BBA FN452 (11) Formula Sheet
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F ormula Sheet for BBA FN452 2011 Sutee Mokkha v esa PhD 1. F orward Rate: (1 + 02 ) 2 = (1 + 01 )(1 + 12 ) 2. Long Hedge: = 2 ¡ ( 2 ¡ 1 ) = 1 + 3. Short Hedge: = 2 + ( 1 ¡ 2 ) = 1 + 4. F orward Contract (on asset with investment income): 0 = ( 0 ¡ ) where is the present v alue of the income during the life of the forward contract 5. F orward Contract (on asset with known yield): 0 = 0 (¡) where is the averge yield during the life of the contract. 6. V alue of a Long forward contract: = ( 0 ¡ ) ¡ = 0 ¡ ¡ 7. V alue of a Long forward contract: = ( ¡ 0 ) ¡ = ¡ ¡ 0 8. V alue of FRA: = ( ¡ )( 2 ¡ 1 ) ¡ 2 2 9. Minimum V ariance 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 2 2 12. Black Scholes Merton Option Pricing Equation + + 1 2 2 2 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
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Financial Derivatives, Risk Management, formula
Transcript of BBA FN452 (11) Formula Sheet
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
