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HW14

HW14. 100071021. Range Forward. function [ K2,price ] = blsranfow ( F,K1,price,r,rf,T,sigma ) [temp,f1] = blsprice (F,K1,r,T,sigma,rf); price = max(price,0); f2 = price + f1; tryK = K1; found = 0; while 1 Vec = tryK-K1:0.0001:tryK; tryV = blsprice ( F,Vec,r,T,sigma,rf );.

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HW14

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  1. HW14 100071021

  2. Range Forward function [ K2,price ] = blsranfow( F,K1,price,r,rf,T,sigma ) [temp,f1] = blsprice(F,K1,r,T,sigma,rf); price = max(price,0); f2 = price + f1; tryK = K1; found = 0; while 1 Vec = tryK-K1:0.0001:tryK; tryV = blsprice(F,Vec,r,T,sigma,rf); if( min( find( tryV<=f2 ) ) ) found = min(find(tryV<=f2)); K2lb = Vec(found); ubprice = tryV(found); break; else tryK = tryK+K1; end end lbprice = blsprice(F,K2lb-0.0001,r,T,sigma,rf); K2 = K2lb + (f2-lbprice)/(ubprice-lbprice)*0.0001; end

  3. Demo Code %demo for range forward F = 27; K1 = 26.7; sigma = 0.0311; rf = 0.0304; r = 0.0565; T = 3/12; priceV= linspace(0,5); for i = 1:length(priceV) K2(i) = blsranfow( F,K1,priceV(i),r,rf,T,sigma ); end plot(priceV,K2); title('Price vs K2'); xlabel('price'); ylabel('K2');

  4. Sallie Mae function [ price, lattice ] = SallieMae( F, K, r, T, sigma, N ) deltaT = T/N; u = exp( sigma * sqrt(deltaT) ); d = 1/u; p = ( exp( r * deltaT ) - d ) / ( u - d ); P = ones(1,N+1) * 6.25; lattice(1:N+1,N+1) = P; for i = N : -1 : 1 for j = 0 : i-1 P(j+1) = exp(-r*deltaT) * ( P(j+1)*p + P(j+2)*(1-p) ); now_f = F * u^(i-1-j) * d^(j) ; early = 50 * ( now_f - K( ceil(i*length(K)/N) ) ) / now_f; P(j+1) = max( P(j+1) , early ); end lattice(1:i,i) = P(1:i); end price = P(1); end

  5. Demo Code F = 131.75; K = [131.75,129.50,127.00,124.50]; r = 0.1; T = 4; sigma = 0.1; N = 4; [ price, lattice ] = SallieMae( F, K, r, T, sigma, N ) price = 11.1103 lattice =

  6. Demo Code figure; timeV= linspace(0.01,10); for i = 1:length(timeV) P(i) = SallieMae( F, K, r, timeV(i), sigma, N ); end plot(timeV,P); title('Maturity vs Price'); xlabel('Time to Maturity'); ylabel('Price'); figure; for i = 1:200 L(i) = SallieMae( F, K, r, T, sigma, i ); end plot(1:200,L); title('N vs Price'); xlabel('N'); ylabel('Price');

  7. Finite Difference Explicit Method function [ call,put,cmatval,pmatval,vecS,vecT ] = blsFDEP( S,K,r,T,sigma,Smax,dS,dt) M = round(Smax/dS); dS = Smax/M; N = round(T/dt); dt = T/N; cmatval = zeros(M+1,N+1); pmatval = zeros(M+1,N+1); vecS = linspace(0,Smax,M+1); vecT = linspace(0,T,N+1);

  8. cmatval(:,N+1) = max(vecS - K, 0 ); pmatval(:,N+1) = max(K - vecS, 0 ); cmatval(M+1,:) = (Smax - K) * exp( -r*dt*(N:-1:0) ); pmatval(1,:) = K * exp( -r*dt*(N:-1:0) ); a = 0.5 * dt * (sigma^2*(0:M) - r) .* (0:M) ; b = 1 - dt * (sigma^2 * ((0:M).^2) + r) ; c = 0.5 * dt * (sigma^2*(0:M) + r) .* (0:M) ; for j = N:-1:1 for i = 2:M cmatval(i,j) = a(i)*cmatval(i-1,j+1) + b(i)*cmatval(i,j+1) + c(i)*cmatval(i+1,j+1); pmatval(i,j) = a(i)*pmatval(i-1,j+1) + b(i)*pmatval(i,j+1) + c(i)*pmatval(i+1,j+1); end end

  9. idown= floor(S/dS); iup = ceil(S/dS); if idown == iup call = cmatval(idown+1,1); put = pmatval(idown+1,1); else call = cmatval(idown+1,1) + (cmatval(idown+2,1)-cmatval(idown+1,1)) * (S - idown*dS)/dS ; put = pmatval(idown+1,1) + (pmatval(idown+2,1)-pmatval(idown+1,1)) * (S - idown*dS)/dS ; end end

  10. Demo Code S=50; K=50; r=0.1; T=5/12; sigma=0.3; Smax=100; dS=2; dt=5/1200; [ call,put,cmatval,pmatval,vecS,vecT ] = blsFDEP( S,K,r,T,sigma,Smax,dS,dt); call = 4.8695 put = 2.8288

  11. Demo Code figure; mesh(vecT,vecS,cmatval); xlabel('Stock Price'); ylabel('Time'); zlabel('Call Payoff'); figure; mesh(vecT,vecS,pmatval); xlabel('Stock Price'); ylabel('Time'); zlabel('Put Payoff');

  12. Demo Code figure; dSv = linspace(0.5,5); for i = 1 : length(dSv) C(i) = blsFDEP( S,K,r,T,sigma,Smax,dSv(i),dt); end plot(dSv,C);

  13. Demo Code figure; dtv = linspace(5/120000,5/12); for i = 1 : length(dtv) Q(i) = blsFDEP( S,K,r,T,sigma,Smax,dS,dtv(i)); end plot(dtv,Q);

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