HW12100071021

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

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

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);

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

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

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)

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)