Financial Derivatives

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Our company "Saint Derivatives" offers a wide range of financial derivative instruments.

1. Our first customer is investor from China who invested large sum of money into KKB’s stocks. He decided to hedge his portfolio and contacted us. We offered him European put option on KKB’s stocks which matures in 9 months with the strike price of $13,1 per GDR. To estimate how much we are to charge for put option, we used data taken from the website of London Stock Exchange (www.londonstockexchange.com), as KKB’s GDR is quoted on this stock exchange. Latest price of the GDR is $16,29 (on 18 April,2008). To calculate volatility we used historical prices of the stock in the interval from 1 January until 18 April, and it is equal to 47,98%. Having all these figures we used Black-Scholes formula and found out the price of put option, which is $0,79. We also checked it on DerivaGem program.

1.

X 13,1 Strike Price

S 16,29 Stock Price

T 0,75 Time

r 2,64% 9-Month LIBOR

sigma 47,98% Volatility

d1 0,779909502 -0,779909502

d2 0,364390513 -0,364390513

N(d1) 0,782277927

N(d2) 0,642216791

N(-d2) 0,357783209

N(-d1) 0,217722073

p 1,048378375

The calculation of volatility is in Excel’s file.

2. Our second client is investor from Turkey, who also has KKB’s stocks. As he believes that credit crunch in our country will persist and KKB’s stocks will falter, we decided to offer him butterfly spreads with calls. The reason why we chose these strategy is from investor’s expectations of not large price variation in the next 6 months. Having analyzed historical prices of the stock, we offer him to long call options with strike prices of $15 and $18, and to short two calls with the strike of $16,5. Here investor has an initial cost of $0,15, and maximum profit is made when the stock price in 6 months is 16,5 and is equal to 16,5-15-0,13=$1,37.

Butterfly spread with calls for the maturity 6 months

Long call option with lower strike price K1=$15

Long call option with higher strike price K3=$18

Short two calls with average strike price K2=$16,5

Having calculated the option prices by DerivaGem program, we obtained:

c1=$3,42

c3=$2,17

c2=$2,73

Initial costs of investor=3,42+2,17-2*2,73=$0,13

3. Now we can offer our clients not only European options, but also American ones. To calculate the prices of options, both puts and calls on the same underlying asset (KKB’s stock) we used DerivaGem, because we have no information of company’s dividends. To have more exact results of the American puts and calls, we use DerivaGem program with maximum 500 steps by Binomial Method.

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