RESEARCH REPORT
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DLR = DLR 1 DLR < 1 DLR 1 7
DLR > 1 DLR > 1 DLR > 1 DLR > 1 DLR < 1 8
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t = 0 t = T r t = 0 t = T S( t2 ) 2 ln ~ N( µ ( t2 t1), σ ( t2 t1)) S( t1) S 45
( T t) c = S t) N( d ) Xe r N( ) ( 1 d 2 p = Xe r( T t) N( d 2 ) S( t) N( d1) N( ) 2 ln( S( t) X ) + ( r + σ 2)( T t) d1 = d = d1 σ T t σ T t 2 S X r T σ p S S q = 1 p S d u 46
S u us0 S S0 S d = ds d t ds S W P P = µ dt + σdw P Q ds S Q = rdt + σdw dw P Q µ r = dw ( ) dt σ 47
µ r σ Q 2 σ Q d ln St = ( r ) dt + σ W T 2 S σ ) 2 2 Q T = S exp( r T + σ W T Q E [ S S > K] T S T K Q rt E [ ST ST > K] Se N( d1) 2 d1 1 x 2 N( d1) = e dx = 2π T T Q E [ S S > K] T T r r r T P T rt P = E e P ) E( ) r ( T 48
ds S = µ dt + σdw N t S S = µ Sdt + σsε t S t S ε N t 2 t T S S M M P 1T P 2T P MT P = e rt 1 M M i= 1 P it 49
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