1. OPTION PRICING OF CRUDE OIL: AN APPLICATION OF BLACK-SCHOLES MODEL Jamaladeen Abubakar Department of mathematics and statistics Hussaaini Adamu Federal polytechnic, kazaure 08034067081, 07053555571 ajafuntua@yahoo.com Nafiu Bashir Abdussalam Department of Economics Bayero University, Kano 07037880962 Nafiu_bashir@yahoo.com

2. Introduction Crude price fluctuation at the international market Efforts made by governments to hedge the price fluctuation using derivative instrument i)Forwards contract ii)Futures contract iii)Options contract iv)Swaps contract and v)Caps and Floors contract

3. Introduction Cont……. Option contract : are different from other derivative instruments because they give the option holders the right (but not the obligation) to buy an underlying asset at a specified price during an agreed period of time. Types of Option i)Call option which give the holder the right to buy ii)Put Option which give the holder the right to sell

4. Introduction Cont……. Method of Exercising Option i)American Option: this type of contract can be exercised at any time up to the expiry date ii)European Options: this contract can only be exercised at the expiry date. Option Trading position There are four basic option trading position i)To buy a call

5. Introduction Cont……. Payoff KSt Purchased call= Max(0, K-St)

6. Introduction Cont…… ii) is to buy a put K K 0 St Purchased Put=Max(0, K-S T

7. Introduction cont iii) Is to sell a call 0 K St Written Call= -Max(0, K-St)

8. Introduction Cont….. iv) Written put=-Max(0, K-St) 0 -K St

9. Methodology Black-Scholes Model Assumption of the Model There is no arbitrage opportunity (i.e., there is no way to make a riskless profit). It is possible to borrow and lend cash at a known constant risk-free interest rate. It is possible to buy and sell any amount, even fractional, of stock (this includes short selling). The above transactions do not incur any fees or costs. The stock price follows a geometric Brownian motion with constant drift and volatility. The underlying security does not pay a divident.

10. Black-Scoles Model

11. Empirical Analysis Data source DateS0KN(d1)N(d2)C CertStPayoffProfit Dec-1050.7752.130.520.472.742.8172.8620.7417.92 Jan-1153.6555.080.520.472.892.9769.4714.3911.41 Feb-1158.6860.280.520.473.163.2573.8813.6110.26 March- 11 63.6765.370.520.473.433.5278.1512.779.25 April- 11 63.965.610.520.473.443.5488.823.2419.7 May-1166.8968.860.520.473.613.787.1618.9315.22 Jun-1172.8674.810.520.473.934.0389.8615.0411.00 July-1169.4771.330.520.473.753.8590.8119.4715.16 Aug-1173.8875.850.520.473.984.09100.4824.1620.54 Sep-1178.1180.240.520.474.214.33104.9824.7320.40 Oct. 1188.8691.230.520.474.794.92118.9227.6822.26 Nov-1187.6289.960.520.474.724.85128.0638.0933.24 Dec-1188.7393.480.520.474.824.93139.2040.1234.01

12. Conclusion and Recommendations The above analysis shows that, it is prudent and financially beneficial for the government of Nigeria to go into hedging using short maturity options. Hedging stabilizes the fluctuations of company’s cash flows. Hedging decreases company’s price risk exposure when being involved with physical products

13. Conclusion and Recommendations It also provides effective financial management of the company and enables management to focus on other factors of the business. Also, options are more flexible compared to other derivative instruments used in price risk management

14. Conclusion and Recommendations Short maturity options are cheaper and with less risk as compared to long maturity options and hedging with options secure competitive advantage by locking in high/low prices.