Formulae Sheet
2
Long Call = −¿ Short Call =Max (S T – K, 0); Long Put = −¿ Short Put =Max (K – S T , 0) Efective rice o!taine" #ith he"ging = S $ % & ' – & $ = & ' % ! $ Mini u variance he"ge ratio h= ρ σ s σ F *e"ge Efectivene++ ¿ h 2 σ s 2 σ F 2 ti al - o. contract+, N = h N A Q F *e"ging E/uit β P A Continuou+ Co oun"ing R c = m ln 1 + R m m ÷ R m =m e R c / m − 1 ( ) Par iel", c = (100 − 100 d) m A &or#ar" rate .or erio" = R 2 T 2 − R 1 T 1 T 2 − T 1 R F = R 2 + ( R 2 − R 1 ) T 1 T 2 − T 1 ❑ ❑ ∆ B = − BD ∆ y 1+ y m 1on" Price, B = c i e − yt i i = 1 n ∑ ∆ B B =− D ∆ y + 0.5 C ( ∆ y ) 2 2uration, D = t i i = 1 n ∑ c i e − yt i B 3alue o. &or#ar" Price '4 5nve+t ent 6++et+ & 0 = S 0 e rT $4 7ith 8no#n inco e & 0 = (S 0 – 5 )e rT 94 7ith 8no#n iel", & 0 = S 0 e (r–/ )T 3alue o. &or#ar" Contract+ '4 3alue o. Long &or#ar" contract, : = (& 0 – K )e –rT = −¿ Short &or#ar" contract $4 7ith 8no#n inco e o. re+ent value 5, . = S 0 – 5 – Ke –rT 94 7ith 8no#n iel", . = S 0 e –/T – Ke –rT '4 &uture+ rice o. +toc8 in"ex, & 0 = S 0 e (r–/ )T $4 7ith .oreign currenc F 0 = S 0 e ( r − r f ) T 3. With per unit time storage cost u F 0 = S 0 e (r!u )T ". With storage cost present #a$ue % F 0 = (S 0 !% )e rT 4 7ith convenience iel", & 0 = S 0 e (r%u – )T &uture+ rice an" execte" .uture +toc8 rice F 0 = & ( S T ) e ( r − ' ) T Euro"ollar Contract 3alue '0,000<'00 04$ ('00 Q)> Forward rate=Futures rate − 1 2 σ 2 t 1 t 2
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Transcript of Formulae Sheet
Long Call = Short Call =Max (ST K, 0); Long Put = Short Put =Max (K ST, 0)Effective price obtained with hedging = S2 + F1 F2 = F1 + b2 Minimum variance hedge ratio: Hedge Effectiveness
Optimal # of contracts,Hedging Equity:
Continuous Compounding:
Par yield, Forward rate for period =
Bond Price,
Duration,Value of Forward Price:1. Investment Assets: F0 = S0erT 2. With known income F0 = (S0 I )erT3. With known yield, F0 = S0 e(rq )T
Value of Forward Contracts:1. Value of Long Forward contract, = (F0 K )erT = Short Forward contract 2. With known income of present value I, f = S0 I KerT3. With known yield, f = S0eqT KerT
1. Futures price of stock index, F0 = S0 e(rq )T
2. With foreign currency:3. With per unit time storage cost u, F0 = S0 e(r+u )T4. With storage cost present value U, F0 = (S0+U )erT5. With convenience yield, F0 = S0e(r+u y)T
Futures price and expected future stock price:Eurodollar Contract Value: 10,000[100-0.25(100-Q)]
Tailing the hedge: d = (100 P)
Duration based number of Contracts to hedge,
Vswap = Bfl - Bfx, , , ,Vswap = BD S0BF
European call: c S0, c S0 Ke rT, c S0 D Ke -rT American call: C S0, C S0 Ke -rTEuropean put: p K, p Ke -rTS0 p D + Ke -rTS0American put: P Kert,P K S0
Put Call Parity European: c + D + Ke -rT = p + S0Put Call Parity American: S0 - D - K < C - P < S0 - Ke -rT
