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HW12

HW12. 100071021. Barrier Option (Conditioning). function [ c, p ] = BO_CD ( S0,K,r,T,sigma,Sb,ud,io,NRepl,NStep ) [ cw , pw] = blsprice (S0,K,r,T,sigma); dt = T / NStep ; Ncross = 0; C_Payoffs = zeros (NRepl,1); P_Payoffs = zeros (NRepl,1); Times = zeros (NRepl,1);

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HW12

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  1. HW12 100071021

  2. Barrier Option (Conditioning) function [ c, p ] = BO_CD ( S0,K,r,T,sigma,Sb,ud,io,NRepl,NStep ) [cw, pw] = blsprice(S0,K,r,T,sigma); dt = T / NStep; Ncross = 0; C_Payoffs = zeros(NRepl,1); P_Payoffs = zeros(NRepl,1); Times = zeros(NRepl,1); StockVals = zeros(NRepl,1); for i = 1 : NRepl Path = AssetPaths( S0,r,sigma,T,NStep,1); if ud == 0 % up tcross = min(find(Path >= Sb)); else % down tcross = min(find(Path <= Sb)); end if not(isempty(tcross)) Ncross = Ncross + 1; Times(Ncross) = (tcross-1) * dt; StockVals(Ncross) = Path(tcross); end end

  3. if Ncross>0 [Caux, Paux] = blsprice(StockVals(1:Ncross),K,r,T-Times(1:Ncross),sigma); C_Payoffs(1:Ncross) = exp(-r*Times(1:Ncross)) .* Caux; P_Payoffs(1:Ncross) = exp(-r*Times(1:Ncross)) .* Paux; end if io == 0 % in c = mean(C_Payoffs); p = mean(P_Payoffs); else % out c = mean(cw - C_Payoffs); p = mean(pw - P_Payoffs); end end

  4. Demo code %demo for BO S0=50; K=52; r=0.1; T=2/12; sigma=0.4; Sb=60; NStep=60; NRepl=200; mccd_cui = zeros(NRepl,1); for i = 1 : NRepl mccd_cui(i) = BO_CD(S0,K,r,T,sigma,Sb,0,0,i*1000,60); end plot(1:NRepl,mccd_cui);

  5. SIGN without Puttable (Monte Carlo) function [ payoff, var, CI ] = SIGN_MC( S,K,r,sigma,T,NRepl ) Days = T * 250; Payoffs = zeros(NRepl,1); Paths = AssetPaths(S,r,sigma,T,Days,NRepl); for i = 1 : NRepl Pm = mean( Paths(i,Days-32:Days-2) ); if Pm >= K Payoffs(i) = 10 * (1+(Pm-K)/K); else Payoffs(i) = 10; end end [payoff, var, CI] = normfit(Payoffs); end

  6. SIGN as European (Binomial Tree) function [ payoff, lattice ] = SIGN_bit( S0, K, r, T, sigma, N ) deltaT = T/N; u = exp( sigma * sqrt(deltaT) ); d = 1/u; p = ( exp( r * deltaT ) - d ) / ( u - d ); for i = 0 : N P = S0 * u^(N-i) * d^(i); S(i+1) = 10; if P > K S(i+1) = 10 * (1+(P-K)/K); end end for i = N : -1 : 1 for j = 0 : i-1 S(j+1) = max(10, exp(-r*deltaT) * ( S(j+1)*p + S(j+2)*(1-p) ) ); end lattice(1:i,i) = S(1:i); end payoff = S(1); end

  7. Demo code %demo for SIGN S = 400; K = 336.69; r = 0.1; sigma = 0.2; T = 1; N = 5000; for i = 1:200 MC(i) = SIGN_MC(i+300,K,r,sigma,T,N); bit(i) = SIGN_bit(i+300,K,r,sigma,T,N); end plot(301:500,MC,301:500,bit)

  8. for i = 1:200 MC(i) = SIGN_MC(S,i+300,r,sigma,T,N); bit(i) = SIGN_bit(S,i+300,r,sigma,T,N); end plot(301:500,MC,301:500,bit)

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