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HW6

HW6. 100071021 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;

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HW6

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  1. HW6 100071021 楊佑濬

  2. 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

  3. 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

  4. 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 clapla] = bitprice_p(50,50,0.02,1,0.2,0.1,3,10,0) c = 2.0767 p = 6.0867

  5. 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 clapla] = bitprice_p(50,50,0.02,1,0.2,0.1,3,10,1) c = 2.6130 p = 6.2852

  6. Compare European American c = 2.6130 p = 6.2852 c = 2.0767 p = 6.0867

  7. 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

  8. 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

  9. 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

  10. 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

  11. Compare European American c = 2.4588 p = 6.2673 c = 2.0904 p = 6.0704

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