Formula Sheet for BBA FN452 2011Sutee Mokkhavesa PhD

1. Forward Rate: (1 + 02)2 = (1 + 01)(1 + 12)

2. Long Hedge: = 2 ¡ (2 ¡ 1) = 1 +

3. Short Hedge: = 2 + (1 ¡ 2) = 1 +

4. Forward Contract (on asset with investment income): 0 = (0 ¡ )

where is the present value of the income during the life of the forward contract

5. Forward Contract (on asset with known yield): 0 = 0(¡)

where is the averge yield during the life of the contract.

6. Value of a Long forward contract: = (0 ¡) ¡ = 0 ¡¡

7. Value of a Long forward contract: = ( ¡ 0) ¡ = ¡ ¡ 0

8. Value of FRA: = ( ¡ )(2 ¡ 1)¡22

9. Minimum Variance Hedge Ratio: ¤ =

where 2 ==1(¡)

2

¡1

10. Optimal Number of Contracts: ¤ = ¤

is the size of the position being hedged (units), is the size of one futures contract(units), ¤ is the optimal number of futures contracts for hedging.

11. Ito’s lemma: if ( )

=

+

+

1

2

2

22

12. Black Scholes Merton Option Pricing Equation

+

+

1

222

2

2¡ = 0

13. Black-Scholes call option pricing: = 0 (1) ¡¡ (2)

1 =ln(0)+ +2

2

p

2 = 1 ¡ p

14. Black-Scholes put option pricing: = ¡ (¡2) ¡ 0 (¡1)

15. Binomial Model (up and down step): = p¢ and = ¡

p¢

16. Probability of an up movement: = ¢¡¡

17. Delta of European stock option (non-dividend paying)

¢() = (1)

¢ () = (1) ¡ 1

1

18. Gamma of a European call or put on a non-dividend paying stock

¡ = 0 (1)

0p

where 0 () = 1p2¡2

2

19. Theta of European stock option (non-dividend paying)

£() = ¡0

0 (1)

2p

¡ ¡ (2)

£ () = ¡0

0 (1)

2p

+ ¡ (¡2)

where 0 () = 1p2¡2

2

2