HW6100071021 楊佑濬

PROPORTION DIVIDENDS (1)function [ Cprice, Pprice, Clattice, Plattice] = bitprice_p( S, K, r, T, sigma, q, tau, N, mode )

% mode : 1=>American 0=>European

% dividend : proportion

deltaT = T/N;

u = exp( sigma * sqrt(deltaT) );

d = 1/u;

p = ( exp( r * deltaT ) - d ) / ( u - d );

for i = 0 : N

C(i+1) = max( 0, S * (1-q) * u^(N-i) * d^(i) - K );

P(i+1) = max( 0, K - S * (1-q) * u^(N-i) * d^(i) );

end

PROPORTION DIVIDENDS (2) for i = N : -1 : 1

for j = 0 : i-1

C(j+1) = exp(-r*deltaT) * ( C(j+1)*p + C(j+2)*(1-p) );

P(j+1) = exp(-r*deltaT) * ( P(j+1)*p + P(j+2)*(1-p) );

if mode == 1

now_p = S * u^(i-1-j) * d^(j) ;

if i>tau

now_p = now_p * (1-q);

end

C(j+1) = max( C(j+1) , now_p - K );

P(j+1) = max( P(j+1) , K - now_p );

end

end

Clattice(1:i,i) = C(1:i);

Plattice(1:i,i) = P(1:i);

end

EXAMPLE - EUROPEAN

S0=50, K=50, r=0.02, T=1, sigma=0.2, q=0.1, tau=3, N=10, mode=European

>> [c p cla pla] = bitprice_p(50,50,0.02,1,0.2,0.1,3,10,0)

c =

2.0767

p =

6.0867

EXAMPLE - AMERICAN

S0=50, K=50, r=0.02, T=1, sigma=0.2, q=0.1, tau=3, N=10, mode=American

>> [c p cla pla] = bitprice_p(50,50,0.02,1,0.2,0.1,3,10,1)

c =

2.6130

p =

6.2852

COMPARE

European

c =

2.0767

p =

6.0867

American

c =

2.6130

p =

6.2852

DOLLAR DIVIDENDS (1)function [ Cprice, Pprice, Clattice, Plattice] = bitprice_d( S, K, r, T, sigma, D, tau, N, mode )

% mode : 1=>American 0=>European

% dividend : dollar

deltaT = T/N;

u = exp( sigma * sqrt(deltaT) );

d = 1/u;

p = ( exp( r * deltaT ) - d ) / ( u - d );

Sa = S - D * exp( -r * tau * deltaT );

for i = 0 : N

C(i+1) = max( 0, Sa * u^(N-i) * d^(i) - K );

P(i+1) = max( 0, K - Sa * u^(N-i) * d^(i) );

end

DOLLAR DIVIDENDS (2) for i = N : -1 : 1

for j = 0 : i-1

C(j+1) = exp(-r*deltaT) * ( C(j+1)*p + C(j+2)*(1-p) );

P(j+1) = exp(-r*deltaT) * ( P(j+1)*p + P(j+2)*(1-p) );

if mode == 1

now_p = Sa * u^(i-1-j) * d^(j) ;

if i<=tau

now_p = now_p + D * exp( -r * (tau-i+1) * deltaT );

end

C(j+1) = max( C(j+1) , now_p - K );

P(j+1) = max( P(j+1) , K - now_p );

end

end

Clattice(1:i,i) = C(1:i);

Plattice(1:i,i) = P(1:i);

end

EXAMPLE - EUROPEAN

S0=50, K=50, r=0.02, T=1, sigma=0.2, D=5, tau=3, N=10, mode=European

>> [c p cl pl] = bitprice_d(50,50,0.02,1,0.2,5,3,10,0)

c =

2.0904

p =

6.0704

EXAMPLE - AMERICAN

S0=50, K=50, r=0.02, T=1, sigma=0.2, D=5, tau=3, N=10, mode=American

>> [c p cl pl] = bitprice_d(50,50,0.02,1,0.2,5,3,10,1)

c =

2.4588

p =

6.2673

COMPARE

European

c =

2.0904

p =

6.0704

American

c =

2.4588

p =

6.2673