapman and
Hall/CRC.
Joas, H., 2014. Faith as an option: Possible futures for Christianity. Stanford University
Press.

12OPTIONS AND FUTURES
Jordan, B.D., Miller, T.W. and Dolvin, S.D., 2015. Fundamentals of investments: valuation
and management. McGraw-Hill Education.
Khalfaoui, R., Boutahar, M. and Boubaker, H., 2015. Analyzing volatility spillovers and
hedging between oil and stock markets: Evidence from wavelet analysis. Energy
Economics, 49, pp.540-549.
White, A., 2014. Pricing options with futures-style margining: a genetic adaptive neural
network approach. Routledge.